vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
During a game of Minesweeper you have arrived in the situation shown in the image, with an $n\times n$ square surrounded by $1$s, themselves surrounded by unknown cells. Your task is to determine which of the $4n+4$ surrounding $1$-cells is guaranteed to not contain a mine. 

If you are unfamiliar with the rules of Minesweeper, here is a description:
 - Each of the red-labelled cells is either empty or contains a mine. All other cells are empty.
 - Each cell with a blue $1$ is adjacent to exactly one mine. Two cells are said to be adjacent if they share an edge or a corner. Thus, except at the border, every cell is adjacent to $8$ other cells.

Determine which of the red-labelled cells are safe, i.e., guaranteed to not contain a mine.

-----Input-----
An integer $n$ with $1 \leq n \leq 1000$, the side length of the square. The image corresponds to $n = 6$.

It can be shown that there exists at least one valid placement of mines for each $n$.

-----Output-----
First print the number $m$ of safe cells. Then print a line with $m$ integers, the indices of the safe cells in increasing order. The cells are indexed clockwise from $1$ to $4n+4$, starting at the bottom left corner, as shown in the image.

-----Examples-----
Sample Input:
3
Sample Output:
8
1 3 5 7 9 11 13 15

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
One tradition of welcoming the New Year is launching fireworks into the sky. Usually a launched firework flies vertically upward for some period of time, then explodes, splitting into several parts flying in different directions. Sometimes those parts also explode after some period of time, splitting into even more parts, and so on.

Limak, who lives in an infinite grid, has a single firework. The behaviour of the firework is described with a recursion depth n and a duration for each level of recursion t_1, t_2, ..., t_{n}. Once Limak launches the firework in some cell, the firework starts moving upward. After covering t_1 cells (including the starting cell), it explodes and splits into two parts, each moving in the direction changed by 45 degrees (see the pictures below for clarification). So, one part moves in the top-left direction, while the other one moves in the top-right direction. Each part explodes again after covering t_2 cells, splitting into two parts moving in directions again changed by 45 degrees. The process continues till the n-th level of recursion, when all 2^{n} - 1 existing parts explode and disappear without creating new parts. After a few levels of recursion, it's possible that some parts will be at the same place and at the same time — it is allowed and such parts do not crash.

Before launching the firework, Limak must make sure that nobody stands in cells which will be visited at least once by the firework. Can you count the number of those cells?


-----Input-----

The first line of the input contains a single integer n (1 ≤ n ≤ 30) — the total depth of the recursion.

The second line contains n integers t_1, t_2, ..., t_{n} (1 ≤ t_{i} ≤ 5). On the i-th level each of 2^{i} - 1 parts will cover t_{i} cells before exploding.


-----Output-----

Print one integer, denoting the number of cells which will be visited at least once by any part of the firework.


-----Examples-----
Input
4
4 2 2 3

Output
39

Input
6
1 1 1 1 1 3

Output
85

Input
1
3

Output
3



-----Note-----

For the first sample, the drawings below show the situation after each level of recursion. Limak launched the firework from the bottom-most red cell. It covered t_1 = 4 cells (marked red), exploded and divided into two parts (their further movement is marked green). All explosions are marked with an 'X' character. On the last drawing, there are 4 red, 4 green, 8 orange and 23 pink cells. So, the total number of visited cells is 4 + 4 + 8 + 23 = 39.

 [Image] 

For the second sample, the drawings below show the situation after levels 4, 5 and 6. The middle drawing shows directions of all parts that will move in the next level.

 [Image]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Iahub has drawn a set of n points in the cartesian plane which he calls "special points". A quadrilateral is a simple polygon without self-intersections with four sides (also called edges) and four vertices (also called corners). Please note that a quadrilateral doesn't have to be convex. A special quadrilateral is one which has all four vertices in the set of special points. Given the set of special points, please calculate the maximal area of a special quadrilateral. 


-----Input-----

The first line contains integer n (4 ≤ n ≤ 300). Each of the next n lines contains two integers: x_{i}, y_{i} ( - 1000 ≤ x_{i}, y_{i} ≤ 1000) — the cartesian coordinates of ith special point. It is guaranteed that no three points are on the same line. It is guaranteed that no two points coincide. 


-----Output-----

Output a single real number — the maximal area of a special quadrilateral. The answer will be considered correct if its absolute or relative error does't exceed 10^{ - 9}.


