// SNIPPET read
pub trait Readable {
    type Output;
    fn words_count() -> usize;
    fn read_words(words: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $t:ty, $words_count:expr, |$words:ident| $read_words:expr ) => {
        impl Readable for $t {
            type Output = $t;
            fn words_count() -> usize { $words_count }
            fn read_words($words: &[&str]) -> Result<$t, String> {
                Ok($read_words)
            }
        }
    };
}
readable!((), 1, |_ss| ());
readable!(String, 1, |ss| ss[0].to_string());
impl Readable for char {
    type Output = char;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<char, String> {
        let chars: Vec<char> = words[0].chars().collect();
        if chars.len() == 1 {
            Ok(chars[0])
        } else {
            Err(format!("cannot parse `{}` as a char", words[0]))
        }
    }
}
pub struct Chars();
impl Readable for Chars {
    type Output = Vec<char>;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
impl Readable for i8 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i8, String> {
        use std::str::FromStr;
        i8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i8", words[0])
        })
    }
}
impl Readable for u8 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u8, String> {
        use std::str::FromStr;
        u8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u8", words[0])
        })
    }
}
impl Readable for i16 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i16, String> {
        use std::str::FromStr;
        i16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i16", words[0])
        })
    }
}
impl Readable for u16 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u16, String> {
        use std::str::FromStr;
        u16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u16", words[0])
        })
    }
}
impl Readable for i32 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i32, String> {
        use std::str::FromStr;
        i32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i32", words[0])
        })
    }
}
impl Readable for u32 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u32, String> {
        use std::str::FromStr;
        u32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u32", words[0])
        })
    }
}
impl Readable for i64 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i64, String> {
        use std::str::FromStr;
        i64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i64", words[0])
        })
    }
}
impl Readable for u64 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u64, String> {
        use std::str::FromStr;
        u64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u64", words[0])
        })
    }
}
impl Readable for isize {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<isize, String> {
        use std::str::FromStr;
        <isize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as isize", words[0])
        })
    }
}
impl Readable for usize {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<usize, String> {
        use std::str::FromStr;
        <usize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as usize", words[0])
        })
    }
}
impl Readable for f32 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<f32, String> {
        use std::str::FromStr;
        f32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as f32", words[0])
        })
    }
}
impl Readable for f64 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<f64, String> {
        use std::str::FromStr;
        f64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as f64", words[0])
        })
    }
}
#[allow(non_camel_case_types)]
pub struct u8_;
impl Readable for u8_ {
    type Output = u8;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u8::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u16_;
impl Readable for u16_ {
    type Output = u16;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u16::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u32_;
impl Readable for u32_ {
    type Output = u32;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u32::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u64_;
impl Readable for u64_ {
    type Output = u64;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u64::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct usize_;
impl Readable for usize_ {
    type Output = usize;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        <usize>::read_words(words).map(|n| n-1)
    }
}
impl<T1: Readable, T2: Readable> Readable for (T1, T2) {
    type Output = (T1::Output, T2::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let val2 = T2::read_words(&words[start..])?;
        Ok((val1, val2))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable> Readable for (T1, T2, T3) {
    type Output = (T1::Output, T2::Output, T3::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let val3 = T3::read_words(&words[start..])?;
        Ok((val1, val2, val3))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable> Readable for (T1, T2, T3, T4) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count() + T4::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::words_count();
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let val4 = T4::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable> Readable for (T1, T2, T3, T4, T5) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count() + T4::words_count() + T5::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::words_count();
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::words_count();
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let val5 = T5::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable, T6: Readable> Readable for (T1, T2, T3, T4, T5, T6) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output, T6::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count() + T4::words_count() + T5::words_count() + T6::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::words_count();
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::words_count();
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let count5 = T5::words_count();
        let val5 = T5::read_words(&words[start .. start+count5])?;
        start += count5;
        let val6 = T6::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5, val6))
    }
}
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    line.trim_end_matches('\n').split_whitespace().collect()
}
impl<T: Readable> ReadableFromLine for T {
    type Output = T::Output;
    fn read_line(line: &str) -> Result<T::Output, String> {
        let words = split_into_words(line);
        if words.len() != T::words_count() {
            return Err(format!("line `{}` has {} words, expected {}",
                               line, words.len(), T::words_count()));
        }
        T::read_words(&words)
    }
}
pub fn read_words_into_vec<T: Readable>(words: &[&str], line: &str) -> Result<Vec<T::Output>, String> {
    let n = T::words_count();
    assert_eq!(words.len() % n, 0);
    let mut result = Vec::new();
    for chunk in words.chunks(n) {
        match T::read_words(chunk) {
            Ok(v) => result.push(v),
            Err(msg) => {
                let fragment_msg = if n == 1 {
                    format!("word {}", result.len())
                } else {
                    let l = result.len();
                    format!("words {}-{}", n*l + 1, (n+1) * l)
                };
                return Err(format!(
                    "{} of line `{}`: {}", fragment_msg, line, msg
                ));
            }
        }
    }
    Ok(result)
}
pub fn split_into_words_for_collection<T: Readable>(
    line: &str, prefix_words_count: usize
) -> Result<Vec<&str>, String> {
    let n = T::words_count();
    let words = split_into_words(line);
    if words.len() < prefix_words_count {
        return Err(
            format!("line `{}` has {} words, expected at least {}",
                    line, words.len(), prefix_words_count)
        );
    }
    if (words.len() - prefix_words_count) % T::words_count() != 0 {
        return Err(
            format!("line `{}` has {} words, expected {} + {}",
                    line, words.len(), prefix_words_count, n)
        );
    }
    Ok(words)
}
#[macro_export]
macro_rules! readable_collection {
    ($u:ident => $collection_in:ty, $collection_out:ty) => {
        readable_collection!($u: => $collection_in, $collection_out);
    };
    ($u:ident : $( $bound:path ),* => $collection_in:ty, $collection_out:ty) => {
        impl<$u: Readable> ReadableFromLine for $collection_in
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = $collection_out;
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let words = split_into_words_for_collection::<$u>(line, 0)?;
                Ok(read_words_into_vec::<$u>(&words, line)?.into_iter().collect())
            }
        }
        impl<T1: Readable, $u: Readable> ReadableFromLine for (T1, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = T1::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let val1 = T1::read_words(&words[..prefix_len])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, $u: Readable> ReadableFromLine for (T1, T2, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2)>::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::words_count();
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::words_count();
                let val2 = T2::read_words(&words[start .. start+count2])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3)>::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::words_count();
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::words_count();
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::words_count();
                let val3 = T3::read_words(&words[start .. start+count3])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, T4, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, T4::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3, T4)>::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::words_count();
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::words_count();
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::words_count();
                let val3 = T3::read_words(&words[start .. start+count3])?;
                start += count3;
                let count4 = T4::words_count();
                let val4 = T4::read_words(&words[start .. start+count4])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, val4, rest.into_iter().collect()))
            }
        }
    };
}
readable_collection!(U => Vec<U>, Vec<U::Output>);
pub fn read<T: ReadableFromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::read_line(&line).unwrap()
}
#[macro_export]
macro_rules! read {
    () => {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
    };
    ( $pat:pat = $t:ty $(,)* ) => {
        let $pat = read::<$t>();
    };
    ( ! $(,)* ) => {
        let _ = read::<()>();
    };
    ( $pat:pat = $t:ty, $( $rest:tt )+ ) => {
        read_inner!($pat = $t; $($rest)+);
    };
    ( !, $( $rest:tt )+ ) => {
        read_inner!(_ = (); $($rest)+);
    };
}
#[macro_export]
#[doc(hidden)]
macro_rules! read_inner {
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; $pat:pat = $t:ty, $( $rest:tt )* ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , $pat = $t ; $($rest)*);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; !, $( $rest:tt )* ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , _ = () ; $($rest)*);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; $pat:pat = $t:ty ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , $pat = $t ;);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; ! ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , _ = () ;);
    };
    ( $( $pat:pat = $t:ty ),+ ; ) => {
        let ($($pat),+) = read::<($($t),+)>();
    };
}
pub trait ReadableFromChunk {
    type Output;
    fn lines_count() -> usize;
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String>;
}
impl<T1: ReadableFromLine, T2: ReadableFromLine> ReadableFromChunk for (T1, T2) {
    type Output = (T1::Output, T2::Output);
    fn lines_count() -> usize { 2 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        Ok((out1, out2))
    }
}
impl<T1: ReadableFromLine, T2: ReadableFromLine, T3: ReadableFromLine> ReadableFromChunk for (T1, T2, T3) {
    type Output = (T1::Output, T2::Output, T3::Output);
    fn lines_count() -> usize { 3 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        let out3 = T3::read_line(&lines[2])?;
        Ok((out1, out2, out3))
    }
}
impl<T1: ReadableFromLine, T2: ReadableFromLine, T3: ReadableFromLine, T4: ReadableFromLine> ReadableFromChunk for (T1, T2, T3, T4) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output);
    fn lines_count() -> usize { 4 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        let out3 = T3::read_line(&lines[2])?;
        let out4 = T4::read_line(&lines[3])?;
        Ok((out1, out2, out3, out4))
    }
}
pub fn read_chunk<T: ReadableFromChunk>() -> T::Output {
    let stdin = std::io::stdin();
    let mut handle = stdin.lock();
    read_chunk_from_handle::<T>(&mut handle).unwrap()
}
fn read_chunk_from_handle<T: ReadableFromChunk>(handle: &mut std::io::StdinLock) -> Option<T::Output> {
    use std::io::BufRead;
    let mut lines = vec![String::new(); T::lines_count()];
    let mut first = true;
    for line in &mut lines {
        if handle.read_line(line).unwrap() == 0 && first {
            return None;
        }
        first = false;
    }
    Some(T::read_chunk(&lines).unwrap())
}
#[macro_export]
macro_rules! read_chunk {
    ( $( $pat:pat = $t:ty ),+ ) => {
        let ($($pat),+) = read_chunk::<($($t),+)>();
    };
}
static mut STDIN: Option<std::io::Stdin> = None;
pub struct ReadLines<T: ReadableFromLine> {
    lock: std::io::StdinLock<'static>,
    phantom: std::marker::PhantomData<T>
}
impl<T: ReadableFromLine> Iterator for ReadLines<T> {
    type Item = T::Output;
    fn next(&mut self) -> Option<T::Output> {
        use std::io::BufRead;
        let mut line = String::new();
        if self.lock.read_line(&mut line).unwrap() > 0 {
            Some(T::read_line(&line).unwrap())
        } else {
            None
        }
    }
}
pub fn read_lines<T: ReadableFromLine>() -> ReadLines<T> {
    unsafe {
        if STDIN.is_none() {
            STDIN = Some(std::io::stdin());
        }
    }
    ReadLines {
        lock: unsafe { STDIN.as_ref().unwrap().lock() },
        phantom: std::marker::PhantomData::<T>
    }
}
pub struct ReadChunks<T: ReadableFromChunk> {
    lock: std::io::StdinLock<'static>,
    phantom: std::marker::PhantomData<T>
}
impl<T: ReadableFromChunk> Iterator for ReadChunks<T> {
    type Item = T::Output;
    fn next(&mut self) -> Option<T::Output> {
        read_chunk_from_handle::<T>(&mut self.lock)
    }
}
pub fn read_chunks<T: ReadableFromChunk>() -> ReadChunks<T> {
    unsafe {
        if STDIN.is_none() {
            STDIN = Some(std::io::stdin());
        }
    }
    ReadChunks {
        lock: unsafe { STDIN.as_ref().unwrap().lock() },
        phantom: std::marker::PhantomData::<T>
    }
}
pub trait Words {
    fn read<T: Readable>(&self) -> T::Output;
}
impl<'a> Words for [&'a str] {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(self).unwrap()
    }
}
impl<'a> Words for &'a str {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(&[self]).unwrap()
    }
}

