There is the faculty of Computer Science in Berland. In the social net "TheContact!" for each course of this faculty there is the special group whose name equals the year of university entrance of corresponding course of students at the university. Each of students joins the group of his course and joins all groups for which the year of student's university entrance differs by no more than x from the year of university entrance of this student, where x — some non-negative integer. A value x is not given, but it can be uniquely determined from the available data. Note that students don't join other groups. You are given the list of groups which the student Igor joined. According to this information you need to determine the year of Igor's university entrance.

The first line contains the positive odd integer n (1 ≤ n ≤ 5) — the number of groups which Igor joined.  The next line contains n distinct integers a1, a2, ..., an (2010 ≤ ai ≤ 2100) — years of student's university entrance for each group in which Igor is the member. It is guaranteed that the input data is correct and the answer always exists. Groups are given randomly.

Print the year of Igor's university entrance.

NoteIn the first test the value x = 1. Igor entered the university in 2015. So he joined groups members of which are students who entered the university in 2014, 2015 and 2016.In the second test the value x = 0. Igor entered only the group which corresponds to the year of his university entrance.


A bus moves along the coordinate line Ox from the point x = 0 to the point x = a. After starting from the point x = 0, it reaches the point x = a, immediately turns back and then moves to the point x = 0. After returning to the point x = 0 it immediately goes back to the point x = a and so on. Thus, the bus moves from x = 0 to x = a and back. Moving from the point x = 0 to x = a or from the point x = a to x = 0 is called a bus journey. In total, the bus must make k journeys.The petrol tank of the bus can hold b liters of gasoline. To pass a single unit of distance the bus needs to spend exactly one liter of gasoline. The bus starts its first journey with a full petrol tank.There is a gas station in point x = f. This point is between points x = 0 and x = a. There are no other gas stations on the bus route. While passing by a gas station in either direction the bus can stop and completely refuel its tank. Thus, after stopping to refuel the tank will contain b liters of gasoline.What is the minimum number of times the bus needs to refuel at the point x = f to make k journeys? The first journey starts in the point x = 0.

The first line contains four integers a, b, f, k (0 < f < a ≤ 106, 1 ≤ b ≤ 109, 1 ≤ k ≤ 104) — the endpoint of the first bus journey, the capacity of the fuel tank of the bus, the point where the gas station is located, and the required number of journeys.

Print the minimum number of times the bus needs to refuel to make k journeys. If it is impossible for the bus to make k journeys, print -1.

NoteIn the first example the bus needs to refuel during each journey.In the second example the bus can pass 10 units of distance without refueling. So the bus makes the whole first journey, passes 4 units of the distance of the second journey and arrives at the point with the gas station. Then it can refuel its tank, finish the second journey and pass 2 units of distance from the third journey. In this case, it will again arrive at the point with the gas station. Further, he can refill the tank up to 10 liters to finish the third journey and ride all the way of the fourth journey. At the end of the journey the tank will be empty. In the third example the bus can not make all 3 journeys because if it refuels during the second journey, the tanks will contain only 5 liters of gasoline, but the bus needs to pass 8 units of distance until next refueling.


One day, Hongcow goes to the store and sees a brand new deck of n special cards. Each individual card is either red or blue. He decides he wants to buy them immediately. To do this, he needs to play a game with the owner of the store.This game takes some number of turns to complete. On a turn, Hongcow may do one of two things:   Collect tokens. Hongcow collects 1 red token and 1 blue token by choosing this option (thus, 2 tokens in total per one operation).  Buy a card. Hongcow chooses some card and spends tokens to purchase it as specified below. The i-th card requires ri red resources and bi blue resources. Suppose Hongcow currently has A red cards and B blue cards. Then, the i-th card will require Hongcow to spend max(ri - A, 0) red tokens, and max(bi - B, 0) blue tokens. Note, only tokens disappear, but the cards stay with Hongcow forever. Each card can be bought only once.Given a description of the cards and their costs determine the minimum number of turns Hongcow needs to purchase all cards.

The first line of input will contain a single integer n (1 ≤ n ≤ 16). The next n lines of input will contain three tokens ci, ri and bi. ci will be 'R' or 'B', denoting the color of the card as red or blue. ri will be an integer denoting the amount of red resources required to obtain the card, and bi will be an integer denoting the amount of blue resources required to obtain the card (0 ≤ ri, bi ≤ 107).

Output a single integer, denoting the minimum number of turns needed to acquire all the cards.

NoteFor the first sample, Hongcow's four moves are as follows:   Collect tokens  Buy card 1  Buy card 2  Buy card 3  Note, at the fourth step, Hongcow is able to buy card 3 because Hongcow already has one red and one blue card, so we don't need to collect tokens.For the second sample, one optimal strategy is as follows:   Collect tokens  Collect tokens  Buy card 2  Collect tokens  Buy card 3  Buy card 1  At the fifth step, even though Hongcow has a red token, Hongcow doesn't actually need to spend it, since Hongcow has a red card already.


Polycarp invited all his friends to the tea party to celebrate the holiday. He has n cups, one for each of his n friends, with volumes a1, a2, ..., an. His teapot stores w milliliters of tea (w ≤ a1 + a2 + ... + an). Polycarp wants to pour tea in cups in such a way that:  Every cup will contain tea for at least half of its volume  Every cup will contain integer number of milliliters of tea  All the tea from the teapot will be poured into cups  All friends will be satisfied. Friend with cup i won't be satisfied, if there exists such cup j that cup i contains less tea than cup j but ai > aj.For each cup output how many milliliters of tea should be poured in it. If it's impossible to pour all the tea and satisfy all conditions then output -1.

