Problem:
Score : 200 points

Problem Statement

Takahashi is standing on a two-dimensional plane, facing north. Find the minimum positive integer K such that Takahashi will be at the starting position again after he does the following action K times:

Go one meter in the direction he is facing. Then, turn X degrees counter-clockwise.

Constraints

1 \leq X \leq 179

X is an integer.

Input

Input is given from Standard Input in the following format:

X

Output

Print the number of times Takahashi will do the action before he is at the starting position again.

Sample Input 1

90

Sample Output 1

4

Takahashi's path is a square.

Sample Input 2

1

Sample Output 2

360

Solution in PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import math
def main():
    N = int(input())
    K = 0
    X = 0
    Y = 0
    R = 90

    while True:
        R = (N+R)%360
        K+=1
        X += math.cos(math.radians(R))
        Y += math.sin(math.radians(R))
        if abs(X)<0.01 and abs(Y)<0.01:
            print(K)
            break

if __name__ == '__main__':
    main()