// SNIPPET utils
pub fn yn(result: bool) {
    if result {
        println!("Yes");
    } else {
        println!("No");
    }
}
#[allow(non_snake_case)]
pub fn YN(result: bool) {
    if result {
        println!("YES");
    } else {
        println!("NO");
    }
}
pub fn exit(msg: impl std::fmt::Display) -> ! {
    println!("{}", msg);
    std::process::exit(0)
}
#[macro_export]
#[cfg(local)]
macro_rules! dbg {
    () => {
        {
            use std::io::{self, Write};
            writeln!(io::stderr(), "{}: dbg", line!()).unwrap();
        }
    };
    ($e: expr) => {
        {
            use std::io::{self, Write};
            let result = $e;
            writeln!(io::stderr(), "{}: {} = {:?}",
                     line!(), stringify!($e), result)
                .unwrap();
            result
        }
    }
}
#[macro_export]
#[cfg(not(local))]
macro_rules! dbg {
    () => {};
    ($e: expr) => {
        { $e }
    }
}

// SNIPPET option
pub trait BoolExt {
    fn then<T>(self, value: T) -> Option<T>;
    fn then_with<T, F>(self, f: F) -> Option<T> where F: FnOnce() -> T;
    fn and<T>(self, option: Option<T>) -> Option<T>;
    fn and_then<T, F>(self, f: F) -> Option<T> where F: FnOnce() -> Option<T>;
}
impl BoolExt for bool {
    fn then<T>(self, value: T) -> Option<T> {
        if self { Some(value) } else { None }
    }
    fn then_with<T, F>(self, f: F) -> Option<T> where F: FnOnce() -> T {
        if self { Some(f()) } else { None }
    }
    fn and<T>(self, option: Option<T>) -> Option<T> {
        if self { option } else { None }
    }
    fn and_then<T, F>(self, f: F) -> Option<T> where F: FnOnce() -> Option<T> {
        if self { f() } else { None }
    }
}
pub trait OptionExt<T> {
    fn to_string_or<U: std::fmt::Display>(&self, default: U) -> String
    where
        T: std::fmt::Display;
}
impl<T> OptionExt<T> for Option<T> {
    fn to_string_or<U: std::fmt::Display>(&self, default: U) -> String
    where
        T: std::fmt::Display
    {
        self.as_ref().map(|x| x.to_string()).unwrap_or(default.to_string())
    }
    /*
    fn get_or_insert_with<F: FnOnce() -> T>(&mut self, f: F) -> &mut T {
        match *self {
            None => *self = Some(f()),
            _ => ()
        }
        self.as_mut().unwrap()
    }
    */
}
pub trait Guard: Sized {
    fn guard(self, pred: impl FnOnce(&Self) -> bool) -> Option<Self>;
}
impl<T> Guard for T {
    fn guard(self, pred: impl FnOnce(&T) -> bool) -> Option<T> {
        if pred(&self) { Some(self) } else { None }
    }
}

// SNIPPET range
pub trait UsizeRangeBoundsExt {
    fn to_range(&self, len: usize) -> Option<std::ops::Range<usize>>;
}
impl<T: std::ops::RangeBounds<usize>> UsizeRangeBoundsExt for T {
    #[allow(unstable_name_collisions)]
    fn to_range(&self, len: usize) -> Option<std::ops::Range<usize>> {
        use std::ops::Bound::*;
        let start = match self.start_bound() {
            Included(&i) => i,
            Excluded(&i) => i+1,
            Unbounded => 0
        };
        let end = match self.end_bound() {
            Included(&i) => i+1,
            Excluded(&i) => i,
            Unbounded => len,
        };
        (start <= end && end <= len).then(start..end)
    }
}
pub trait BoundCloned<T> {
    fn cloned(self) -> std::ops::Bound<T>;
}
impl<T: Clone> BoundCloned<T> for std::ops::Bound<&T> {
    fn cloned(self) -> std::ops::Bound<T> {
        match self {
            std::ops::Bound::Included(x) => std::ops::Bound::Included(x.clone()),
            std::ops::Bound::Excluded(x) => std::ops::Bound::Excluded(x.clone()),
            std::ops::Bound::Unbounded => std::ops::Bound::Unbounded
        }
    }
}
pub trait BoundExt<T> {
    fn map<U>(self, f: impl FnOnce(T) -> U) -> std::ops::Bound<U>;
}
impl<T> BoundExt<T> for std::ops::Bound<T> {
    fn map<U>(self, f: impl FnOnce(T) -> U) -> std::ops::Bound<U> {
        match self {
            std::ops::Bound::Included(x) => std::ops::Bound::Included(f(x)),
            std::ops::Bound::Excluded(x) => std::ops::Bound::Excluded(f(x)),
            std::ops::Bound::Unbounded => std::ops::Bound::Unbounded
        }
    }
}