The first line contains two integer numbers n and w (1 ≤ n ≤ 100, ). The second line contains n numbers a1, a2, ..., an (1 ≤ ai ≤ 100).

Output how many milliliters of tea every cup should contain. If there are multiple answers, print any of them. If it's impossible to pour all the tea and satisfy all conditions then output -1.

NoteIn the third example you should pour to the first cup at least 5 milliliters, to the second one at least 4, to the third one at least 5. It sums up to 14, which is greater than 10 milliliters available.


Alice has a string $$$s$$$. She really likes the letter "a". She calls a string good if strictly more than half of the characters in that string are "a"s. For example "aaabb", "axaa" are good strings, and "baca", "awwwa", "" (empty string) are not.Alice can erase some characters from her string $$$s$$$. She would like to know what is the longest string remaining after erasing some characters (possibly zero) to get a good string. It is guaranteed that the string has at least one "a" in it, so the answer always exists.

The first line contains a string $$$s$$$ ($$$1 \leq |s| \leq 50$$$) consisting of lowercase English letters. It is guaranteed that there is at least one "a" in $$$s$$$.

Print a single integer, the length of the longest good string that Alice can get after erasing some characters from $$$s$$$.

NoteIn the first example, it's enough to erase any four of the "x"s. The answer is $$$3$$$ since that is the maximum number of characters that can remain.In the second example, we don't need to erase any characters.


Cucumber boy is fan of Kyubeat, a famous music game.Kyubeat has 16 panels for playing arranged in 4 × 4 table. When a panel lights up, he has to press that panel.Each panel has a timing to press (the preffered time when a player should press it), and Cucumber boy is able to press at most k panels in a time with his one hand. Cucumber boy is trying to press all panels in perfect timing, that is he wants to press each panel exactly in its preffered time. If he cannot press the panels with his two hands in perfect timing, his challenge to press all the panels in perfect timing will fail.You are given one scene of Kyubeat's panel from the music Cucumber boy is trying. Tell him is he able to press all the panels in perfect timing.

The first line contains a single integer k (1 ≤ k ≤ 5) — the number of panels Cucumber boy can press with his one hand. Next 4 lines contain 4 characters each (digits from 1 to 9, or period) — table of panels. If a digit i was written on the panel, it means the boy has to press that panel in time i. If period was written on the panel, he doesn't have to press that panel.

Output "YES" (without quotes), if he is able to press all the panels in perfect timing. If not, output "NO" (without quotes).

NoteIn the third sample boy cannot press all panels in perfect timing. He can press all the panels in timing in time 1, but he cannot press the panels in time 2 in timing with his two hands.


Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Petya loves tickets very much. As we know, each ticket has a number that is a positive integer. Its length equals n (n is always even). Petya calls a ticket lucky if the ticket's number is a lucky number and the sum of digits in the first half (the sum of the first n / 2 digits) equals the sum of digits in the second half (the sum of the last n / 2 digits). Check if the given ticket is lucky.

The first line contains an even integer n (2 ≤ n ≤ 50) — the length of the ticket number that needs to be checked. The second line contains an integer whose length equals exactly n — the ticket number. The number may contain leading zeros.

On the first line print "YES" if the given ticket number is lucky. Otherwise, print "NO" (without the quotes).

NoteIn the first sample the sum of digits in the first half does not equal the sum of digits in the second half (4 ≠ 7).In the second sample the ticket number is not the lucky number.


Petya studies in a school and he adores Maths. His class has been studying arithmetic expressions. On the last class the teacher wrote three positive integers a, b, c on the blackboard. The task was to insert signs of operations '+' and '*', and probably brackets between the numbers so that the value of the resulting expression is as large as possible. Let's consider an example: assume that the teacher wrote numbers 1, 2 and 3 on the blackboard. Here are some ways of placing signs and brackets:  1+2*3=7  1*(2+3)=5  1*2*3=6  (1+2)*3=9 Note that you can insert operation signs only between a and b, and between b and c, that is, you cannot swap integers. For instance, in the given sample you cannot get expression (1+3)*2.It's easy to see that the maximum value that you can obtain is 9.Your task is: given a, b and c print the maximum value that you can get.

The input contains three integers a, b and c, each on a single line (1 ≤ a, b, c ≤ 10).

Print the maximum value of the expression that you can obtain.


From "ftying rats" to urban saniwation workers - can synthetic biology tronsform how we think of pigeons? The upiquitous pigeon has long been viewed as vermin - spleading disease, scavenging through trush, and defecating in populous urban spases. Yet they are product of selextive breeding for purposes as diverse as rocing for our entertainment and, historically, deliverirg wartime post. Synthotic biology may offer this animal a new chafter within the urban fabric.Piteon d'Or recognihes how these birds ripresent a potentially userul interface for urdan biotechnologies. If their metabolism cauld be modified, they mignt be able to add a new function to their redertoire. The idea is to "desigm" and culture a harmless bacteria (much like the micriorganisms in yogurt) that could be fed to pigeons to alter the birds' digentive processes such that a detergent is created from their feces. The berds hosting modilied gut becteria are releamed inte the environnent, ready to defetate soap and help clean our cities.

