# ---
# title: 1641. Count Sorted Vowel Strings
# id: problem1641
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Math, Dynamic Programming, Backtracking
# link: <https://leetcode.com/problems/count-sorted-vowel-strings/description/>
# hidden: true
# ---
# 
# Given an integer `n`, return _the number of strings of length_`n` _that
# consist only of vowels (_`a` _,_`e` _,_`i` _,_`o` _,_`u` _) and are
# **lexicographically sorted**._
# 
# A string `s` is **lexicographically sorted** if for all valid `i`, `s[i]` is
# the same as or comes before `s[i+1]` in the alphabet.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: n = 1
#     Output: 5
#     Explanation: The 5 sorted strings that consist of vowels only are ["a","e","i","o","u"].
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: n = 2
#     Output: 15
#     Explanation: The 15 sorted strings that consist of vowels only are
#     ["aa","ae","ai","ao","au","ee","ei","eo","eu","ii","io","iu","oo","ou","uu"].
#     Note that "ea" is not a valid string since 'e' comes after 'a' in the alphabet.
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: n = 33
#     Output: 66045
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= n <= 50` 
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