// SNIPPET table
pub struct Table<T> {
    inner: Vec<Vec<T>>
}
pub struct TableIndicesIterator {
    height: usize,
    width: usize,
    y: usize,
    x: usize
}
impl Iterator for TableIndicesIterator {
    type Item = (usize, usize);
    fn next(&mut self) -> Option<(usize, usize)> {
        if self.x < self.width {
            self.x += 1;
            return Some((self.y, self.x-1))
        }
        if self.y+1 < self.height {
            self.y += 1;
            self.x = 1;
            return Some((self.y, 0))
        }
        None
    }
}
pub struct TableRows<'a, T> {
    table: &'a Table<T>,
    index: usize
}
impl<'a, T> Iterator for TableRows<'a, T> {
    type Item = &'a [T];
    fn next(&mut self) -> Option<&'a [T]> {
        if self.index < self.table.height() {
            let i = self.index;
            self.index += 1;
            Some(&self.table.inner[i])
        } else {
            None
        }
    }
}
pub trait TableRangeBounds {
    fn y_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>);
    fn x_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>);
}
/*
impl<T1: std::ops::RangeBounds<usize>, T2: std::ops::RangeBounds<usize>> TableRangeBounds for (T1, T2) {
    fn y_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>) {
        (self.0.start_bound().cloned(), self.0.end_bound().cloned())
    }
    fn x_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>) {
        (self.1.start_bound().cloned(), self.1.end_bound().cloned())
    }
}
*/
impl<T: std::ops::RangeBounds<(usize, usize)>> TableRangeBounds for T {
    fn y_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>) {
        (self.start_bound().map(|&(y, _)| y), self.end_bound().map(|&(y, _)| y))
    }
    fn x_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>) {
        (self.start_bound().map(|&(_, x)| x), self.end_bound().map(|&(_, x)| x))
    }
}
pub struct CumulativeTable<T, F1, F2> {
    op: F1,
    op_inv: F2,
    inner: Table<T>
}
impl<T> Table<T> {
    pub fn from_rows(rows: Vec<Vec<T>>) -> Option<Table<T>> {
        rows.windows(2).all(|window| window[0].len() == window[1].len())
            .then_with(|| Table { inner: rows })
    }
    pub unsafe fn from_rows_unchecked(rows: Vec<Vec<T>>) -> Table<T> {
        Table { inner: rows }
    }
    pub fn height(&self) -> usize {
        self.inner.len()
    }
    pub fn width(&self) -> usize {
        self.inner.first().map_or(0, |row| row.len())
    }
    pub fn shape(&self) -> (usize, usize) {
        (self.height(), self.width())
    }
    pub fn indices(&self) -> impl Iterator<Item=(usize, usize)> {
        TableIndicesIterator {
            height: self.height(),
            width: self.width(),
            y: if self.width() == 0 { self.height() } else { 0 },
            x: 0
        }
    }
    pub fn inside(&self, (y, x): (usize, usize)) -> bool {
        y < self.height() && x < self.width()
    }
    pub fn row(&self, y: usize) -> Option<&[T]> {
        self.inner.get(y).map(|vec| vec.as_slice())
    }
    pub fn row_mut(&mut self, y: usize) -> Option<&mut [T]> {
        self.inner.get_mut(y).map(|vec| vec.as_mut_slice())
    }
    pub fn get(&self, (y, x): (usize, usize)) -> Option<&T> {
        self.inner.get(y).and_then(|row| row.get(x))
    }
    pub fn get_mut(&mut self, (y, x): (usize, usize)) -> Option<&mut T> {
        self.inner.get_mut(y).and_then(|row| row.get_mut(x))
    }
    pub fn rows(&self) -> TableRows<T> {
        TableRows { table: self, index: 0 }
    }
    pub fn adjacent4_indices(&self, (y, x): (usize, usize)) -> Option<Vec<(usize, usize)>> {
        self.inside((y, x)).then_with(|| {
            let mut result = Vec::with_capacity(4);
            if y > 0 {
                result.push((y-1, x));
            }
            if x > 0 {
                result.push((y, x-1));
            }
            if x < self.width()-1 {
                result.push((y, x+1));
            }
            if y < self.height()-1 {
                result.push((y+1, x));
            }
            result
        })
    }
    pub fn adjacent8_indices(&self, (y, x): (usize, usize)) -> Option<Vec<(usize, usize)>> {
        self.inside((y, x)).then_with(|| {
            let mut result = Vec::with_capacity(8);
            let xs = x.saturating_sub(1) ..= std::cmp::min(x+1, self.width()-1);
            if y > 0 {
                for x in xs.clone() {
                    result.push((y-1, x));
                }
            }
            if x > 0 {
                result.push((y, x-1));
            }
            if x < self.width()-1 {
                result.push((y, x+1));
            }
            if y < self.height()-1 {
                for x in xs {
                    result.push((y+1, x));
                }
            }
            result
        })
    }
    pub fn accumulate<F1, F2>(&self, identity: T, op: F1, op_inv: F2)
                              -> CumulativeTable<T, F1, F2>
    where
        T: Clone,
        F1: Fn(&T, &T) -> T,
        F2: Fn(&T, &T) -> T
    {
        let mut inner = vec![vec![identity.clone(); self.width() + 1]];
        for table_row in self.rows() {
            let mut new_row = vec![identity.clone()];
            let last_row = inner.last().unwrap();
            for (x, acc1) in table_row.iter().zip(last_row.windows(2)) {
                let acc2 = new_row.last().unwrap();
                let tmp1 = op(x, &acc1[1]);
                let tmp2 = op(&tmp1, acc2);
                new_row.push(op_inv(&tmp2, &acc1[0]));
            }
            inner.push(new_row);
        }
        CumulativeTable { op, op_inv, inner: Table { inner } }
    }
}
impl<T> std::ops::Index<usize> for Table<T> {
    type Output = [T];
    fn index(&self, y: usize) -> &[T] {
        match self.row(y) {
            Some(row) => row,
            None => panic!(
                "index out of bounds: the table has {} rows but the row index is {}",
                self.height(), y
            )
        }
    }
}
impl<T> std::ops::IndexMut<usize> for Table<T> {
    fn index_mut(&mut self, y: usize) -> &mut [T] {
        let height = self.height();
        match self.row_mut(y) {
            Some(row) => row,
            None => panic!(
                "index out of bounds: the table has {} rows but the index is {}",
                height, y
            )
        }
    }
}
impl<T> std::ops::Index<(usize, usize)> for Table<T> {
    type Output = T;
    fn index(&self, index: (usize, usize)) -> &T {
        match self.get(index) {
            Some(result) => result,
            None => panic!(
                "index out of bounds: the table shape is {:?} but the index is {:?}",
                self.shape(), index
            )
        }
    }
}
impl<T> std::ops::IndexMut<(usize, usize)> for Table<T> {
    fn index_mut(&mut self, index: (usize, usize)) -> &mut T {
        let shape = self.shape();
        match self.get_mut(index) {
            Some(result) => result,
            None => panic!(
                "index out of bounds: the table shape is {:?} but the index is {:?}",
                shape, index
            )
        }
    }
}
impl<T, F1: Fn(&T, &T) -> T, F2: Fn(&T, &T) -> T> CumulativeTable<T, F1, F2> {
    pub fn query(&self, range: impl TableRangeBounds) -> Option<T> {
        self.query_yx(range.y_bounds(), range.x_bounds())
    }
    pub fn query_yx(&self, yrange: impl std::ops::RangeBounds<usize>, xrange: impl std::ops::RangeBounds<usize>) -> Option<T> {
        let y = yrange.to_range(self.inner.height() - 1)?;
        let x = xrange.to_range(self.inner.width() - 1)?;
        let val1 = &self.inner.inner[y.end][x.end];
        let val2 = &self.inner.inner[y.end][x.start];
        let val3 = &self.inner.inner[y.start][x.end];
        let val4 = &self.inner.inner[y.start][x.start];
        let tmp1 = (self.op)(val1, val4);
        let tmp2 = (self.op)(val2, val3);
        let result = (self.op_inv)(&tmp1, &tmp2);
        Some(result)
    }
}
pub fn backward2_indices((y, x): (usize, usize)) -> Vec<(usize, usize)> {
    let mut res = Vec::with_capacity(2);
    if y > 0 {
        res.push((y-1, x));
    }
    if x > 0 {
        res.push((y, x-1));
    }
    res
}
#[macro_export]
macro_rules! table {
    () => {
        unsafe { Table::from_rows_unchecked(Vec::new()) }
    };
    ($element:expr ; $rows:expr , $cols:expr) => {
        unsafe { Table::from_rows_unchecked(vec![vec![$element; $cols]; $rows]) }
    };
}
pub fn read_table<T: Readable>() -> Table<T::Output> {
    let res: Vec<Vec<T::Output>> = read_lines::<Vec<T>>().collect();
    Table::from_rows(res).unwrap()
}
pub fn read_table_rows<T: Readable>(height: usize) -> Table<T::Output> {
    let res: Vec<Vec<T::Output>> = read_lines::<Vec<T>>().take(height).collect();
    if res.len() < height {
        panic!(
            "tried reading {} rows for table, but stdin has only {} lines",
            height, res.len()
        );
    }
    Table::from_rows(res).unwrap()
}
pub fn read_char_table() -> Table<char> {
    let res: Vec<Vec<char>> = read_lines::<Chars>().collect();
    Table::from_rows(res).unwrap()
}
pub fn read_char_table_rows(height: usize) -> Table<char> {
    let res: Vec<Vec<char>> = read_lines::<Chars>().take(height).collect();
    if res.len() < height {
        panic!(
            "tried reading {} rows for table, but stdin has only {} lines",
            height, res.len()
        );
    }
    Table::from_rows(res).unwrap()
}

// END SNIPPETS
// Here is the documentation: https://yoshrc.github.io/rust-atcoder-snippets/atcoder_snippets/index.html

fn main() {
    read!(_n = usize, m = usize);
    read!(s = String);
    let s = s.chars().map(|c| c as usize - 'a' as usize).collect::<Vec<_>>();
    let mut freq = table![0; m, m];
    for w in s.windows(2) {
        let x = w[0];
        let y = w[1];
        freq[x][y] += 1;
        if x != y {
            freq[y][x] += 1;
        }
    }
    let mut freq_sum = table![0; m, 1<<m];
    for i in 0..m {
        for set in 1usize..1<<m {
            let lsb_pos = set.trailing_zeros() as usize;
            freq_sum[i][set] = freq_sum[i][set ^ (1<<lsb_pos)] + freq[i][lsb_pos];
        }
    }

    let mut dp = vec![0i64; 1<<m];
    for set in 1..1<<m {
        dp[set] = (0..m).filter(|&d| (1<<d) & set != 0).map(|x| {
            let subset = set ^ (1<<x);
            let inner = freq_sum[x][subset];
            let outer = freq_sum[x][((1<<m) - 1) & !set];
            dp[subset] + subset.count_ones() as i64 * (inner - outer)
        }).min().unwrap();
    }
    println!("{}", dp.last().unwrap());
}