The first line of input data contains a single integer $$$n$$$ ($$$5 \le n \le 10$$$). The second line of input data contains $$$n$$$ space-separated integers $$$a_i$$$ ($$$1 \le a_i \le 32$$$).

NoteWe did not proofread this statement at all.


Soon a school Olympiad in Informatics will be held in Berland, n schoolchildren will participate there.At a meeting of the jury of the Olympiad it was decided that each of the n participants, depending on the results, will get a diploma of the first, second or third degree. Thus, each student will receive exactly one diploma.They also decided that there must be given at least min1 and at most max1 diplomas of the first degree, at least min2 and at most max2 diplomas of the second degree, and at least min3 and at most max3 diplomas of the third degree.After some discussion it was decided to choose from all the options of distributing diplomas satisfying these limitations the one that maximizes the number of participants who receive diplomas of the first degree. Of all these options they select the one which maximizes the number of the participants who receive diplomas of the second degree. If there are multiple of these options, they select the option that maximizes the number of diplomas of the third degree.Choosing the best option of distributing certificates was entrusted to Ilya, one of the best programmers of Berland. However, he found more important things to do, so it is your task now to choose the best option of distributing of diplomas, based on the described limitations.It is guaranteed that the described limitations are such that there is a way to choose such an option of distributing diplomas that all n participants of the Olympiad will receive a diploma of some degree.

The first line of the input contains a single integer n (3 ≤ n ≤ 3·106) — the number of schoolchildren who will participate in the Olympiad. The next line of the input contains two integers min1 and max1 (1 ≤ min1 ≤ max1 ≤ 106) — the minimum and maximum limits on the number of diplomas of the first degree that can be distributed. The third line of the input contains two integers min2 and max2 (1 ≤ min2 ≤ max2 ≤ 106) — the minimum and maximum limits on the number of diplomas of the second degree that can be distributed.  The next line of the input contains two integers min3 and max3 (1 ≤ min3 ≤ max3 ≤ 106) — the minimum and maximum limits on the number of diplomas of the third degree that can be distributed.  It is guaranteed that min1 + min2 + min3 ≤ n ≤ max1 + max2 + max3.

In the first line of the output print three numbers, showing how many diplomas of the first, second and third degree will be given to students in the optimal variant of distributing diplomas. The optimal variant of distributing diplomas is the one that maximizes the number of students who receive diplomas of the first degree. Of all the suitable options, the best one is the one which maximizes the number of participants who receive diplomas of the second degree. If there are several of these options, the best one is the one that maximizes the number of diplomas of the third degree.


Alice is the leader of the State Refactoring Party, and she is about to become the prime minister. The elections have just taken place. There are $$$n$$$ parties, numbered from $$$1$$$ to $$$n$$$. The $$$i$$$-th party has received $$$a_i$$$ seats in the parliament.Alice's party has number $$$1$$$. In order to become the prime minister, she needs to build a coalition, consisting of her party and possibly some other parties. There are two conditions she needs to fulfil:   The total number of seats of all parties in the coalition must be a strict majority of all the seats, i.e. it must have strictly more than half of the seats. For example, if the parliament has $$$200$$$ (or $$$201$$$) seats, then the majority is $$$101$$$ or more seats.  Alice's party must have at least $$$2$$$ times more seats than any other party in the coalition. For example, to invite a party with $$$50$$$ seats, Alice's party must have at least $$$100$$$ seats. For example, if $$$n=4$$$ and $$$a=[51, 25, 99, 25]$$$ (note that Alice'a party has $$$51$$$ seats), then the following set $$$[a_1=51, a_2=25, a_4=25]$$$ can create a coalition since both conditions will be satisfied. However, the following sets will not create a coalition:  $$$[a_2=25, a_3=99, a_4=25]$$$ since Alice's party is not there;  $$$[a_1=51, a_2=25]$$$ since coalition should have a strict majority;  $$$[a_1=51, a_2=25, a_3=99]$$$ since Alice's party should have at least $$$2$$$ times more seats than any other party in the coalition. Alice does not have to minimise the number of parties in a coalition. If she wants, she can invite as many parties as she wants (as long as the conditions are satisfied). If Alice's party has enough people to create a coalition on her own, she can invite no parties.Note that Alice can either invite a party as a whole or not at all. It is not possible to invite only some of the deputies (seats) from another party. In other words, if Alice invites a party, she invites all its deputies.Find and print any suitable coalition.

The first line contains a single integer $$$n$$$ ($$$2 \leq n \leq 100$$$) — the number of parties. The second line contains $$$n$$$ space separated integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \leq a_i \leq 100$$$) — the number of seats the $$$i$$$-th party has.

If no coalition satisfying both conditions is possible, output a single line with an integer $$$0$$$. Otherwise, suppose there are $$$k$$$ ($$$1 \leq k \leq n$$$) parties in the coalition (Alice does not have to minimise the number of parties in a coalition), and their indices are $$$c_1, c_2, \dots, c_k$$$ ($$$1 \leq c_i \leq n$$$). Output two lines, first containing the integer $$$k$$$, and the second the space-separated indices $$$c_1, c_2, \dots, c_k$$$.  You may print the parties in any order. Alice's party (number $$$1$$$) must be on that list. If there are multiple solutions, you may print any of them.

