Buggy python submission (verdict: Runtime Error):
import math
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = [[0 for _ in range(k+1)] for _ in range(k+1)]
    for i ian range(1, k+1):
        for j in range(i, k+1):
            tmp = math.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()


Fixed submission:
import numpy as np
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for i in range(1, k+1):
        for j in range(i, k+1):
            tmp = np.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import math
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = [[0 for _ in range(k)] for _ in range(k)]
    for i ian range(1, k+1):
        for j in range(i, k+1):
            tmp = math.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()

Fixed submission:
import numpy as np
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for i in range(1, k+1):
        for j in range(i, k+1):
            tmp = np.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
from math import gcd
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = [[0 for _ in range(k)] for _ in range(k)]
    for i in range(1, k+1):
        for j in range(i, k+1):
            tmp = gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()



Fixed submission:
import numpy as np
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for i in range(1, k+1):
        for j in range(i, k+1):
            tmp = np.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
from itertools import combinations

def gcd_memo(memo, a, b):
    if memo[a][b] > 0:
        return memo[a][b]
    res = np.gcd(a, b)
    memo[a][b] = res
    memo[b][a] = res
    return res

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for i in range(1, k+1):
        memo[i][i] = i 
        res += i

    for c in combinations(range(1,k+1),2):
        ab = gcd_memo(memo, c[0], c[1])
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = gcd_memo(memo, c[0], c[1])
        abc = gcd_memo(memo, ab, c[2])
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()



Fixed submission:
import numpy as np
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for i in range(1, k+1):
        for j in range(i, k+1):
            tmp = np.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
from itertools import combinations_with_replacement

def gcd_memo(memo, a, b):
    if memo[a][b] > 0:
        return memo[a][b]
    res = np.gcd(a, b)
    memo[a][b] = res
    memo[b][a] = res
    return res

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for c in combinations_with_replacement(range(1,k+1), 3):
        ab = gcd_memo(memo, c[0], c[1])
        abc = gcd_memo(memo, ab, c[2])
        l = len(set(c))
        mul = 1
        if l == 2:
            mul = 3
        elif l == 3:
            mul = 6
        res += abc * mul
    print(res)


if __name__ == '__main__':
    main()



Fixed submission:
import numpy as np
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for i in range(1, k+1):
        for j in range(i, k+1):
            tmp = np.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
def main():
    n = int(input())
    s = input()
    res = 0
    r = []
    g = []
    b = []
    for i, c in enumerate(s):
        if c == 'R':
            r.append(i)
        elif c == 'G':
            g.append(i)
        else:
            b.append(i)
    
    cnt = 0
    for i in r:
        for j in g:
            diff = abs(j-i)
            for k in b:
                if abs(i-k) != diff and abs(j-k) != diff and abs(j-k) != abs(i-k):
                    cnt += 1
    print(cnt)
                    


if __name__ == '__main__':
    main()



Fixed submission:
import numpy as np
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for i in range(1, k+1):
        for j in range(i, k+1):
            tmp = np.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
from itertools import combinations_with_replacement

def main():
    k = int(input())
    res = 0
    for c in combinations_with_replacement(range(1,k+1), 3):
        tmp = np.gcd.reduce(c)
        l = len(set(c))
        mul = 1
        if l == 2:
            mul = 3
        elif l == 3:
            mul = 6
        res += tmp * mul
    print(res)


if __name__ == '__main__':
    main()



Fixed submission:
import numpy as np
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for i in range(1, k+1):
        for j in range(i, k+1):
            tmp = np.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)

def gcd_list(numbers):
    return reduce(math.gcd, numbers)

def main():
    n = int(input())
    res = 0
    for i in range(n):
        for j in range(n):
            for k in range(n):
                res += gcd(i+1, j+1, k+1)
    print(res)


if __name__ == '__main__':
    main()



Fixed submission:
import numpy as np
from itertools import combinations

def main():
    k = int(input())
    res = 0
    memo = np.zeros((k+1, k+1), int)
    for i in range(1, k+1):
        for j in range(i, k+1):
            tmp = np.gcd(i,j)
            memo[i][j] = tmp
            memo[j][i] = tmp

    for i in range(1, k+1):
        res += i 

    for c in combinations(range(1,k+1),2):
        ab = memo[c[0], c[1]]
        res += ab * 6

    for c in combinations(range(1,k+1), 3):
        ab = memo[c[0], c[1]]
        abc = memo[ab, c[2]]
        res += abc * 6
    print(res)


if __name__ == '__main__':
    main()