// SNIPPET read
pub trait Readable {
    type Output;
    fn words_count() -> usize;
    fn read_words(words: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $t:ty, $words_count:expr, |$words:ident| $read_words:expr ) => {
        impl Readable for $t {
            type Output = $t;
            fn words_count() -> usize { $words_count }
            fn read_words($words: &[&str]) -> Result<$t, String> {
                Ok($read_words)
            }
        }
    };
}
readable!((), 1, |_ss| ());
readable!(String, 1, |ss| ss[0].to_string());
impl Readable for char {
    type Output = char;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<char, String> {
        let chars: Vec<char> = words[0].chars().collect();
        if chars.len() == 1 {
            Ok(chars[0])
        } else {
            Err(format!("cannot parse `{}` as a char", words[0]))
        }
    }
}
pub struct Chars();
impl Readable for Chars {
    type Output = Vec<char>;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
impl Readable for i8 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i8, String> {
        use std::str::FromStr;
        i8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i8", words[0])
        })
    }
}
impl Readable for u8 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u8, String> {
        use std::str::FromStr;
        u8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u8", words[0])
        })
    }
}
impl Readable for i16 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i16, String> {
        use std::str::FromStr;
        i16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i16", words[0])
        })
    }
}
impl Readable for u16 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u16, String> {
        use std::str::FromStr;
        u16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u16", words[0])
        })
    }
}
impl Readable for i32 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i32, String> {
        use std::str::FromStr;
        i32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i32", words[0])
        })
    }
}
impl Readable for u32 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u32, String> {
        use std::str::FromStr;
        u32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u32", words[0])
        })
    }
}
impl Readable for i64 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i64, String> {
        use std::str::FromStr;
        i64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i64", words[0])
        })
    }
}
impl Readable for u64 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u64, String> {
        use std::str::FromStr;
        u64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u64", words[0])
        })
    }
}
impl Readable for isize {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<isize, String> {
        use std::str::FromStr;
        <isize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as isize", words[0])
        })
    }
}
impl Readable for usize {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<usize, String> {
        use std::str::FromStr;
        <usize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as usize", words[0])
        })
    }
}
impl Readable for f32 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<f32, String> {
        use std::str::FromStr;
        f32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as f32", words[0])
        })
    }
}
impl Readable for f64 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<f64, String> {
        use std::str::FromStr;
        f64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as f64", words[0])
        })
    }
}
#[allow(non_camel_case_types)]
pub struct u8_;
impl Readable for u8_ {
    type Output = u8;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u8::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u16_;
impl Readable for u16_ {
    type Output = u16;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u16::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u32_;
impl Readable for u32_ {
    type Output = u32;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u32::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u64_;
impl Readable for u64_ {
    type Output = u64;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u64::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct usize_;
impl Readable for usize_ {
    type Output = usize;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        <usize>::read_words(words).map(|n| n-1)
    }
}
impl<T1: Readable, T2: Readable> Readable for (T1, T2) {
    type Output = (T1::Output, T2::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let val2 = T2::read_words(&words[start..])?;
        Ok((val1, val2))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable> Readable for (T1, T2, T3) {
    type Output = (T1::Output, T2::Output, T3::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let val3 = T3::read_words(&words[start..])?;
        Ok((val1, val2, val3))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable> Readable for (T1, T2, T3, T4) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count() + T4::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::words_count();
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let val4 = T4::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable> Readable for (T1, T2, T3, T4, T5) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count() + T4::words_count() + T5::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::words_count();
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::words_count();
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let val5 = T5::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable, T6: Readable> Readable for (T1, T2, T3, T4, T5, T6) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output, T6::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count() + T4::words_count() + T5::words_count() + T6::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::words_count();
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::words_count();
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let count5 = T5::words_count();
        let val5 = T5::read_words(&words[start .. start+count5])?;
        start += count5;
        let val6 = T6::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5, val6))
    }
}
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    line.trim_end_matches('\n').split_whitespace().collect()
}
impl<T: Readable> ReadableFromLine for T {
    type Output = T::Output;
    fn read_line(line: &str) -> Result<T::Output, String> {
        let words = split_into_words(line);
        if words.len() != T::words_count() {
            return Err(format!("line `{}` has {} words, expected {}",
                               line, words.len(), T::words_count()));
        }
        T::read_words(&words)
    }
}
pub fn read_words_into_vec<T: Readable>(words: &[&str], line: &str) -> Result<Vec<T::Output>, String> {
    let n = T::words_count();
    assert_eq!(words.len() % n, 0);
    let mut result = Vec::new();
    for chunk in words.chunks(n) {
        match T::read_words(chunk) {
            Ok(v) => result.push(v),
            Err(msg) => {
                let fragment_msg = if n == 1 {
                    format!("word {}", result.len())
                } else {
                    let l = result.len();
                    format!("words {}-{}", n*l + 1, (n+1) * l)
                };
                return Err(format!(
                    "{} of line `{}`: {}", fragment_msg, line, msg
                ));
            }
        }
    }
    Ok(result)
}
pub fn split_into_words_for_collection<T: Readable>(
    line: &str, prefix_words_count: usize
) -> Result<Vec<&str>, String> {
    let n = T::words_count();
    let words = split_into_words(line);
    if words.len() < prefix_words_count {
        return Err(
            format!("line `{}` has {} words, expected at least {}",
                    line, words.len(), prefix_words_count)
        );
    }
    if (words.len() - prefix_words_count) % T::words_count() != 0 {
        return Err(
            format!("line `{}` has {} words, expected {} + {}",
                    line, words.len(), prefix_words_count, n)
        );
    }
    Ok(words)
}
#[macro_export]
macro_rules! readable_collection {
    ($u:ident => $collection_in:ty, $collection_out:ty) => {
        readable_collection!($u: => $collection_in, $collection_out);
    };
    ($u:ident : $( $bound:path ),* => $collection_in:ty, $collection_out:ty) => {
        impl<$u: Readable> ReadableFromLine for $collection_in
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = $collection_out;
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let words = split_into_words_for_collection::<$u>(line, 0)?;
                Ok(read_words_into_vec::<$u>(&words, line)?.into_iter().collect())
            }
        }
        impl<T1: Readable, $u: Readable> ReadableFromLine for (T1, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = T1::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let val1 = T1::read_words(&words[..prefix_len])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, $u: Readable> ReadableFromLine for (T1, T2, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2)>::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::words_count();
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::words_count();
                let val2 = T2::read_words(&words[start .. start+count2])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3)>::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::words_count();
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::words_count();
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::words_count();
                let val3 = T3::read_words(&words[start .. start+count3])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, T4, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, T4::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3, T4)>::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::words_count();
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::words_count();
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::words_count();
                let val3 = T3::read_words(&words[start .. start+count3])?;
                start += count3;
                let count4 = T4::words_count();
                let val4 = T4::read_words(&words[start .. start+count4])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, val4, rest.into_iter().collect()))
            }
        }
    };
}
readable_collection!(U => Vec<U>, Vec<U::Output>);
pub fn read<T: ReadableFromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::read_line(&line).unwrap()
}
#[macro_export]
macro_rules! read {
    () => {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
    };
    ( $pat:pat = $t:ty $(,)* ) => {
        let $pat = read::<$t>();
    };
    ( ! $(,)* ) => {
        let _ = read::<()>();
    };
    ( $pat:pat = $t:ty, $( $rest:tt )+ ) => {
        read_inner!($pat = $t; $($rest)+);
    };
    ( !, $( $rest:tt )+ ) => {
        read_inner!(_ = (); $($rest)+);
    };
}
#[macro_export]
#[doc(hidden)]
macro_rules! read_inner {
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; $pat:pat = $t:ty, $( $rest:tt )* ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , $pat = $t ; $($rest)*);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; !, $( $rest:tt )* ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , _ = () ; $($rest)*);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; $pat:pat = $t:ty ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , $pat = $t ;);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; ! ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , _ = () ;);
    };
    ( $( $pat:pat = $t:ty ),+ ; ) => {
        let ($($pat),+) = read::<($($t),+)>();
    };
}
pub trait ReadableFromChunk {
    type Output;
    fn lines_count() -> usize;
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String>;
}
impl<T1: ReadableFromLine, T2: ReadableFromLine> ReadableFromChunk for (T1, T2) {
    type Output = (T1::Output, T2::Output);
    fn lines_count() -> usize { 2 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        Ok((out1, out2))
    }
}
impl<T1: ReadableFromLine, T2: ReadableFromLine, T3: ReadableFromLine> ReadableFromChunk for (T1, T2, T3) {
    type Output = (T1::Output, T2::Output, T3::Output);
    fn lines_count() -> usize { 3 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        let out3 = T3::read_line(&lines[2])?;
        Ok((out1, out2, out3))
    }
}
impl<T1: ReadableFromLine, T2: ReadableFromLine, T3: ReadableFromLine, T4: ReadableFromLine> ReadableFromChunk for (T1, T2, T3, T4) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output);
    fn lines_count() -> usize { 4 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        let out3 = T3::read_line(&lines[2])?;
        let out4 = T4::read_line(&lines[3])?;
        Ok((out1, out2, out3, out4))
    }
}
pub fn read_chunk<T: ReadableFromChunk>() -> T::Output {
    let stdin = std::io::stdin();
    let mut handle = stdin.lock();
    read_chunk_from_handle::<T>(&mut handle).unwrap()
}
fn read_chunk_from_handle<T: ReadableFromChunk>(handle: &mut std::io::StdinLock) -> Option<T::Output> {
    use std::io::BufRead;
    let mut lines = vec![String::new(); T::lines_count()];
    let mut first = true;
    for line in &mut lines {
        if handle.read_line(line).unwrap() == 0 && first {
            return None;
        }
        first = false;
    }
    Some(T::read_chunk(&lines).unwrap())
}
#[macro_export]
macro_rules! read_chunk {
    ( $( $pat:pat = $t:ty ),+ ) => {
        let ($($pat),+) = read_chunk::<($($t),+)>();
    };
}
static mut STDIN: Option<std::io::Stdin> = None;
pub struct ReadLines<T: ReadableFromLine> {
    lock: std::io::StdinLock<'static>,
    phantom: std::marker::PhantomData<T>
}
impl<T: ReadableFromLine> Iterator for ReadLines<T> {
    type Item = T::Output;
    fn next(&mut self) -> Option<T::Output> {
        use std::io::BufRead;
        let mut line = String::new();
        if self.lock.read_line(&mut line).unwrap() > 0 {
            Some(T::read_line(&line).unwrap())
        } else {
            None
        }
    }
}
pub fn read_lines<T: ReadableFromLine>() -> ReadLines<T> {
    unsafe {
        if STDIN.is_none() {
            STDIN = Some(std::io::stdin());
        }
    }
    ReadLines {
        lock: unsafe { STDIN.as_ref().unwrap().lock() },
        phantom: std::marker::PhantomData::<T>
    }
}
pub struct ReadChunks<T: ReadableFromChunk> {
    lock: std::io::StdinLock<'static>,
    phantom: std::marker::PhantomData<T>
}
impl<T: ReadableFromChunk> Iterator for ReadChunks<T> {
    type Item = T::Output;
    fn next(&mut self) -> Option<T::Output> {
        read_chunk_from_handle::<T>(&mut self.lock)
    }
}
pub fn read_chunks<T: ReadableFromChunk>() -> ReadChunks<T> {
    unsafe {
        if STDIN.is_none() {
            STDIN = Some(std::io::stdin());
        }
    }
    ReadChunks {
        lock: unsafe { STDIN.as_ref().unwrap().lock() },
        phantom: std::marker::PhantomData::<T>
    }
}
pub trait Words {
    fn read<T: Readable>(&self) -> T::Output;
}
impl<'a> Words for [&'a str] {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(self).unwrap()
    }
}
impl<'a> Words for &'a str {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(&[self]).unwrap()
    }
}