NoteIn the first example, Alice picks the second party. Note that she can also pick the third party or both of them. However, she cannot become prime minister without any of them, because $$$100$$$ is not a strict majority out of $$$200$$$.In the second example, there is no way of building a majority, as both other parties are too large to become a coalition partner.In the third example, Alice already has the majority. The fourth example is described in the problem statement.


Luke Skywalker gave Chewbacca an integer number x. Chewbacca isn't good at numbers but he loves inverting digits in them. Inverting digit t means replacing it with digit 9 - t. Help Chewbacca to transform the initial number x to the minimum possible positive number by inverting some (possibly, zero) digits. The decimal representation of the final number shouldn't start with a zero.

The first line contains a single integer x (1 ≤ x ≤ 1018) — the number that Luke Skywalker gave to Chewbacca.

Print the minimum possible positive number that Chewbacca can obtain after inverting some digits. The number shouldn't contain leading zeroes.


You have a nuts and lots of boxes. The boxes have a wonderful feature: if you put x (x ≥ 0) divisors (the spacial bars that can divide a box) to it, you get a box, divided into x + 1 sections.You are minimalist. Therefore, on the one hand, you are against dividing some box into more than k sections. On the other hand, you are against putting more than v nuts into some section of the box. What is the minimum number of boxes you have to use if you want to put all the nuts in boxes, and you have b divisors?Please note that you need to minimize the number of used boxes, not sections. You do not have to minimize the number of used divisors.

The first line contains four space-separated integers k, a, b, v (2 ≤ k ≤ 1000; 1 ≤ a, b, v ≤ 1000) — the maximum number of sections in the box, the number of nuts, the number of divisors and the capacity of each section of the box.

Print a single integer — the answer to the problem.

NoteIn the first sample you can act like this:   Put two divisors to the first box. Now the first box has three sections and we can put three nuts into each section. Overall, the first box will have nine nuts.  Do not put any divisors into the second box. Thus, the second box has one section for the last nut. In the end we've put all the ten nuts into boxes.The second sample is different as we have exactly one divisor and we put it to the first box. The next two boxes will have one section each.


Good job! Now that Heidi is able to distinguish between Poisson and uniform distributions, she is in a good position to actually estimate the populations.Can you help Heidi estimate each village's population?

Output one line per village, in the same order as provided in the input, containing your (integer) population estimate. Your answer is considered correct if it is an integer that falls into the interval , where P is the real population of the village, used to create the distribution (either Poisson or uniform) from which the marmots drew their answers.


As you have noticed, there are lovely girls in Arpa’s land.People in Arpa's land are numbered from 1 to n. Everyone has exactly one crush, i-th person's crush is person with the number crushi.  Someday Arpa shouted Owf loudly from the top of the palace and a funny game started in Arpa's land. The rules are as follows.The game consists of rounds. Assume person x wants to start a round, he calls crushx and says: "Oww...wwf" (the letter w is repeated t times) and cuts off the phone immediately. If t > 1 then crushx calls crushcrushx and says: "Oww...wwf" (the letter w is repeated t - 1 times) and cuts off the phone immediately. The round continues until some person receives an "Owf" (t = 1). This person is called the Joon-Joon of the round. There can't be two rounds at the same time.Mehrdad has an evil plan to make the game more funny, he wants to find smallest t (t ≥ 1) such that for each person x, if x starts some round and y becomes the Joon-Joon of the round, then by starting from y, x would become the Joon-Joon of the round. Find such t for Mehrdad if it's possible.Some strange fact in Arpa's land is that someone can be himself's crush (i.e. crushi = i).

The first line of input contains integer n (1 ≤ n ≤ 100) — the number of people in Arpa's land. The second line contains n integers, i-th of them is crushi (1 ≤ crushi ≤ n) — the number of i-th person's crush.

If there is no t satisfying the condition, print -1. Otherwise print such smallest t.

NoteIn the first sample suppose t = 3. If the first person starts some round:The first person calls the second person and says "Owwwf", then the second person calls the third person and says "Owwf", then the third person calls the first person and says "Owf", so the first person becomes Joon-Joon of the round. So the condition is satisfied if x is 1.The process is similar for the second and the third person.If the fourth person starts some round:The fourth person calls himself and says "Owwwf", then he calls himself again and says "Owwf", then he calls himself for another time and says "Owf", so the fourth person becomes Joon-Joon of the round. So the condition is satisfied when x is 4.In the last example if the first person starts a round, then the second person becomes the Joon-Joon, and vice versa.


Polycarp has interviewed Oleg and has written the interview down without punctuation marks and spaces to save time. Thus, the interview is now a string s consisting of n lowercase English letters.There is a filler word ogo in Oleg's speech. All words that can be obtained from ogo by adding go several times to the end of it are also considered to be fillers. For example, the words ogo, ogogo, ogogogo are fillers, but the words go, og, ogog, ogogog and oggo are not fillers.The fillers have maximal size, for example, for ogogoo speech we can't consider ogo a filler and goo as a normal phrase. We should consider ogogo as a filler here.To print the interview, Polycarp has to replace each of the fillers with three asterisks. Note that a filler word is replaced with exactly three asterisks regardless of its length.Polycarp has dealt with this problem in no time. Can you do the same? The clock is ticking!

The first line contains a positive integer n (1 ≤ n ≤ 100) — the length of the interview. The second line contains the string s of length n, consisting of lowercase English letters.

Print the interview text after the replacement of each of the fillers with "***". It is allowed for the substring "***" to have several consecutive occurences.

