apaz/codeforces-genesys huggingface dataset:
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Haiku is a genre of Japanese traditional poetry.

A haiku poem consists of 17 syllables split into three phrases, containing 5, 7 and 5 syllables correspondingly (the first phrase should contain exactly 5 syllables, the second phrase should contain exactly 7 syllables, and the third phrase should contain exactly 5 syllables). A haiku masterpiece contains a description of a moment in those three phrases. Every word is important in a small poem, which is why haiku are rich with symbols. Each word has a special meaning, a special role. The main principle of haiku is to say much using a few words.

To simplify the matter, in the given problem we will consider that the number of syllable in the phrase is equal to the number of vowel letters there. Only the following letters are regarded as vowel letters: "a", "e", "i", "o" and "u".

Three phases from a certain poem are given. Determine whether it is haiku or not.

## Input Format
The input data consists of three lines. The length of each line is between 1 and 100, inclusive. The i-th line contains the i-th phrase of the poem. Each phrase consists of one or more words, which are separated by one or more spaces. A word is a non-empty sequence of lowercase Latin letters. Leading and/or trailing spaces in phrases are allowed. Every phrase has at least one non-space character. See the example for clarification.

## Output Format
Print "YES" (without the quotes) if the poem is a haiku. Otherwise, print "NO" (also without the quotes).

## Examples
```input
on  codeforces
beta round is running
a rustling of keys
```
```output
YES
```
-----
```input
how many gallons
of edo s rain did you drink
cuckoo
```
```output
NO
```

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
The Easter Rabbit laid n eggs in a circle and is about to paint them.

Each egg should be painted one color out of 7: red, orange, yellow, green, blue, indigo or violet. Also, the following conditions should be satisfied:

- Each of the seven colors should be used to paint at least one egg.
- Any four eggs lying sequentially should be painted different colors.

Help the Easter Rabbit paint the eggs in the required manner. We know that it is always possible.

## Input Format
The only line contains an integer n — the amount of eggs (7 ≤ n ≤ 100).

## Output Format
Print one line consisting of n characters. The i-th character should describe the color of the i-th egg in the order they lie in the circle. The colors should be represented as follows: "R" stands for red, "O" stands for orange, "Y" stands for yellow, "G" stands for green, "B" stands for blue, "I" stands for indigo, "V" stands for violet.

If there are several answers, print any of them.

## Examples
```input
8
```
```output
ROYGRBIV
```
-----
```input
13
```
```output
ROYGBIVGBIVYG
```

## Note
The way the eggs will be painted in the first sample is shown on the picture:

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Two beavers, Timur and Marsel, play the following game.

There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.

Timur makes the first move. The players play in the optimal way. Determine the winner.

## Input Format
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).

## Output Format
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.

## Examples
```input
1 15 4
```
```output
Timur
```
-----
```input
4 9 5
```
```output
Marsel
```

## Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.

In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
A monster is chasing after Rick and Morty on another planet. They're so frightened that sometimes they scream. More accurately, Rick screams at times b, b + a, b + 2a, b + 3a, ... and Morty screams at times d, d + c, d + 2c, d + 3c, ....

The Monster will catch them if at any point they scream at the same time, so it wants to know when it will catch them (the first time they scream at the same time) or that they will never scream at the same time.

## Input Format
The first line of input contains two integers a and b (1 ≤ a, b ≤ 100).

The second line contains two integers c and d (1 ≤ c, d ≤ 100).

## Output Format
Print the first time Rick and Morty will scream at the same time, or  - 1 if they will never scream at the same time.

## Examples
```input
20 2
9 19
```
```output
82
```
-----
```input
2 1
16 12
```
```output
-1
```

## Note
In the first sample testcase, Rick's 5th scream and Morty's 8th time are at time 82.

In the second sample testcase, all Rick's screams will be at odd times and Morty's will be at even times, so they will never scream at the same time.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Since the giant heads have appeared in the sky all humanity is in danger, so all Ricks and Mortys from all parallel universes are gathering in groups to find a solution to get rid of them.

There are n parallel universes participating in this event (n Ricks and n Mortys). I. e. each of n universes has one Rick and one Morty. They're gathering in m groups. Each person can be in many groups and a group can contain an arbitrary number of members.

Ricks and Mortys have registered online in these groups. So, a person can have joined a group more than once (developer of this website hadn't considered this possibility).

