Buggy python submission (verdict: Time Limit Exceeded):
from fractions import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Runtime Error):
from fraction import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Runtime Error):
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Runtime Error):
import gcd from math
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Runtime Error):
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush,heapify
from fractions import gcd
from copy import deepcopy
import math
import queue
#import sympy as syp(素因数分解とか)
Mod = 1000000007
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)

def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush,heapify
from fractions import gcd
from copy import deepcopy
import math
import queue
#import sympy as syp(素因数分解とか)
Mod = 1000000007
import sys
sys.setrecursionlimit(100000) 
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)

def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush,heapify
from fractions import gcd
from copy import deepcopy
import math
import queue
#import sympy as syp(素因数分解とか)
Mod = 1000000007
import sys
sys.setrecursionlimit(100000) 
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)

def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush,heapify
from fractions import gcd
from copy import deepcopy
import math
import queue
#import sympy as syp(素因数分解とか)
Mod = 1000000007
import sys
sys.setrecursionlimit(100000) 
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)

def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush,heapify
from fractions import gcd
from copy import deepcopy
import math
import queue
#import sympy as syp(素因数分解とか)
Mod = 1000000007
import sys
sys.setrecursionlimit(100000) 
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)

def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(i,k+1):
            for l in range(j,k+1):
                plist = list(set((i,j,l)))
                if len(plist) == 1:
                    ans += plist[0]
                elif len(plist) == 2:
                    ans += gcd(plist[0],plist[1])*3
                else:
                    ans += gcd(gcd(plist[0],plist[1]),plist[2])*6
    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush,heapify
from fractions import gcd
from copy import deepcopy
import math
import queue
#import sympy as syp(素因数分解とか)
Mod = 1000000007
import sys
sys.setrecursionlimit(100000) 
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)

def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(i,k+1):
            for l in range(j,k+1):
                ans += gcd(gcd(i,j),l)*6//math.factorial(4-len(set([i,j,l])))
    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush,heapify
from fractions import gcd
from copy import deepcopy
import math
import queue
#import sympy as syp(素因数分解とか)
Mod = 1000000007
import sys
sys.setrecursionlimit(100000) 
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)

def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    l = [i for i in range(1,k+1)]
    p_list = list(itertools.combinations_with_replacement(l,3))
    for i in p_list:
        ans += gcd(gcd(i[0],i[1]),i[2])*(6//math.factorial((4-len(set(i)))))
    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Runtime Error):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush,heapify
from fractions import gcd
from copy import deepcopy
import math
import queue
import numpy as np
#import sympy as syp(素因数分解とか)
Mod = 1000000007
import sys
sys.setrecursionlimit(100000) 
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)

def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    l = [i for i in range(1,k+1)]
    p_list = list(itertools.combinations_with_replacement(l,3))
    for i in p_list:
        ans += gcd(gcd(i[0],i[1]),i[2])*(6//math.factorial((4-len(set(i)))))
    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush,heapify
from fractions import gcd
from copy import deepcopy
import math
import queue
import numpy as np
#import sympy as syp(素因数分解とか)
Mod = 1000000007
import sys
sys.setrecursionlimit(100000) 
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)

def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    l = [i for i in range(1,k+1)]
    p_list = list(itertools.combinations_with_replacement(l,3))
    for i in p_list:
        ans += gcd(gcd(i[0],i[1]),i[2])*(6//math.factorial((4-len(set(i)))))
    print(ans)
if __name__ == "__main__":
    main() #endline===============================================

Fixed submission:
from math import gcd
def main(): #startline-------------------------------------------
    k = int(input())
    ans = 0
    for i in range(1,k+1):
        for j in range(1,k+1):
            for l in range(1,k+1):
                ans += gcd(gcd(i,j),l)

    print(ans)
if __name__ == "__main__":
    main() #endline===============================================