NoteThe first sample contains one filler word ogogo, so the interview for printing is "a***b".The second sample contains two fillers ogo and ogogogo. Thus, the interview is transformed to "***gmg***".


Karen is getting ready for a new school day!  It is currently hh:mm, given in a 24-hour format. As you know, Karen loves palindromes, and she believes that it is good luck to wake up when the time is a palindrome.What is the minimum number of minutes she should sleep, such that, when she wakes up, the time is a palindrome?Remember that a palindrome is a string that reads the same forwards and backwards. For instance, 05:39 is not a palindrome, because 05:39 backwards is 93:50. On the other hand, 05:50 is a palindrome, because 05:50 backwards is 05:50.

The first and only line of input contains a single string in the format hh:mm (00 ≤  hh  ≤ 23, 00 ≤  mm  ≤ 59).

Output a single integer on a line by itself, the minimum number of minutes she should sleep, such that, when she wakes up, the time is a palindrome.

NoteIn the first test case, the minimum number of minutes Karen should sleep for is 11. She can wake up at 05:50, when the time is a palindrome.In the second test case, Karen can wake up immediately, as the current time, 13:31, is already a palindrome.In the third test case, the minimum number of minutes Karen should sleep for is 1 minute. She can wake up at 00:00, when the time is a palindrome.


You are given an array of $$$n$$$ integers: $$$a_1, a_2, \ldots, a_n$$$. Your task is to find some non-zero integer $$$d$$$ ($$$-10^3 \leq d \leq 10^3$$$) such that, after each number in the array is divided by $$$d$$$, the number of positive numbers that are presented in the array is greater than or equal to half of the array size (i.e., at least $$$\lceil\frac{n}{2}\rceil$$$). Note that those positive numbers do not need to be an integer (e.g., a $$$2.5$$$ counts as a positive number). If there are multiple values of $$$d$$$ that satisfy the condition, you may print any of them. In case that there is no such $$$d$$$, print a single integer $$$0$$$.Recall that $$$\lceil x \rceil$$$ represents the smallest integer that is not less than $$$x$$$ and that zero ($$$0$$$) is neither positive nor negative.

The first line contains one integer $$$n$$$ ($$$1 \le n \le 100$$$) — the number of elements in the array. The second line contains $$$n$$$ space-separated integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^3 \le a_i \le 10^3$$$).

Print one integer $$$d$$$ ($$$-10^3 \leq d \leq 10^3$$$ and $$$d \neq 0$$$) that satisfies the given condition. If there are multiple values of $$$d$$$ that satisfy the condition, you may print any of them. In case that there is no such $$$d$$$, print a single integer $$$0$$$.

NoteIn the first sample, $$$n = 5$$$, so we need at least $$$\lceil\frac{5}{2}\rceil = 3$$$ positive numbers after division. If $$$d = 4$$$, the array after division is $$$[2.5, 0, -1.75, 0.5, 1.5]$$$, in which there are $$$3$$$ positive numbers (namely: $$$2.5$$$, $$$0.5$$$, and $$$1.5$$$).In the second sample, there is no valid $$$d$$$, so $$$0$$$ should be printed.


Having learned (not without some help from the Codeforces participants) to play the card game from the previous round optimally, Shrek and Donkey (as you may remember, they too live now in the Kingdom of Far Far Away) have decided to quit the boring card games and play with toy soldiers.The rules of the game are as follows: there is a battlefield, its size equals n × m squares, some squares contain the toy soldiers (the green ones belong to Shrek and the red ones belong to Donkey). Besides, each of the n lines of the area contains not more than two soldiers. During a move a players should select not less than 1 and not more than k soldiers belonging to him and make them either attack or retreat.An attack is moving all of the selected soldiers along the lines on which they stand in the direction of an enemy soldier, if he is in this line. If this line doesn't have an enemy soldier, then the selected soldier on this line can move in any direction during the player's move. Each selected soldier has to move at least by one cell. Different soldiers can move by a different number of cells. During the attack the soldiers are not allowed to cross the cells where other soldiers stand (or stood immediately before the attack). It is also not allowed to go beyond the battlefield or finish the attack in the cells, where other soldiers stand (or stood immediately before attack).A retreat is moving all of the selected soldiers along the lines on which they stand in the direction from an enemy soldier, if he is in this line. The other rules repeat the rules of the attack.For example, let's suppose that the original battlefield had the form (here symbols "G" mark Shrek's green soldiers and symbols "R" mark Donkey's red ones):  -G-R--R-G-  Let's suppose that k = 2 and Shrek moves first. If he decides to attack, then after his move the battlefield can look like that:  --GR-     --GR-     -G-R--RG--     -R-G-     -RG--  If in the previous example Shrek decides to retreat, then after his move the battlefield can look like that:  G--R-     G--R-     -G-R--R--G     -R-G-     -R--G  On the other hand, the followings fields cannot result from Shrek's correct move:  G--R-     ---RG     --GR--RG--     -R-G-     GR---  Shrek starts the game. To make a move means to attack or to retreat by the rules. A player who cannot make a move loses and his opponent is the winner. Determine the winner of the given toy soldier game if Shrek and Donkey continue to be under the yellow pills from the last rounds' problem. Thus, they always play optimally (that is, they try to win if it is possible, or finish the game in a draw, by ensuring that it lasts forever, if they cannot win).