// SNIPPET utils
pub fn yn(result: bool) {
    if result {
        println!("Yes");
    } else {
        println!("No");
    }
}
#[allow(non_snake_case)]
pub fn YN(result: bool) {
    if result {
        println!("YES");
    } else {
        println!("NO");
    }
}
pub fn exit(msg: impl std::fmt::Display) -> ! {
    println!("{}", msg);
    std::process::exit(0)
}
#[macro_export]
#[cfg(local)]
macro_rules! dbg {
    () => {
        {
            use std::io::{self, Write};
            writeln!(io::stderr(), "{}: dbg", line!()).unwrap();
        }
    };
    ($e: expr) => {
        {
            use std::io::{self, Write};
            let result = $e;
            writeln!(io::stderr(), "{}: {} = {:?}",
                     line!(), stringify!($e), result)
                .unwrap();
            result
        }
    }
}
#[macro_export]
#[cfg(not(local))]
macro_rules! dbg {
    () => {};
    ($e: expr) => {
        { $e }
    }
}

// SNIPPET option
pub trait BoolExt {
    fn then<T>(self, value: T) -> Option<T>;
    fn then_with<T, F>(self, f: F) -> Option<T> where F: FnOnce() -> T;
    fn and<T>(self, option: Option<T>) -> Option<T>;
    fn and_then<T, F>(self, f: F) -> Option<T> where F: FnOnce() -> Option<T>;
}
impl BoolExt for bool {
    fn then<T>(self, value: T) -> Option<T> {
        if self { Some(value) } else { None }
    }
    fn then_with<T, F>(self, f: F) -> Option<T> where F: FnOnce() -> T {
        if self { Some(f()) } else { None }
    }
    fn and<T>(self, option: Option<T>) -> Option<T> {
        if self { option } else { None }
    }
    fn and_then<T, F>(self, f: F) -> Option<T> where F: FnOnce() -> Option<T> {
        if self { f() } else { None }
    }
}
pub trait OptionExt<T> {
    fn to_string_or<U: std::fmt::Display>(&self, default: U) -> String
    where
        T: std::fmt::Display;
}
impl<T> OptionExt<T> for Option<T> {
    fn to_string_or<U: std::fmt::Display>(&self, default: U) -> String
    where
        T: std::fmt::Display
    {
        self.as_ref().map(|x| x.to_string()).unwrap_or(default.to_string())
    }
    /*
    fn get_or_insert_with<F: FnOnce() -> T>(&mut self, f: F) -> &mut T {
        match *self {
            None => *self = Some(f()),
            _ => ()
        }
        self.as_mut().unwrap()
    }
    */
}
pub trait Guard: Sized {
    fn guard(self, pred: impl FnOnce(&Self) -> bool) -> Option<Self>;
}
impl<T> Guard for T {
    fn guard(self, pred: impl FnOnce(&T) -> bool) -> Option<T> {
        if pred(&self) { Some(self) } else { None }
    }
}

// SNIPPET range
pub trait UsizeRangeBoundsExt {
    fn to_range(&self, len: usize) -> Option<std::ops::Range<usize>>;
}
impl<T: std::ops::RangeBounds<usize>> UsizeRangeBoundsExt for T {
    #[allow(unstable_name_collisions)]
    fn to_range(&self, len: usize) -> Option<std::ops::Range<usize>> {
        use std::ops::Bound::*;
        let start = match self.start_bound() {
            Included(&i) => i,
            Excluded(&i) => i+1,
            Unbounded => 0
        };
        let end = match self.end_bound() {
            Included(&i) => i+1,
            Excluded(&i) => i,
            Unbounded => len,
        };
        (start <= end && end <= len).then(start..end)
    }
}
pub trait BoundCloned<T> {
    fn cloned(self) -> std::ops::Bound<T>;
}
impl<T: Clone> BoundCloned<T> for std::ops::Bound<&T> {
    fn cloned(self) -> std::ops::Bound<T> {
        match self {
            std::ops::Bound::Included(x) => std::ops::Bound::Included(x.clone()),
            std::ops::Bound::Excluded(x) => std::ops::Bound::Excluded(x.clone()),
            std::ops::Bound::Unbounded => std::ops::Bound::Unbounded
        }
    }
}
pub trait BoundExt<T> {
    fn map<U>(self, f: impl FnOnce(T) -> U) -> std::ops::Bound<U>;
}
impl<T> BoundExt<T> for std::ops::Bound<T> {
    fn map<U>(self, f: impl FnOnce(T) -> U) -> std::ops::Bound<U> {
        match self {
            std::ops::Bound::Included(x) => std::ops::Bound::Included(f(x)),
            std::ops::Bound::Excluded(x) => std::ops::Bound::Excluded(f(x)),
            std::ops::Bound::Unbounded => std::ops::Bound::Unbounded
        }
    }
}