-----Examples-----
Input
5
0 0
0 4
4 0
4 4
2 3

Output
16.000000


-----Note-----

In the test example we can choose first 4 points to be the vertices of the quadrilateral. They form a square by side 4, so the area is 4·4 = 16.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In this problem you are given a sequence of $N$ positive integers $S[1],S[2],\dots,S[N]$. In addition you are given an integer $T$, and your aim  is to find the number of quadruples $(i,j,k,l)$, such that $1 \le i < j < k < l \le N$, and $S[i] + S[j] + S[k] + S[l] = T$.  That is, the number of ways of picking four numbers from the sequence summing up to $T$.

-----Constraints:-----
For all test cases,
- $1 \le N \le 5000$
- $1 \le T \le 10^6$
- $1 \le S[i] \le 10^9$, for all $i$.
Subtask $1:10\%$
It is guaranteed that $N \le 50$.
Subtask $2:50\%$
It is guaranteed that $N \le 300$.
Subtask $3:40\%$
No additional guarantees.

-----Input Format:-----
There is only one line of input with $N+2$ space separated integers. The first two integers are $N$ and $T$. The next $N$ integers are $S[1],S[2],\dots,S[N]$.

-----Output Format:-----
A single integer which is the number of valid quadruples.

-----Sample Input 1:-----
6 20 3 1 1 2 5 10

-----Sample Output 1:-----
1

-----Explanation 1:-----
The quadruple $(1,4,5,6)$ is valid  because $S[1]+S[4]+S[5]+S[6]=3+2+5+10=20$. You can check that no other quadruple is valid and hence the answer is $1$.

-----Sample Input 2:-----
6 13 1 2 3 4 5 4 

-----Sample Output 2:-----
3

-----Explanation 2:-----
You can verify that the only quadruples that are valid are $(2,3,4,6),(1,3,4,5)$  and $(1,3,5,6)$. Thus, the answer is $3$.

-----Note:-----
As the answer might be large, please use 64 bit integers (long long int in
C/C++ and long in Java) instead of 32 bit int.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
ZS the Coder and Chris the Baboon arrived at the entrance of Udayland. There is a n × n magic grid on the entrance which is filled with integers. Chris noticed that exactly one of the cells in the grid is empty, and to enter Udayland, they need to fill a positive integer into the empty cell.

Chris tried filling in random numbers but it didn't work. ZS the Coder realizes that they need to fill in a positive integer such that the numbers in the grid form a magic square. This means that he has to fill in a positive integer so that the sum of the numbers in each row of the grid ($\sum a_{r, i}$), each column of the grid ($\sum a_{i, c}$), and the two long diagonals of the grid (the main diagonal — $\sum a_{i, i}$ and the secondary diagonal — $\sum a_{i, n - i + 1}$) are equal. 

Chris doesn't know what number to fill in. Can you help Chris find the correct positive integer to fill in or determine that it is impossible?


-----Input-----

The first line of the input contains a single integer n (1 ≤ n ≤ 500) — the number of rows and columns of the magic grid.

n lines follow, each of them contains n integers. The j-th number in the i-th of them denotes a_{i}, j (1 ≤ a_{i}, j ≤ 10^9 or a_{i}, j = 0), the number in the i-th row and j-th column of the magic grid. If the corresponding cell is empty, a_{i}, j will be equal to 0. Otherwise, a_{i}, j is positive.

It is guaranteed that there is exactly one pair of integers i, j (1 ≤ i, j ≤ n) such that a_{i}, j = 0.


-----Output-----

Output a single integer, the positive integer x (1 ≤ x ≤ 10^18) that should be filled in the empty cell so that the whole grid becomes a magic square. If such positive integer x does not exist, output  - 1 instead.

If there are multiple solutions, you may print any of them.


-----Examples-----
Input
3
4 0 2
3 5 7
8 1 6

Output
9

Input
4
1 1 1 1
1 1 0 1
1 1 1 1
1 1 1 1

Output
1

Input
4
1 1 1 1
1 1 0 1
1 1 2 1
1 1 1 1

Output
-1



-----Note-----

In the first sample case, we can fill in 9 into the empty cell to make the resulting grid a magic square. Indeed, 

The sum of numbers in each row is:

4 + 9 + 2 = 3 + 5 + 7 = 8 + 1 + 6 = 15.