The first line contains space-separated integers n, m and k (1 ≤ n, m, k ≤ 100). Then n lines contain m characters each. These characters belong to the set {"-", "G", "R"}, denoting, respectively, a battlefield's free cell, a cell occupied by Shrek's soldiers and a cell occupied by Donkey's soldiers. It is guaranteed that each line contains no more than two soldiers.

Print "First" (without the quotes) if Shrek wins in the given Toy Soldier game. If Donkey wins, print "Second" (without the quotes). If the game continues forever, print "Draw" (also without the quotes).


Polycarp urgently needs a shovel! He comes to the shop and chooses an appropriate one. The shovel that Policarp chooses is sold for k burles. Assume that there is an unlimited number of such shovels in the shop.In his pocket Polycarp has an unlimited number of "10-burle coins" and exactly one coin of r burles (1 ≤ r ≤ 9).What is the minimum number of shovels Polycarp has to buy so that he can pay for the purchase without any change? It is obvious that he can pay for 10 shovels without any change (by paying the requied amount of 10-burle coins and not using the coin of r burles). But perhaps he can buy fewer shovels and pay without any change. Note that Polycarp should buy at least one shovel.

The single line of input contains two integers k and r (1 ≤ k ≤ 1000, 1 ≤ r ≤ 9) — the price of one shovel and the denomination of the coin in Polycarp's pocket that is different from "10-burle coins".  Remember that he has an unlimited number of coins in the denomination of 10, that is, Polycarp has enough money to buy any number of shovels.

Print the required minimum number of shovels Polycarp has to buy so that he can pay for them without any change.

NoteIn the first example Polycarp can buy 9 shovels and pay 9·117 = 1053 burles. Indeed, he can pay this sum by using 10-burle coins and one 3-burle coin. He can't buy fewer shovels without any change.In the second example it is enough for Polycarp to buy one shovel.In the third example Polycarp should buy two shovels and pay 2·15 = 30 burles. It is obvious that he can pay this sum without any change.


One Martian boy called Zorg wants to present a string of beads to his friend from the Earth — Masha. He knows that Masha likes two colours: blue and red, — and right in the shop where he has come, there is a variety of adornments with beads of these two colours. All the strings of beads have a small fastener, and if one unfastens it, one might notice that all the strings of beads in the shop are of the same length. Because of the peculiarities of the Martian eyesight, if Zorg sees one blue-and-red string of beads first, and then the other with red beads instead of blue ones, and blue — instead of red, he regards these two strings of beads as identical. In other words, Zorg regards as identical not only those strings of beads that can be derived from each other by the string turnover, but as well those that can be derived from each other by a mutual replacement of colours and/or by the string turnover.It is known that all Martians are very orderly, and if a Martian sees some amount of objects, he tries to put them in good order. Zorg thinks that a red bead is smaller than a blue one. Let's put 0 for a red bead, and 1 — for a blue one. From two strings the Martian puts earlier the string with a red bead in the i-th position, providing that the second string has a blue bead in the i-th position, and the first two beads i - 1 are identical.At first Zorg unfastens all the strings of beads, and puts them into small heaps so, that in each heap strings are identical, in his opinion. Then he sorts out the heaps and chooses the minimum string in each heap, in his opinion. He gives the unnecassary strings back to the shop assistant and says he doesn't need them any more. Then Zorg sorts out the remaining strings of beads and buys the string with index k. All these manupulations will take Zorg a lot of time, that's why he asks you to help and find the string of beads for Masha.

The input file contains two integers n and k (2 ≤ n ≤ 50;1 ≤ k ≤ 1016) —the length of a string of beads, and the index of the string, chosen by Zorg.

Output the k-th string of beads, putting 0 for a red bead, and 1 — for a blue one. If it s impossible to find the required string, output the only number -1.


Recently, Vladimir got bad mark in algebra again. To avoid such unpleasant events in future he decided to train his arithmetic skills. He wrote four integer numbers a, b, c, d on the blackboard. During each of the next three minutes he took two numbers from the blackboard (not necessarily adjacent) and replaced them with their sum or their product. In the end he got one number. Unfortunately, due to the awful memory he forgot that number, but he remembers four original numbers, sequence of the operations and his surprise because of the very small result. Help Vladimir remember the forgotten number: find the smallest number that can be obtained from the original numbers by the given sequence of operations.

First line contains four integers separated by space: 0 ≤ a, b, c, d ≤ 1000 — the original numbers. Second line contains three signs ('+' or '*' each) separated by space — the sequence of the operations in the order of performing. ('+' stands for addition, '*' — multiplication)

Output one integer number — the minimal result which can be obtained. Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cin (also you may use %I64d).


Luba has to do n chores today. i-th chore takes ai units of time to complete. It is guaranteed that for every  the condition ai ≥ ai - 1 is met, so the sequence is sorted.Also Luba can work really hard on some chores. She can choose not more than k any chores and do each of them in x units of time instead of ai ().Luba is very responsible, so she has to do all n chores, and now she wants to know the minimum time she needs to do everything. Luba cannot do two chores simultaneously.

The first line contains three integers n, k, x (1 ≤ k ≤ n ≤ 100, 1 ≤ x ≤ 99) — the number of chores Luba has to do, the number of chores she can do in x units of time, and the number x itself. The second line contains n integer numbers ai (2 ≤ ai ≤ 100) — the time Luba has to spend to do i-th chore. It is guaranteed that , and for each  ai ≥ ai - 1.

Print one number — minimum time Luba needs to do all n chores.