Summer from universe #1 knows that in each parallel universe (including hers) exactly one of Rick and Morty from that universe is a traitor and is loyal, but no one knows which one. She knows that we are doomed if there's a group such that every member in that group is a traitor (they will plan and destroy the world).

Summer knows that if there's a possibility that world ends (there's a group where all members are traitors) she should immediately cancel this event. So she wants to know if she should cancel the event. You have to tell her yes if and only if there's at least one scenario (among all 2n possible scenarios, 2 possible scenarios for who a traitor in each universe) such that in that scenario the world will end.

## Input Format
The first line of input contains two integers n and m (1 ≤ n, m ≤ 104) — number of universes and number of groups respectively.

The next m lines contain the information about the groups. i-th of them first contains an integer k (number of times someone joined i-th group, k > 0) followed by k integers vi, 1, vi, 2, ..., vi, k. If vi, j is negative, it means that Rick from universe number  - vi, j has joined this group and otherwise it means that Morty from universe number vi, j has joined it.

Sum of k for all groups does not exceed 104.

## Output Format
In a single line print the answer to Summer's question. Print "YES" if she should cancel the event and "NO" otherwise.

## Examples
```input
4 2
1 -3
4 -2 3 2 -3
```
```output
YES
```
-----
```input
5 2
5 3 -2 1 -1 5
3 -5 2 5
```
```output
NO
```
-----
```input
7 2
3 -1 6 7
7 -5 4 2 4 7 -3 4
```
```output
YES
```

## Note
In the first sample testcase, 1st group only contains the Rick from universe number 3, so in case he's a traitor, then all members of this group are traitors and so Summer should cancel the event.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Bear Limak wants to become the largest of bears, or at least to become larger than his brother Bob.

Right now, Limak and Bob weigh a and b respectively. It's guaranteed that Limak's weight is smaller than or equal to his brother's weight.

Limak eats a lot and his weight is tripled after every year, while Bob's weight is doubled after every year.

After how many full years will Limak become strictly larger (strictly heavier) than Bob?

## Input Format
The only line of the input contains two integers a and b (1 ≤ a ≤ b ≤ 10) — the weight of Limak and the weight of Bob respectively.

## Output Format
Print one integer, denoting the integer number of years after which Limak will become strictly larger than Bob.

## Examples
```input
4 7
```
```output
2
```
-----
```input
4 9
```
```output
3
```
-----
```input
1 1
```
```output
1
```

## Note
In the first sample, Limak weighs 4 and Bob weighs 7 initially. After one year their weights are 4·3 = 12 and 7·2 = 14 respectively (one weight is tripled while the other one is doubled). Limak isn't larger than Bob yet. After the second year weights are 36 and 28, so the first weight is greater than the second one. Limak became larger than Bob after two years so you should print 2.

In the second sample, Limak's and Bob's weights in next years are: 12 and 18, then 36 and 36, and finally 108 and 72 (after three years). The answer is 3. Remember that Limak wants to be larger than Bob and he won't be satisfied with equal weights.

In the third sample, Limak becomes larger than Bob after the first year. Their weights will be 3 and 2 then.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Seyyed and MoJaK are friends of Sajjad. Sajjad likes a permutation. Seyyed wants to change the permutation in a way that Sajjad won't like it. Seyyed thinks more swaps yield more probability to do that, so he makes MoJaK to perform a swap between every pair of positions (i, j), where i < j, exactly once. MoJaK doesn't like to upset Sajjad.

Given the permutation, determine whether it is possible to swap all pairs of positions so that the permutation stays the same. If it is possible find how to do that.

## Input Format
The first line contains single integer n (1 ≤ n ≤ 1000) — the size of the permutation.

As the permutation is not important, you can consider ai = i, where the permutation is a1, a2, ..., an.

## Output Format
If it is not possible to swap all pairs of positions so that the permutation stays the same, print "NO",

Otherwise print "YES", then print $$\frac{n(n-1)}{2}$$ lines: the i-th of these lines should contain two integers a and b (a < b) — the positions where the i-th swap is performed.

## Examples
```input
3
```
```output
NO
```
-----
```input
1
```
```output
YES
```

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Two boys decided to compete in text typing on the site "Key races". During the competition, they have to type a text consisting of s characters. The first participant types one character in v1 milliseconds and has ping t1 milliseconds. The second participant types one character in v2 milliseconds and has ping t2 milliseconds.