The sum of numbers in each column is:

4 + 3 + 8 = 9 + 5 + 1 = 2 + 7 + 6 = 15.

The sum of numbers in the two diagonals is:

4 + 5 + 6 = 2 + 5 + 8 = 15.

In the third sample case, it is impossible to fill a number in the empty square such that the resulting grid is a magic square.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You have a laser with P amount of energy in it. You are playing a game where you have to use the laser to destroy some crystals, each with some health of their own. Initially, you have 0 points.
Each crystal has an associated health. The health of the ith crystal is given by health[i]. You can perform one of the two actions:
- 
At the cost of health[i] energy, you can destroy the ith crystal and gain 1 point. You can only perform this action if your laser has atleast health[i] energy in it.
- 
At the cost of 1 point, you can destroy the ith crystal and refuel the laser's energy by an amount equal to health[i]. This action can only be performed if you have atleast one point.
Note: Each crystal can only be destroyed once.
Determine the maximum number of points you can obtain by destroying any number of crystals and performing either action as you wish.

-----Input:-----
- First line will contain n, number of crystals. 
- Second line will contain space separated integers, health of each crystal.
- Third line will contain an integer P, initial energy of the laser.

-----Output:-----
Print the largest number of points we can have after destroying any number of crystals.

-----Constraints-----
- health.length <= 1000
- 0 <= health[i] < 10000
- 0 <= P < 10000

-----Subtasks-----
- 40 points : 1 <= health.length <= 100
- 60 points : health.length > 100

-----Sample Input 1:-----
1
200
100

-----Sample Output 1:-----
0

-----Explanation:-----
The laser initially has only 100 energy. Since the only crystal requires 200 energy to destroy, we cannot perform any action here, and the game ends. The number of points is zero.

-----Sample Input 2:-----
2
100 200
150

-----Sample Output 2:-----
1

-----Explanation:-----
The laser has 150 energy. We can consume 100 energy and destroy the first crystal and gain 1 point. The remaining energy is 50, which is not enough to destroy the other crystal. We end the game here as we have the maximum possible points attainable.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A string is called palindrome if it reads the same from left to right and from right to left. For example "kazak", "oo", "r" and "mikhailrubinchikkihcniburliahkim" are palindroms, but strings "abb" and "ij" are not.

You are given string s consisting of lowercase Latin letters. At once you can choose any position in the string and change letter in that position to any other lowercase letter. So after each changing the length of the string doesn't change. At first you can change some letters in s. Then you can permute the order of letters as you want. Permutation doesn't count as changes. 

You should obtain palindrome with the minimal number of changes. If there are several ways to do that you should get the lexicographically (alphabetically) smallest palindrome. So firstly you should minimize the number of changes and then minimize the palindrome lexicographically.


-----Input-----

The only line contains string s (1 ≤ |s| ≤ 2·10^5) consisting of only lowercase Latin letters.


-----Output-----

Print the lexicographically smallest palindrome that can be obtained with the minimal number of changes.


-----Examples-----
Input
aabc

Output
abba

Input
aabcd

Output
abcba

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Write a program which calculates the area and circumference of a circle for given radius r.

Constraints

* 0 < r < 10000

Input

A real number r is given.

Output

Print the area and circumference of the circle in a line. Put a single space between them. The output should not contain an absolute error greater than 10-5.

Examples

Input

2


Output

12.566371 12.566371


Input

3


Output

28.274334 18.849556

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Sereja and his friends went to a picnic. The guys had n soda bottles just for it. Sereja forgot the bottle opener as usual, so the guys had to come up with another way to open bottles.

Sereja knows that the i-th bottle is from brand a_{i}, besides, you can use it to open other bottles of brand b_{i}. You can use one bottle to open multiple other bottles. Sereja can open bottle with opened bottle or closed bottle.

Knowing this, Sereja wants to find out the number of bottles they've got that they won't be able to open in any way. Help him and find this number.


-----Input-----

The first line contains integer n (1 ≤ n ≤ 100) — the number of bottles. The next n lines contain the bottles' description. The i-th line contains two integers a_{i}, b_{i} (1 ≤ a_{i}, b_{i} ≤ 1000) — the description of the i-th bottle.


-----Output-----

In a single line print a single integer — the answer to the problem.