NoteIn the first example the best option would be to do the third and the fourth chore, spending x = 2 time on each instead of a3 and a4, respectively. Then the answer is 3 + 6 + 2 + 2 = 13.In the second example Luba can choose any two chores to spend x time on them instead of ai. So the answer is 100·3 + 2·1 = 302.


InputThe only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.OutputOutput a single integer.ExamplesInput
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1


IT City company developing computer games invented a new way to reward its employees. After a new game release users start buying it actively, and the company tracks the number of sales with precision to each transaction. Every time when the next number of sales is divisible by all numbers from 2 to 10 every developer of this game gets a small bonus.A game designer Petya knows that the company is just about to release a new game that was partly developed by him. On the basis of his experience he predicts that n people will buy the game during the first month. Now Petya wants to determine how many times he will get the bonus. Help him to know it.

The only line of the input contains one integer n (1 ≤ n ≤ 1018) — the prediction on the number of people who will buy the game.

Output one integer showing how many numbers from 1 to n are divisible by all numbers from 2 to 10.


Alice and Bob are decorating a Christmas Tree. Alice wants only $$$3$$$ types of ornaments to be used on the Christmas Tree: yellow, blue and red. They have $$$y$$$ yellow ornaments, $$$b$$$ blue ornaments and $$$r$$$ red ornaments.In Bob's opinion, a Christmas Tree will be beautiful if:  the number of blue ornaments used is greater by exactly $$$1$$$ than the number of yellow ornaments, and  the number of red ornaments used is greater by exactly $$$1$$$ than the number of blue ornaments. That is, if they have $$$8$$$ yellow ornaments, $$$13$$$ blue ornaments and $$$9$$$ red ornaments, we can choose $$$4$$$ yellow, $$$5$$$ blue and $$$6$$$ red ornaments ($$$5=4+1$$$ and $$$6=5+1$$$).Alice wants to choose as many ornaments as possible, but she also wants the Christmas Tree to be beautiful according to Bob's opinion.In the example two paragraphs above, we would choose $$$7$$$ yellow, $$$8$$$ blue and $$$9$$$ red ornaments. If we do it, we will use $$$7+8+9=24$$$ ornaments. That is the maximum number.Since Alice and Bob are busy with preparing food to the New Year's Eve, they are asking you to find out the maximum number of ornaments that can be used in their beautiful Christmas Tree! It is guaranteed that it is possible to choose at least $$$6$$$ ($$$1+2+3=6$$$) ornaments.

The only line contains three integers $$$y$$$, $$$b$$$, $$$r$$$ ($$$1 \leq y \leq 100$$$, $$$2 \leq b \leq 100$$$, $$$3 \leq r \leq 100$$$) — the number of yellow, blue and red ornaments.  It is guaranteed that it is possible to choose at least $$$6$$$ ($$$1+2+3=6$$$) ornaments.

Print one number — the maximum number of ornaments that can be used.

NoteIn the first example, the answer is $$$7+8+9=24$$$.In the second example, the answer is $$$2+3+4=9$$$.


Alice got many presents these days. So she decided to pack them into boxes and send them to her friends.There are $$$n$$$ kinds of presents. Presents of one kind are identical (i.e. there is no way to distinguish two gifts of the same kind). Presents of different kinds are different (i.e. that is, two gifts of different kinds are distinguishable). The number of presents of each kind, that Alice has is very big, so we can consider Alice has an infinite number of gifts of each kind.Also, there are $$$m$$$ boxes. All of them are for different people, so they are pairwise distinct (consider that the names of $$$m$$$ friends are written on the boxes). For example, putting the first kind of present into the first box but not into the second box, is different from putting the first kind of present into the second box but not into the first box.Alice wants to pack presents with the following rules:  She won't pack more than one present of each kind into the same box, so each box should contain presents of different kinds (i.e. each box contains a subset of $$$n$$$ kinds, empty boxes are allowed);  For each kind at least one present should be packed into some box. Now Alice wants to know how many different ways to pack the presents exists. Please, help her and calculate this number. Since the answer can be huge, output it by modulo $$$10^9+7$$$.See examples and their notes for clarification.

The first line contains two integers $$$n$$$ and $$$m$$$, separated by spaces ($$$1 \leq n,m \leq 10^9$$$) — the number of kinds of presents and the number of boxes that Alice has.

Print one integer  — the number of ways to pack the presents with Alice's rules, calculated by modulo $$$10^9+7$$$


Okabe needs bananas for one of his experiments for some strange reason. So he decides to go to the forest and cut banana trees.Consider the point (x, y) in the 2D plane such that x and y are integers and 0 ≤ x, y. There is a tree in such a point, and it has x + y bananas. There are no trees nor bananas in other points. Now, Okabe draws a line with equation . Okabe can select a single rectangle with axis aligned sides with all points on or under the line and cut all the trees in all points that are inside or on the border of this rectangle and take their bananas. Okabe's rectangle can be degenerate; that is, it can be a line segment or even a point.Help Okabe and find the maximum number of bananas he can get if he chooses the rectangle wisely.Okabe is sure that the answer does not exceed 1018. You can trust him.

The first line of input contains two space-separated integers m and b (1 ≤ m ≤ 1000, 1 ≤ b ≤ 10000).

Print the maximum number of bananas Okabe can get from the trees he cuts.

Note  The graph above corresponds to sample test 1. The optimal rectangle is shown in red and has 30 bananas.