// SNIPPET table
pub struct Table<T> {
    inner: Vec<Vec<T>>
}
pub struct TableIndicesIterator {
    height: usize,
    width: usize,
    y: usize,
    x: usize
}
impl Iterator for TableIndicesIterator {
    type Item = (usize, usize);
    fn next(&mut self) -> Option<(usize, usize)> {
        if self.x < self.width {
            self.x += 1;
            return Some((self.y, self.x-1))
        }
        if self.y+1 < self.height {
            self.y += 1;
            self.x = 1;
            return Some((self.y, 0))
        }
        None
    }
}
pub struct TableRows<'a, T> {
    table: &'a Table<T>,
    index: usize
}
impl<'a, T> Iterator for TableRows<'a, T> {
    type Item = &'a [T];
    fn next(&mut self) -> Option<&'a [T]> {
        if self.index < self.table.height() {
            let i = self.index;
            self.index += 1;
            Some(&self.table.inner[i])
        } else {
            None
        }
    }
}
pub trait TableRangeBounds {
    fn y_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>);
    fn x_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>);
}
/*
impl<T1: std::ops::RangeBounds<usize>, T2: std::ops::RangeBounds<usize>> TableRangeBounds for (T1, T2) {
    fn y_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>) {
        (self.0.start_bound().cloned(), self.0.end_bound().cloned())
    }
    fn x_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>) {
        (self.1.start_bound().cloned(), self.1.end_bound().cloned())
    }
}
*/
impl<T: std::ops::RangeBounds<(usize, usize)>> TableRangeBounds for T {
    fn y_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>) {
        (self.start_bound().map(|&(y, _)| y), self.end_bound().map(|&(y, _)| y))
    }
    fn x_bounds(&self) -> (std::ops::Bound<usize>, std::ops::Bound<usize>) {
        (self.start_bound().map(|&(_, x)| x), self.end_bound().map(|&(_, x)| x))
    }
}
pub struct CumulativeTable<T, F1, F2> {
    op: F1,
    op_inv: F2,
    inner: Table<T>
}
impl<T> Table<T> {
    pub fn from_rows(rows: Vec<Vec<T>>) -> Option<Table<T>> {
        rows.windows(2).all(|window| window[0].len() == window[1].len())
            .then_with(|| Table { inner: rows })
    }
    pub unsafe fn from_rows_unchecked(rows: Vec<Vec<T>>) -> Table<T> {
        Table { inner: rows }
    }
    pub fn height(&self) -> usize {
        self.inner.len()
    }
    pub fn width(&self) -> usize {
        self.inner.first().map_or(0, |row| row.len())
    }
    pub fn shape(&self) -> (usize, usize) {
        (self.height(), self.width())
    }
    pub fn indices(&self) -> impl Iterator<Item=(usize, usize)> {
        TableIndicesIterator {
            height: self.height(),
            width: self.width(),
            y: if self.width() == 0 { self.height() } else { 0 },
            x: 0
        }
    }
    pub fn inside(&self, (y, x): (usize, usize)) -> bool {
        y < self.height() && x < self.width()
    }
    pub fn row(&self, y: usize) -> Option<&[T]> {
        self.inner.get(y).map(|vec| vec.as_slice())
    }
    pub fn row_mut(&mut self, y: usize) -> Option<&mut [T]> {
        self.inner.get_mut(y).map(|vec| vec.as_mut_slice())
    }
    pub fn get(&self, (y, x): (usize, usize)) -> Option<&T> {
        self.inner.get(y).and_then(|row| row.get(x))
    }
    pub fn get_mut(&mut self, (y, x): (usize, usize)) -> Option<&mut T> {
        self.inner.get_mut(y).and_then(|row| row.get_mut(x))
    }
    pub fn rows(&self) -> TableRows<T> {
        TableRows { table: self, index: 0 }
    }
    pub fn adjacent4_indices(&self, (y, x): (usize, usize)) -> Option<Vec<(usize, usize)>> {
        self.inside((y, x)).then_with(|| {
            let mut result = Vec::with_capacity(4);
            if y > 0 {
                result.push((y-1, x));
            }
            if x > 0 {
                result.push((y, x-1));
            }
            if x < self.width()-1 {
                result.push((y, x+1));
            }
            if y < self.height()-1 {
                result.push((y+1, x));
            }
            result
        })
    }
    pub fn adjacent8_indices(&self, (y, x): (usize, usize)) -> Option<Vec<(usize, usize)>> {
        self.inside((y, x)).then_with(|| {
            let mut result = Vec::with_capacity(8);
            let xs = x.saturating_sub(1) ..= std::cmp::min(x+1, self.width()-1);
            if y > 0 {
                for x in xs.clone() {
                    result.push((y-1, x));
                }
            }
            if x > 0 {
                result.push((y, x-1));
            }
            if x < self.width()-1 {
                result.push((y, x+1));
            }
            if y < self.height()-1 {
                for x in xs {
                    result.push((y+1, x));
                }
            }
            result
        })
    }
    pub fn accumulate<F1, F2>(&self, identity: T, op: F1, op_inv: F2)
                              -> CumulativeTable<T, F1, F2>
    where
        T: Clone,
        F1: Fn(&T, &T) -> T,
        F2: Fn(&T, &T) -> T
    {
        let mut inner = vec![vec![identity.clone(); self.width() + 1]];
        for table_row in self.rows() {
            let mut new_row = vec![identity.clone()];
            let last_row = inner.last().unwrap();
            for (x, acc1) in table_row.iter().zip(last_row.windows(2)) {
                let acc2 = new_row.last().unwrap();
                let tmp1 = op(x, &acc1[1]);
                let tmp2 = op(&tmp1, acc2);
                new_row.push(op_inv(&tmp2, &acc1[0]));
            }
            inner.push(new_row);
        }
        CumulativeTable { op, op_inv, inner: Table { inner } }
    }
}
impl<T> std::ops::Index<usize> for Table<T> {
    type Output = [T];
    fn index(&self, y: usize) -> &[T] {
        match self.row(y) {
            Some(row) => row,
            None => panic!(
                "index out of bounds: the table has {} rows but the row index is {}",
                self.height(), y
            )
        }
    }
}
impl<T> std::ops::IndexMut<usize> for Table<T> {
    fn index_mut(&mut self, y: usize) -> &mut [T] {
        let height = self.height();
        match self.row_mut(y) {
            Some(row) => row,
            None => panic!(
                "index out of bounds: the table has {} rows but the index is {}",
                height, y
            )
        }
    }
}
impl<T> std::ops::Index<(usize, usize)> for Table<T> {
    type Output = T;
    fn index(&self, index: (usize, usize)) -> &T {
        match self.get(index) {
            Some(result) => result,
            None => panic!(
                "index out of bounds: the table shape is {:?} but the index is {:?}",
                self.shape(), index
            )
        }
    }
}
impl<T> std::ops::IndexMut<(usize, usize)> for Table<T> {
    fn index_mut(&mut self, index: (usize, usize)) -> &mut T {
        let shape = self.shape();
        match self.get_mut(index) {
            Some(result) => result,
            None => panic!(
                "index out of bounds: the table shape is {:?} but the index is {:?}",
                shape, index
            )
        }
    }
}
impl<T, F1: Fn(&T, &T) -> T, F2: Fn(&T, &T) -> T> CumulativeTable<T, F1, F2> {
    pub fn query(&self, range: impl TableRangeBounds) -> Option<T> {
        self.query_yx(range.y_bounds(), range.x_bounds())
    }
    pub fn query_yx(&self, yrange: impl std::ops::RangeBounds<usize>, xrange: impl std::ops::RangeBounds<usize>) -> Option<T> {
        let y = yrange.to_range(self.inner.height() - 1)?;
        let x = xrange.to_range(self.inner.width() - 1)?;
        let val1 = &self.inner.inner[y.end][x.end];
        let val2 = &self.inner.inner[y.end][x.start];
        let val3 = &self.inner.inner[y.start][x.end];
        let val4 = &self.inner.inner[y.start][x.start];
        let tmp1 = (self.op)(val1, val4);
        let tmp2 = (self.op)(val2, val3);
        let result = (self.op_inv)(&tmp1, &tmp2);
        Some(result)
    }
}
pub fn backward2_indices((y, x): (usize, usize)) -> Vec<(usize, usize)> {
    let mut res = Vec::with_capacity(2);
    if y > 0 {
        res.push((y-1, x));
    }
    if x > 0 {
        res.push((y, x-1));
    }
    res
}
#[macro_export]
macro_rules! table {
    () => {
        unsafe { Table::from_rows_unchecked(Vec::new()) }
    };
    ($element:expr ; $rows:expr , $cols:expr) => {
        unsafe { Table::from_rows_unchecked(vec![vec![$element; $cols]; $rows]) }
    };
}
pub fn read_table<T: Readable>() -> Table<T::Output> {
    let res: Vec<Vec<T::Output>> = read_lines::<Vec<T>>().collect();
    Table::from_rows(res).unwrap()
}
pub fn read_table_rows<T: Readable>(height: usize) -> Table<T::Output> {
    let res: Vec<Vec<T::Output>> = read_lines::<Vec<T>>().take(height).collect();
    if res.len() < height {
        panic!(
            "tried reading {} rows for table, but stdin has only {} lines",
            height, res.len()
        );
    }
    Table::from_rows(res).unwrap()
}
pub fn read_char_table() -> Table<char> {
    let res: Vec<Vec<char>> = read_lines::<Chars>().collect();
    Table::from_rows(res).unwrap()
}
pub fn read_char_table_rows(height: usize) -> Table<char> {
    let res: Vec<Vec<char>> = read_lines::<Chars>().take(height).collect();
    if res.len() < height {
        panic!(
            "tried reading {} rows for table, but stdin has only {} lines",
            height, res.len()
        );
    }
    Table::from_rows(res).unwrap()
}

// END SNIPPETS
// Here is the documentation: https://yoshrc.github.io/rust-atcoder-snippets/atcoder_snippets/index.html

fn main() {
    read!(_n = usize, m = usize);
    read!(s = String);
    let s = s.chars().map(|c| c as usize - 'a' as usize).collect::<Vec<_>>();
    let mut freq = table![0; m, m];
    for w in s.windows(2) {
        let x = w[0];
        let y = w[1];
        freq[x][y] += 1;
        if x != y {
            freq[y][x] += 1;
        }
    }
    let mut freq_sum = table![0; 1<<m, m];
    for set in 1usize..1<<m {
        for i in 0..m {
            let b = set.trailing_zeros() as usize;
            freq_sum[set][i] = freq_sum[set ^ (1<<b)][i] + freq[i][b];
        }
    }

    let mut dp = vec![0i64; 1<<m];
    for set in 1..1<<m {
        dp[set] = (0..m).filter(|&d| (1<<d) & set != 0).map(|x| {
            let subset = set ^ (1<<x);
            let inner = freq_sum[subset][x];
            let outer = freq_sum[((1<<m) - 1) & !set][x];
            dp[subset] + subset.count_ones() as i64 * (inner - outer)
        }).min().unwrap();
    }
    println!("{}", dp.last().unwrap());
}