-----Examples-----
Input
4
1 1
2 2
3 3
4 4

Output
4

Input
4
1 2
2 3
3 4
4 1

Output
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
**This Kata is intended as a small challenge for my students**

All Star Code Challenge #18

Create a function called that accepts 2 string arguments and returns an integer of the count of occurrences the 2nd argument is found in the first one.

If no occurrences can be found, a count of 0 should be returned.

Notes:
* The first argument can be an empty string  
* The second string argument will always be of length 1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Pia is a famous bartender at the hip Stockholm night club Supernova. One of her most impressive feats is the mixing a series of drinks using each of the $N$ distinct drink ingredients in the bar exactly once. She does this in the following way.

First, Pia chooses a number of drinks to make. Each of the drink ingredients are then lined up in front of her in order $1, 2, \dots , N$. For the first drink, she uses some positive number $K$ of ingredients starting from the left, i.e. $1, 2, ..., K$. For the next drink, she uses some positive number $L$ of ingredients starting from the first unused ingredient, i.e. $K + 1, K + 2, \dots , K + L$. She continues this process until the final drink, which uses some set of ingredients $N - M, N - M + 1, \dots , N$.

However, not every pair of ingredients work well in a drink. For example, milk and water would not go very well together. She may not include a bad pair of ingredients in any drink.

So far, she has managed to make a different set of drinks every night. For how many nights can she mix a new set of drinks? We call two sets of drinks different if they do not consist of the exact same drinks (though they are allowed to have drinks in common).

-----Input-----
The first line of the input contains two integers $1 \le N \le 100000$ and $0 \le P \le 100000$, the number of ingredients and bad pairs of ingredients.

Each of the next $P$ lines contains two integers $1 \le a \not= b \le N$, two ingredients that do not work well together in a drink. The same pair of ingredients may appear multiple times in this list.

-----Output-----
Output a single integer, the number of nights Pia can construct a different set of drinks. Since this number may be large, output the remainder when divided by $10^9 + 7$.

-----Examples-----
Sample Input:
5 3
1 3
4 5
2 4
Sample Output:
5

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
$n$ boys and $m$ girls came to the party. Each boy presented each girl some integer number of sweets (possibly zero). All boys are numbered with integers from $1$ to $n$ and all girls are numbered with integers from $1$ to $m$. For all $1 \leq i \leq n$ the minimal number of sweets, which $i$-th boy presented to some girl is equal to $b_i$ and for all $1 \leq j \leq m$ the maximal number of sweets, which $j$-th girl received from some boy is equal to $g_j$.

More formally, let $a_{i,j}$ be the number of sweets which the $i$-th boy give to the $j$-th girl. Then $b_i$ is equal exactly to the minimum among values $a_{i,1}, a_{i,2}, \ldots, a_{i,m}$ and $g_j$ is equal exactly to the maximum among values $b_{1,j}, b_{2,j}, \ldots, b_{n,j}$.

You are interested in the minimum total number of sweets that boys could present, so you need to minimize the sum of $a_{i,j}$ for all $(i,j)$ such that $1 \leq i \leq n$ and $1 \leq j \leq m$. You are given the numbers $b_1, \ldots, b_n$ and $g_1, \ldots, g_m$, determine this number. 


-----Input-----

The first line contains two integers $n$ and $m$, separated with space — the number of boys and girls, respectively ($2 \leq n, m \leq 100\,000$). The second line contains $n$ integers $b_1, \ldots, b_n$, separated by spaces — $b_i$ is equal to the minimal number of sweets, which $i$-th boy presented to some girl ($0 \leq b_i \leq 10^8$). The third line contains $m$ integers $g_1, \ldots, g_m$, separated by spaces — $g_j$ is equal to the maximal number of sweets, which $j$-th girl received from some boy ($0 \leq g_j \leq 10^8$).


-----Output-----

If the described situation is impossible, print $-1$. In another case, print the minimal total number of sweets, which boys could have presented and all conditions could have satisfied.


-----Examples-----
Input
3 2
1 2 1
3 4

Output
12
Input
2 2
0 1
1 0

Output
-1
Input
2 3
1 0
1 1 2

Output
4


-----Note-----

In the first test, the minimal total number of sweets, which boys could have presented is equal to $12$. This can be possible, for example, if the first boy presented $1$ and $4$ sweets, the second boy presented $3$ and $2$ sweets and the third boy presented $1$ and $1$ sweets for the first and the second girl, respectively. It's easy to see, that all conditions are satisfied and the total number of sweets is equal to $12$.