If connection ping (delay) is t milliseconds, the competition passes for a participant as follows:

1. Exactly after t milliseconds after the start of the competition the participant receives the text to be entered.
2. Right after that he starts to type it.
3. Exactly t milliseconds after he ends typing all the text, the site receives information about it.

The winner is the participant whose information on the success comes earlier. If the information comes from both participants at the same time, it is considered that there is a draw.

Given the length of the text and the information about participants, determine the result of the game.

## Input Format
The first line contains five integers s, v1, v2, t1, t2 (1 ≤ s, v1, v2, t1, t2 ≤ 1000) — the number of characters in the text, the time of typing one character for the first participant, the time of typing one character for the the second participant, the ping of the first participant and the ping of the second participant.

## Output Format
If the first participant wins, print "First". If the second participant wins, print "Second". In case of a draw print "Friendship".

## Examples
```input
5 1 2 1 2
```
```output
First
```
-----
```input
3 3 1 1 1
```
```output
Second
```
-----
```input
4 5 3 1 5
```
```output
Friendship
```

## Note
In the first example, information on the success of the first participant comes in 7 milliseconds, of the second participant — in 14 milliseconds. So, the first wins.

In the second example, information on the success of the first participant comes in 11 milliseconds, of the second participant — in 5 milliseconds. So, the second wins.

In the third example, information on the success of the first participant comes in 22 milliseconds, of the second participant — in 22 milliseconds. So, it is be a draw.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Some natural number was written on the board. Its sum of digits was not less than k. But you were distracted a bit, and someone changed this number to n, replacing some digits with others. It's known that the length of the number didn't change.

You have to find the minimum number of digits in which these two numbers can differ.

## Input Format
The first line contains integer k (1 ≤ k ≤ 109).

The second line contains integer n (1 ≤ n < 10100000).

There are no leading zeros in n. It's guaranteed that this situation is possible.

## Output Format
Print the minimum number of digits in which the initial number and n can differ.

## Examples
```input
3
11
```
```output
1
```
-----
```input
3
99
```
```output
0
```

## Note
In the first example, the initial number could be 12.

In the second example the sum of the digits of n is not less than k. The initial number could be equal to n.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
One day Kefa found n baloons. For convenience, we denote color of i-th baloon as si — lowercase letter of the Latin alphabet. Also Kefa has k friends. Friend will be upset, If he get two baloons of the same color. Kefa want to give out all baloons to his friends. Help Kefa to find out, can he give out all his baloons, such that no one of his friens will be upset — print «YES», if he can, and «NO», otherwise. Note, that Kefa's friend will not upset, if he doesn't get baloons at all.

## Input Format
The first line contains two integers n and k (1 ≤ n, k ≤ 100) — the number of baloons and friends.

Next line contains string s — colors of baloons.

## Output Format
Answer to the task — «YES» or «NO» in a single line.

You can choose the case (lower or upper) for each letter arbitrary.

## Examples
```input
4 2
aabb
```
```output
YES
```
-----
```input
6 3
aacaab
```
```output
NO
```

## Note
In the first sample Kefa can give 1-st and 3-rd baloon to the first friend, and 2-nd and 4-th to the second.

In the second sample Kefa needs to give to all his friends baloons of color a, but one baloon will stay, thats why answer is «NO».

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Leha somehow found an array consisting of n integers. Looking at it, he came up with a task. Two players play the game on the array. Players move one by one. The first player can choose for his move a subsegment of non-zero length with an odd sum of numbers and remove it from the array, after that the remaining parts are glued together into one array and the game continues. The second player can choose a subsegment of non-zero length with an even sum and remove it. Loses the one who can not make a move. Who will win if both play optimally?

## Input Format
First line of input data contains single integer n (1 ≤ n ≤ 106) — length of the array.

Next line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).

## Output Format
Output answer in single line. "First", if first player wins, and "Second" otherwise (without quotes).

## Examples
```input
4
1 3 2 3
```
```output
First
```
-----
```input
2
2 2
```
```output
Second
```

## Note
In first sample first player remove whole array in one move and win.

In second sample first player can't make a move and lose.

Now solve the problem and return the code.