//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

// ここまで

fn run() {
    input! {
        n: usize,
        m: usize,
        s: String,
    }
    let s: Vec<usize> = s.chars().map(|c| c as usize - 'a' as usize).collect();
    let mut cnt = vec![vec![0; m]; m];
    for i in 1..n {
        cnt[s[i - 1]][s[i]] += 1;
    }
    let mut dp = vec![1_000_000_000i64; 1 << m];
    dp[0] = 0;
    for i in 1..(1 << m) {
        let len = (i as usize).count_ones() as i64;
        for j in 0..m {
            if (i >> j) & 1 == 0 {
                continue;
            }
            let bit = i ^ (1 << j);
            let mut local = dp[bit];
            for k in 0..m {
                if (bit >> k) & 1 == 1 {
                    local += len * (cnt[j][k] + cnt[k][j]);
                } else if k != j {
                    local -= len * (cnt[j][k] + cnt[k][j]);
                }
            }
            dp[i] = std::cmp::min(dp[i], local);
        }
    }
    println!("{}", dp[(1 << m) - 1]);
}

fn main() {
    run();
}


use std::io::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let _len: usize = it.next().unwrap().parse().unwrap();
    let n: usize = it.next().unwrap().parse().unwrap();
    let s: Vec<usize> = it.next().unwrap().chars().map(|c| c.to_digit(36).unwrap() as usize - 10).collect();
    let mut cnt = vec![vec![0u64; n]; n];
    for s in s.windows(2) {
        let a = s[0];
        let b = s[1];
        cnt[a][b] += 1;
    }
    let mut cost = vec![0; 1 << n];
    for i in 1..n {
        for j in 0..i {
            let s = cnt[i][j] + cnt[j][i];
            cost[1 << i] += s;
            cost[1 << j] += s;
            cost[(1 << i) | (1 << j)] -= 2 * s;
        }
    }
    for i in 0..n {
        for j in 0..(1 << n) {
            if j >> i & 1 == 1 {
                cost[j] += cost[j ^ (1 << i)];
            }
        }
    }
    let mut dp = vec![std::u64::MAX; 1 << n];
    dp[0] = 0;
    for i in 0..(1 << n) {
        dp[i] += cost[i];
        let v = dp[i];
        for j in 0..n {
            if i >> j & 1 == 0 {
                let k = i | (1 << j);
                dp[k] = std::cmp::min(dp[k], v);
            }
        }
    }
    let ans = dp[(1 << n) - 1];
    println!("{}", ans);
}

fn main() {
    run();
}


//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

// ここまで

fn run() {
    input! {
        n: usize,
        m: usize,
        s: String,
    }
    let s: Vec<usize> = s.chars().map(|c| c as usize - 'a' as usize).collect();
    let mut cnt = vec![vec![0; m]; m];
    for i in 1..n {
        if s[i - 1] == s[i] {
            continue;
        }
        cnt[s[i - 1]][s[i]] += 1;
    }
    let mut sum = 0;
    let mut add = vec![0; 1 << m];
    for i in 0..m {
        for j in 0..m {
            add[(1 << i)|(1 << j)] += cnt[i][j];
            sum += cnt[i][j];
        }
    }
    for j in 0..m {
        for i in 1..(1 << m) {
            if (i >> j) & 1 == 1 {
                add[i] += add[i ^ (1 << j)];
            }
        }
    }
    let mut dp = vec![1_000_000_000i64; 1 << m];
    dp[0] = 0;
    for i in 1..(1 << m) {
        for j in 0..m {
            if (i >> j) & 1 == 0 {
                continue;
            }
            let bit = i ^ (1 << j);
            let local = dp[bit] + sum - add[bit] - add[bit ^ ((1 << m) - 1)];
            dp[i] = std::cmp::min(dp[i], local);
        }
    }
    println!("{}", dp[(1 << m) - 1]);
}

fn main() {
    run();
}


package main

import (
	"fmt"
	"bytes"
	"io/ioutil"
	"os"
)

var adj [20][20]uint

var dp [1048576]int64
var visited [1048576]bool

var n uint
var m uint
func dfs(mask int, one uint) {
	if visited[mask] {
		return
	} else {
		visited[mask] = true
		var min int64 = 0x3fffffffffffffff
		for i := uint(0);i < m;i ++ {
			if mask & (1 << i) != 0 {
				oldMask := mask - (1 << i)
				dfs(oldMask, one - 1)
				var ans int64 = dp[oldMask]
				for j := uint(0);j < m;j ++ {
					if mask & (1 << j) != 0 {
						ans += int64(one * adj[i][j])
					} else {
						ans -= int64(one * adj[i][j])
					}
				}
				if ans < min {
					min = ans
				}
			}
		}
		dp[mask] = min
	}
}

func main() {
	bs, _ := ioutil.ReadAll(os.Stdin)
	reader := bytes.NewBuffer(bs)
	var s string
	fmt.Fscanf(reader, "%d %d\n", &n, &m)
	fmt.Fscanf(reader, "%s", &s)

	for i := 0;i < len(s) - 1;i ++ {
		letterLeft := int(s[i] - 'a')
		letterRight := int(s[i + 1] - 'a')
		if letterLeft != letterRight {
			adj[letterLeft][letterRight] ++
			adj[letterRight][letterLeft] ++
		}
	}
	visited[0] = true
	dfs((1 << m) - 1, m)
	fmt.Printf("%d", dp[(1 << m) - 1])
}


package main

import (
    "bufio"
    "fmt"
    "os"
    "strconv"
    //"sort"
)

//скопипизжено из разбора

//от a! перейдем к 2^a - рассмотрим минимальную медленность на множестве символов без учета порядка
//будем строить клавиатуру: брать какие-то символы и добавлять их в клавиатуру справа

const U0 = uint(0)

func count(p string, m uint) [][]int {
    res := make([][]int, m)
    for i := uint(0); i < m; i++ {
        res[i] = make([]int, m)
    }
    prev := p[0] - 'a'
    for _, c := range p[1:] {
        cur := byte(c - 'a')
        res[prev][cur] ++
        res[cur][prev] ++
        prev = cur
    }
    return res
}

func process(p string, n, m uint) int {
    cnt := count(p, m)

    large := int(n * m * 2)
    dp := make([]int, 1 << m)
    size := make([]int, 1 << m)
    dist := make([][]int, 1 << m)
    last := make([]uint, 1 << m)

    for msk := 0; msk < (1<<m); msk++ {
        dp[msk] = large
        dist[msk] = make([]int, m)
        for i := U0; i < m; i++ {
            if msk & (1 << i) > 0 {
                size[msk]++
            }
        }
        for i := U0; i < m; i++ {
            if msk & (1<<i) > 0 {
                last[msk] = i
                break
            }
        }
    }
    for i := U0; i < m; i++ {
        dist[0][i] = 0
    }
    for msk := 0; msk < (1<<m); msk++ {
        for i := U0; i < m; i++ {
            if msk & (1 << i) > 0 {
                continue
            }
            b := last[msk]
            dist[msk][i] = cnt[i][b] + dist[msk ^ (1<<b)][i]
        }
    }
    dp[0] = 0

    //for msk := 0; msk < (1<<m); msk++ {
    //    fmt.Printf("%b ", msk)
    //}
    //fmt.Println("")
    //fmt.Println("size", size)
    //fmt.Println("dist", dist)
    //fmt.Println("last", last)

    all := (1 << m) - 1

    for msk := 0; msk < (1<<m); msk++ {
        //fmt.Println("processing", msk)
        for l := U0; l < m; l++ {
            if msk & (1 << l) > 0 {
                continue
            }
            pos := size[msk]
            nmsk := msk | (1<<l)
            //fmt.Print("  processing ", l, " pos+1 ", pos+1, " nmsk ", nmsk, " ", dp[nmsk], "->")
            dp[nmsk] = min(dp[nmsk], dp[msk] + (pos+1)*(dist[msk][l] - dist[all ^ nmsk][l]))
            //fmt.Println(dp[nmsk], "//", fmt.Sprintf("%b",all ^ nmsk), ":", dist[all ^ nmsk][l])
        }
    }
    //fmt.Println("dp", dp)
    return dp[all]
}

func min(a, b int) int {
    if a < b {
        return a
    }
    return b
}

func main() {
    scanner := bufio.NewScanner(os.Stdin)
    buf := make([]byte, 200000)
    scanner.Buffer(buf, 200000)
    scanner.Split(bufio.ScanWords)

    n := scanInt(scanner)
    m := scanInt(scanner)

    scanner.Scan()
    p := scanner.Text()

    if err := scanner.Err(); err != nil {
		fmt.Fprintln(os.Stderr, "reading standard input:", err)
	}

    fmt.Println(process(p, uint(n), uint(m)))
}

func scanInt64(scanner *bufio.Scanner) int64 {
    scanner.Scan()
    return parseInt(scanner.Text())
}

func scanInt(scanner *bufio.Scanner) int {
    return int(scanInt64(scanner))
}

func parseInt(s string) int64 {
    v, err := strconv.ParseInt(s, 10, 64)
    if err != nil {
        panic(err)
    }
    return v
}


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

left = [0]*m
DP = [-1]*(2**m)
DP[0] = 0

score = [0]*n
for c1 in range(m):
    for c2 in range(m):
        score[c1] -= trans[c1][c2]

s = 0
for i in range(1, 2**m):
    left[0] += 1
    j = 0
    while left[j] > 1:
        t = trans[j]
        for c2 in range(m):
            score[c2] -= 2 * t[c2]

        left[j] = 0
        j += 1
        left[j] += 1

    t = trans[j]
    for c2 in range(m):
        score[c2] += 2 * t[c2]

    N = sum(left)
    besta = 10**9
    for x in range(m):
        val = DP[i ^ (1 << x)] + N * score[x]
        if left[x] and val < besta:
            besta = val
    DP[i] = besta

print DP[-1]


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

left = [0]*m
DP = [-1.0]*(2**m)
DP[0] = 0.0

score = [0]*n
for c1 in range(m):
    for c2 in range(m):
        score[c1] -= trans[c1][c2]

for i in range(1, 2**m):
    left[0] += 1
    j = 0
    while left[j] > 1:
        for c2 in range(m):
            score[c2] -= 2 * trans[j][c2]

        left[j] = 0
        j += 1
        left[j] += 1

    for c2 in range(m):
        score[c2] += 2 * trans[j][c2]