In the second test, the boys couldn't have presented sweets in such way, that all statements satisfied.

In the third test, the minimal total number of sweets, which boys could have presented is equal to $4$. This can be possible, for example, if the first boy presented $1$, $1$, $2$ sweets for the first, second, third girl, respectively and the second boy didn't present sweets for each girl. It's easy to see, that all conditions are satisfied and the total number of sweets is equal to $4$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A multi-subject competition is coming! The competition has $m$ different subjects participants can choose from. That's why Alex (the coach) should form a competition delegation among his students. 

He has $n$ candidates. For the $i$-th person he knows subject $s_i$ the candidate specializes in and $r_i$ — a skill level in his specialization (this level can be negative!). 

The rules of the competition require each delegation to choose some subset of subjects they will participate in. The only restriction is that the number of students from the team participating in each of the chosen subjects should be the same.

Alex decided that each candidate would participate only in the subject he specializes in. Now Alex wonders whom he has to choose to maximize the total sum of skill levels of all delegates, or just skip the competition this year if every valid non-empty delegation has negative sum.

(Of course, Alex doesn't have any spare money so each delegate he chooses must participate in the competition).


-----Input-----

The first line contains two integers $n$ and $m$ ($1 \le n \le 10^5$, $1 \le m \le 10^5$) — the number of candidates and the number of subjects.

The next $n$ lines contains two integers per line: $s_i$ and $r_i$ ($1 \le s_i \le m$, $-10^4 \le r_i \le 10^4$) — the subject of specialization and the skill level of the $i$-th candidate.


-----Output-----

Print the single integer — the maximum total sum of skills of delegates who form a valid delegation (according to rules above) or $0$ if every valid non-empty delegation has negative sum.


-----Examples-----
Input
6 3
2 6
3 6
2 5
3 5
1 9
3 1

Output
22

Input
5 3
2 6
3 6
2 5
3 5
1 11

Output
23

Input
5 2
1 -1
1 -5
2 -1
2 -1
1 -10

Output
0



-----Note-----

In the first example it's optimal to choose candidates $1$, $2$, $3$, $4$, so two of them specialize in the $2$-nd subject and other two in the $3$-rd. The total sum is $6 + 6 + 5 + 5 = 22$.

In the second example it's optimal to choose candidates $1$, $2$ and $5$. One person in each subject and the total sum is $6 + 6 + 11 = 23$.

In the third example it's impossible to obtain a non-negative sum.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
I have the `par` value for each hole on a golf course and my stroke `score` on each hole. I have them stored as strings, because I wrote them down on a sheet of paper.  Right now, I'm using those strings to calculate my golf score by hand: take the difference between my actual `score` and the `par` of the hole, and add up the results for all 18 holes.

For example:
* If I took 7 shots on a hole where the par was 5, my score would be: 7 - 5 = 2
* If I got a hole-in-one where the par was 4, my score would be: 1 - 4 = -3.

Doing all this math by hand is really hard! Can you help make my life easier?


## Task Overview

Complete the function which accepts two strings and calculates the golf score of a game. Both strings will be of length 18, and each character in the string will be a number between 1 and 9 inclusive.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
After Derek (of district 5) discovered how to compute the greatest common divisor (gcd) of Fibonacci numbers, he now tried to answer the next obvious question: how does one compute the least common multiple (lcm) of Fibonacci numbers? Unfortunately, Derek found out that this wasn't as easy as the original problem, so he asked you to answer it for him.

The Fibonacci numbers are defined as:

$F_1=F_2=1$
$F_n=F_{n-1}+F_{n-2}$

Given $N$ integers $a_1,a_2,\ldots,a_N$, find $\text{lcm}(F_{a_1},F_{a_2},\ldots,F_{a_N})$, and give your answer modulo $10^9+7$.

Input Format 

The first line of input contains $N$. 

Each of the next $N$ lines contains a number: the $i^{th}$ line contains $a_i$.

Constraints 

$1\leq N\leq100$ 

$1\leq a_i\leq10^9$  

Output Format 

Print a single integer, which is the least common multiple of the ${F}_{a_i}$, modulo $10^9+7$.

Sample Input  

5
1
3
3
6
9

Sample Output  

136

Explanation 

$\text{lcm}(F_1,F_3,F_3,F_6,F_9)=\text{lcm}(1,2,2,8,34)=136$

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.