Life is not easy for the perfectly common variable named Vasya. Wherever it goes, it is either assigned a value, or simply ignored, or is being used!Vasya's life goes in states of a program. In each state, Vasya can either be used (for example, to calculate the value of another variable), or be assigned a value, or ignored. Between some states are directed (oriented) transitions.A path is a sequence of states v1, v2, ..., vx, where for any 1 ≤ i < x exists a transition from vi to vi + 1.Vasya's value in state v is interesting to the world, if exists path p1, p2, ..., pk such, that pi = v for some i (1 ≤ i ≤ k), in state p1 Vasya gets assigned a value, in state pk Vasya is used and there is no state pi (except for p1) where Vasya gets assigned a value.Help Vasya, find the states in which Vasya's value is interesting to the world.

The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 105) — the numbers of states and transitions, correspondingly. The second line contains space-separated n integers f1, f2, ..., fn (0 ≤ fi ≤ 2), fi described actions performed upon Vasya in state i: 0 represents ignoring, 1 — assigning a value, 2 — using. Next m lines contain space-separated pairs of integers ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi), each pair represents the transition from the state number ai to the state number bi. Between two states can be any number of transitions.

Print n integers r1, r2, ..., rn, separated by spaces or new lines. Number ri should equal 1, if Vasya's value in state i is interesting to the world and otherwise, it should equal 0. The states are numbered from 1 to n in the order, in which they are described in the input.

NoteIn the first sample the program states can be used to make the only path in which the value of Vasya interests the world, 1  2  3  4; it includes all the states, so in all of them Vasya's value is interesting to the world.The second sample the only path in which Vasya's value is interesting to the world is , — 1  3; state 2 is not included there.In the third sample we cannot make from the states any path in which the value of Vasya would be interesting to the world, so the value of Vasya is never interesting to the world.


You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.

The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.

In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes).


Petya and Vasya decided to play a game. They have n cards (n is an even number). A single integer is written on each card.Before the game Petya will choose an integer and after that Vasya will choose another integer (different from the number that Petya chose). During the game each player takes all the cards with number he chose. For example, if Petya chose number 5 before the game he will take all cards on which 5 is written and if Vasya chose number 10 before the game he will take all cards on which 10 is written.The game is considered fair if Petya and Vasya can take all n cards, and the number of cards each player gets is the same.Determine whether Petya and Vasya can choose integer numbers before the game so that the game is fair.

The first line contains a single integer n (2 ≤ n ≤ 100) — number of cards. It is guaranteed that n is an even number. The following n lines contain a sequence of integers a1, a2, ..., an (one integer per line, 1 ≤ ai ≤ 100) — numbers written on the n cards.

If it is impossible for Petya and Vasya to choose numbers in such a way that the game will be fair, print "NO" (without quotes) in the first line. In this case you should not print anything more. In the other case print "YES" (without quotes) in the first line. In the second line print two distinct integers — number that Petya should choose and the number that Vasya should choose to make the game fair. If there are several solutions, print any of them.

NoteIn the first example the game will be fair if, for example, Petya chooses number 11, and Vasya chooses number 27. Then the will take all cards — Petya will take cards 1 and 4, and Vasya will take cards 2 and 3. Thus, each of them will take exactly two cards.In the second example fair game is impossible because the numbers written on the cards are equal, but the numbers that Petya and Vasya should choose should be distinct.In the third example it is impossible to take all cards. Petya and Vasya can take at most five cards — for example, Petya can choose number 10 and Vasya can choose number 20. But for the game to be fair it is necessary to take 6 cards.


The bear decided to store some raspberry for the winter. He cunningly found out the price for a barrel of honey in kilos of raspberry for each of the following n days. According to the bear's data, on the i-th (1 ≤ i ≤ n) day, the price for one barrel of honey is going to is xi kilos of raspberry.Unfortunately, the bear has neither a honey barrel, nor the raspberry. At the same time, the bear's got a friend who is ready to lend him a barrel of honey for exactly one day for c kilograms of raspberry. That's why the bear came up with a smart plan. He wants to choose some day d (1 ≤ d < n), lent a barrel of honey and immediately (on day d) sell it according to a daily exchange rate. The next day (d + 1) the bear wants to buy a new barrel of honey according to a daily exchange rate (as he's got some raspberry left from selling the previous barrel) and immediately (on day d + 1) give his friend the borrowed barrel of honey as well as c kilograms of raspberry for renting the barrel.The bear wants to execute his plan at most once and then hibernate. What maximum number of kilograms of raspberry can he earn? Note that if at some point of the plan the bear runs out of the raspberry, then he won't execute such a plan.

The first line contains two space-separated integers, n and c (2 ≤ n ≤ 100, 0 ≤ c ≤ 100), — the number of days and the number of kilos of raspberry that the bear should give for borrowing the barrel. The second line contains n space-separated integers x1, x2, ..., xn (0 ≤ xi ≤ 100), the price of a honey barrel on day i.

Print a single integer — the answer to the problem.

NoteIn the first sample the bear will lend a honey barrel at day 3 and then sell it for 7. Then the bear will buy a barrel for 3 and return it to the friend. So, the profit is (7 - 3 - 1) = 3.In the second sample bear will lend a honey barrel at day 1 and then sell it for 100. Then the bear buy the barrel for 1 at the day 2. So, the profit is (100 - 1 - 2) = 97.