    N = 1.0* sum(left)
    DP[i] = min(DP[i ^ (1 << x)] + N * score[x] for x in range(m) if left[x])

print int(DP[-1])


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

DP = [-1]*(2**m)
DP[0] = 0
for i in range(1, 2**m):

    left = [x for x in range(m) if (1 << x) & i]
    used = [x for x in range(m) if (1 << x) & i == 0]

    N = len(left)

    besta = 10**9
    for x in left:
        tx = trans[x]
        score = DP[i ^ (1 << x)]
        for j in left:
            score += tx[j] * N
        for j in used:
            score -= tx[j] * N

        if score < besta:
            besta = score

    DP[i] = besta

print DP[2**m - 1]


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

DP = [-1]*(2**m)
DP[0] = 0
for i in range(1, 2**m):

    left = [x for x in range(m) if (1 << x) & i]
    used = [x for x in range(m) if (1 << x) & i == 0]

    N = len(left)

    besta = 10**9
    for x in left:
        tx = trans[x]
        score = 0;
        for j in left:
            score += tx[j]
        for j in used:
            score -= tx[j]

        score = score * N + DP[i ^ (1 << x)]
        if score < besta:
            besta = score

    DP[i] = besta

print DP[2**m - 1]


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

left = [0]*m
DP = [-1]*(2**m)
DP[0] = 0

score = [0]*n
for c1 in range(m):
    for c2 in range(m):
        score[c1] -= trans[c1][c2]

s = 0
for i in range(1, 2**m):
    left[0] += 1
    j = 0
    while left[j] > 1:
        t = trans[j]
        for c2 in range(m):
            score[c2] -= 2 * t[c2]

        left[j] = 0
        j += 1
        left[j] += 1

    t = trans[j]
    for c2 in range(m):
        score[c2] += 2 * t[c2]

    N = sum(left)
    DP[i] = min(DP[i ^ (1 << x)] + N * score[x] for x in range(m) if left[x])

print DP[-1]


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

left = [0]*m
DP = [-1]*(2**m)
DP[0] = 0

score = [0]*n
for c1 in range(m):
    for c2 in range(m):
        score[c1] -= trans[c1][c2]

s = 0
for i in range(1, 2**m):
    left[0] += 1
    s += 1
    j = 0
    while left[j] > 1:
        t = trans[j]
        for c2 in range(m):
            score[c2] -= 2 * t[c2]

        left[j] = 0
        j += 1
        left[j] += 1
        s -= 1

    t = trans[j]
    for c2 in range(m):
        score[c2] += 2 * t[c2]

    besta = 10**9
    for x in range(m):
        val = DP[i ^ (1 << x)] + s * score[x]
        if left[x] and val < besta:
            besta = val
    DP[i] = besta

print DP[-1]


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

left = [0]*m
DP = [-1]*(2**m)
DP[0] = 0

score = [0]*n
for c1 in range(m):
    for c2 in range(m):
        score[c1] -= trans[c1][c2]

for c1 in range(m):
    for c2 in range(m):
        trans[c1][c2] *= 2

s = 0
for i in range(1, 2**m):
    s += 1
    j = 0
    while left[j] == 1:
        t = trans[j]
        for c2 in range(m):
            score[c2] -= t[c2]

        left[j] = 0
        j += 1
        s -= 1

    left[j] = 1
    t = trans[j]
    for c2 in range(m):
        score[c2] += t[c2]

    besta = 10**9
    for x in range(m):
        val = DP[i ^ (1 << x)] + s * score[x]
        if i & (1 << x) and val < besta:
            besta = val
    DP[i] = besta

print DP[-1]


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

def solve():
    DP = [-1]*(2**m)
    DP[0] = 0
    for i in range(1, 2**m):

        left = [x for x in range(m) if (1 << x) & i]
        used = [x for x in range(m) if (1 << x) & i == 0]

        N = len(left)

        besta = 10**9
        for x in left:
            tx = trans[x]
            score = 0;
            for j in left:
                score += tx[j]
            for j in used:
                score -= tx[j]

            score = score * N + DP[i ^ (1 << x)]
            if score < besta:
                besta = score

        DP[i] = besta
    return DP[-1]
print solve()


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

left = [0]*m
DP = [-1]*(2**m)
DP[0] = 0

score = [0]*n
for c1 in range(m):
    for c2 in range(m):
        score[c1] -= trans[c1][c2]

for i in range(1, 2**m):
    left[0] += 1
    j = 0
    while left[j] > 1:
        for c2 in range(m):
            score[c2] -= 2 * trans[j][c2]

        left[j] = 0
        j += 1
        left[j] += 1

    for c2 in range(m):
        score[c2] += 2 * trans[j][c2]

    N = sum(left)
    DP[i] = min(DP[i ^ (1 << x)] + N * score[x] for x in range(m) if left[x])

print DP[-1]


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

left = [0]*m
DP = [-1]*(2**m)
DP[0] = 0

score = [0]*n
for c1 in range(m):
    for c2 in range(m):
        score[c1] -= trans[c1][c2]

for c1 in range(m):
    for c2 in range(m):
        trans[c1][c2] *= 2

s = 0
for i in range(1, 2**m):
    j = 0
    while left[j]:
        t = trans[j]
        for c2 in range(m):
            score[c2] -= t[c2]

        left[j] = 0
        j += 1
    s += 1 - j

    left[j] = 1
    t = trans[j]
    for c2 in range(m):
        score[c2] += t[c2]

    besta = 10**9
    for x in range(m):
        val = DP[i ^ (1 << x)] + s * score[x]
        if i & (1 << x) and val < besta:
            besta = val
    DP[i] = besta

print DP[-1]


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

left = [0]*m
DP = [-1]*(2**m)
DP[0] = 0

score = [0]*n
for c1 in range(m):
    for c2 in range(m):
        score[c1] -= trans[c1][c2]

for c1 in range(m):
    for c2 in range(m):
        trans[c1][c2] *= 2

s = 0
for i in range(1, 2**m):
    left[0] += 1
    s += 1
    j = 0
    while left[j] > 1:
        t = trans[j]
        for c2 in range(m):
            score[c2] -= t[c2]

        left[j] = 0
        j += 1
        left[j] += 1
        s -= 1

    t = trans[j]
    for c2 in range(m):
        score[c2] += t[c2]

    besta = 10**9
    for x in range(m):
        val = DP[i ^ (1 << x)] + s * score[x]
        if left[x] and val < besta:
            besta = val
    DP[i] = besta

print DP[-1]


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    elif S[i] > S[i + 1]:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

left = [0]*m
DP = [-1.0]*(2**m)
DP[0] = 0.0

score = [0]*n
for c1 in range(m):
    for c2 in range(m):
        score[c1] -= trans[c1][c2]

for i in range(1, 2**m):
    left[0] += 1
    j = 0
    while left[j] > 1:
        for c2 in range(m):
            score[c2] -= 2 * trans[j][c2]

        left[j] = 0
        j += 1
        left[j] += 1

    for c2 in range(m):
        score[c2] += 2 * trans[j][c2]

    N = 1.0 + sum(left)
    DP[i] = min(DP[i ^ (1 << x)] + N * score[x] for x in range(m) if left[x])

print int(DP[-1])


import sys
range = xrange
input = raw_input

n, m = [int(x) for x in input().split()]
orda = ord('a')
S = [ord(c) - orda for c in input()]

trans = [[0]*m for _ in range(m)]
for i in range(n - 1):
    if S[i] < S[i + 1]:
        trans[S[i]][S[i + 1]] += 1
    else:
        trans[S[i + 1]][S[i]] += 1

for c1 in range(m):
    for c2 in range(c1 + 1, m):
        trans[c2][c1] = trans[c1][c2]

chars = list(range(m))
picked  = []
while chars:
    score = []
    for i in range(len(chars)):
        Si = S[i]
        L = 0
        for c in picked:
            L += trans[c][Si]
        R = 0
        for c in chars:
            R += trans[c][Si]

        score.append(L - R)
    i = max(range(len(chars)), key = score.__getitem__)
    picked.append(chars.pop(i))

pos = [0]*m
for i in range(m):
    pos[picked[i]] = i

ans = 0
for i in range(n - 1):
    ans += abs(pos[S[i]] - pos[S[i + 1]])

print ans


import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline

INF = 10**9

n, m = [int(item) for item in input().split()]
s = input().rstrip()

# Calculate adjacent count in subset
adj_in_subset = [0] * (1 << m)
ord_a = ord("a")
for c1, c2 in zip(s, s[1:]):
    c1 = ord(c1) - ord_a
    c2 = ord(c2) - ord_a
    if c1 != c2:
        adj_in_subset[(1 << c1) + (1 << c2)] += 1
for i in range(m):
    for j in range(1 << m):
        if j & (1 << i):
            adj_in_subset[j] += adj_in_subset[j ^ (1 << i)]

total_adj = adj_in_subset[-1]
dp = [INF] * (1 << m)
dp[0] = 0

for i in range(1 << m):
    for j in range(m):
        if i & 1 << j:
            continue
        cost = total_adj - adj_in_subset[i] - adj_in_subset[~i]
        dp[i | (1 << j)] = min(dp[i | (1 << j)], dp[i] + cost)
print(dp[-1])