Harryxun/GPT-100-sft-dataset huggingface dataset:
Problem p02574 (python)

Fixed submission:
from math import gcd
n = int(input())
A = list(map(int, input().split()))
min_A = min(A)
max_A = max(A)

def is_pairwise():
    arr = [0] * (max_A + 1)
    for a in A:
        arr[a] += 1
    max_counter = 0
    for num in range(2, max_A + 1):
        counter = 0
        for i in range(1, 10**6 + 1):
            try:
                counter += arr[num * i]
            except:
                break
        max_counter = max(max_counter, counter)
    if max_counter == 1:
        return True
    else:
        return False

if min_A == 1 and max_A == 1:
    print("pairwise coprime")
elif min_A == 1 and max_A != 1:
    A = [num for num in A if num != 1]
    if is_pairwise():
        print("pairwise coprime")
    else:
        print("setwise coprime")
else:
    if is_pairwise():
        print("pairwise coprime")
    else:
        g = A[0]
        for a in A:
            g = gcd(a, g)
        if g == 1:
            print("setwise coprime")
        else:
            print("not coprime")

Buggy submission (verdict: Runtime Error):
n = int(input())
A = list(map(int, input().split()))
max_A = max(A)
import math
from collections import Counter
def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)
    for serial in range(3, num, 2):
        if serial >= sqrt:
            return input_list
        for s in range(serial ** 2, num, serial):
            input_list[s] = False
if max_A >= 8:
    input_list = sieve_of_erastosthenes(max_A + 1)
    prime_list = [i for i, b in enumerate(input_list) if b == True]
else:
    input_list = [2, 3, 5, 7]
    prime_list = [num for num in input_list if num <= max_A]
#print(prime_list)


cnt = Counter()
set_primes = set(prime_list)
for a in A:
    soinsu = []
    for prime in prime_list:
        if prime ** 2 > a:
            break
        if a % prime == 0:
            soinsu.append(prime)
            if a // prime in set_primes:
                soinsu.append(a // prime)
    if a in set_primes:
        soinsu.append(a)

    for num in list(set(soinsu)):
        cnt[num] += 1
#print(cnt)

max_cnt = max(cnt.values())
if max_cnt == 1:
    print("pairwise coprime")
elif max_cnt == n:
    print("not coprime")
else:
    print("setwise coprime")
Problem p02616 (python)

Fixed submission:
import copy
from sys import exit
n, k = map(int, input().split())
A = list(map(int, input().split()))

mod = 10**9 + 7

plus = []
minus = []
for a in A:
    if a >= 0:
        plus.append(a)
    else:
        minus.append(a)
plus.sort()
minus.sort(reverse=True)

def is_ans_plus():
    if len(plus) > 0:
        if n == k:
            if len(minus) % 2 == 0:
                return True
            else:
                return  False
        else:
            return True
    else:
        if k % 2 == 0:
            return True
        else:
            return False

ans = 1
if is_ans_plus():
    if k % 2 == 1:
        ans *= plus.pop()
        k -= 1
    for i in range(k // 2):
        plus_pair, minus_pair = -1, -1
        if len(plus) >= 2:
            plus_pair = plus[-1] * plus[-2]
        if len(minus) >= 2:
            minus_pair = minus[-1] * minus[-2]
        if plus_pair >= minus_pair:
            ans *= plus_pair
            plus.pop()
            plus.pop()
        else:
            ans *= minus_pair
            minus.pop()
            minus.pop()
        ans %= mod
else:
    ans = -1
    A = sorted([abs(a) for a in A])
    for i in range(k):
        ans *= A[i]
        ans %= mod
print(ans)

Buggy submission (verdict: Runtime Error):
import copy
from sys import exit
n, k = map(int, input().split())
A = list(map(int, input().split()))

mod = 10**9 + 7

plus = []
minus = []
for a in A:
    if a >= 0:
        plus.append(a)
    else:
        minus.append(a)
plus.sort()
minus.sort(reverse=True)

def is_ans_plus():
    if len(plus) > 0:
        if n == k:
            if len(minus) % 2 == 0:
                return True
            else:
                return  False
        else:
            return True
    else:
        if k % 2 == 0:
            return True
        else:
            return False

ans = 1
if is_ans_plus():
    if k % 2 == 1:
        ans *= plus.pop()
        k -= 1
    for i in range(k // 2):
        plus_pair, minus_pair = -1, -1
        if len(plus) >= 2:
            plus_pair = plus[-1] * plus[-2]
        if len(minus) >= 2:
            minus_pair = minus[-1] * minus[-2]
        if plus_pair >= minus_pair:
            ans *= plus_pair
            plus.pop()
            plus.pop()
        else:
            ans *= minus_pair
            minus.pop()
            minus.pop()
        ans %= mod
else:
    ans = 1
    for i in range(k):
        ans *= minus[i]
        ans %= mod
print(ans)
Problem p02621 (python)

Fixed submission:
a = int(input())
print(a + a**2 + a**3)

Buggy submission (verdict: Runtime Error):
import copy
from sys import exit
from math import ceil
from collections import defaultdict as dd
n = int(input())
yakusuu_dic = dd(lambda: dd(int))
f = [0] * (n+1)
f[1] = 1
f[2] = 2

if n == 1:
    print(1)
    exit()
if n == 2:
    print(5)
    exit()
sosus = [2]

counter = 0
yakusuu_dic[2] = {2: 1}
for num in range(3, n+1):
    #print(num)
    for divider in sosus:
        if num % divider == 0:
            yakusuu_dic[num] = copy.deepcopy(yakusuu_dic[num // divider])
            yakusuu_dic[num][divider] += 1
            if divider in yakusuu_dic[num // divider]:
                f[num] = f[num // divider] // (yakusuu_dic[num // divider][divider] + 1) * (yakusuu_dic[num // divider][divider] + 2)
            else:
                f[num] = f[num // divider] * 2
            break
    else:
        yakusuu_dic[num][num] = 1
        f[num] = 2
        sosus.append(num)

counter = 0
for i in range(1, n+1):
    counter += i * f[i]
print(counter)
Problem p02843 (python)

Fixed submission:
x = int(input())
dp = [False] * (x+1)
dp[0] = 1
for i in range(0, x+1):
    if dp[i]:
        try:
            dp[i + 100] = True
            dp[i + 101] = True
            dp[i + 102] = True
            dp[i + 103] = True
            dp[i + 104] = True
            dp[i + 105] = True
        except:
            pass

if dp[x]:
    print(1)
else:
    print(0)

Buggy submission (verdict: Runtime Error):
x = int(input())
dp = [False] * (x+1)
dp[0] = 1
for i in range(0, x+1):
    if dp[i]:
        try:
            dp[i + 100] = True
            dp[i + 101] = True
            dp[i + 102] = True
            dp[i + 103] = True
            dp[i + 104] = True
            dp[i + 105] = True
        except IndexError:
            pass

if dp[x]:
    print(1)
else:
    print(0)x = int(input())
dp = [False] * (x+1)
dp[0] = 1
for i in range(0, x+1):
    if dp[i]:
        try:
            dp[i + 100] = True
            dp[i + 101] = True
            dp[i + 102] = True
            dp[i + 103] = True
            dp[i + 104] = True
            dp[i + 105] = True
        except IndexError:
            pass

if dp[x]:
    print(1)
else:
    print(0)
Problem p02844 (python)

Fixed submission:
n = int(input())
s = list(input())

def search(s, c, left):
  for idx in range(left, len(s)):
    if s[idx] == c:
      return idx
  return -1

total = 0
for keta1 in range(10):
  first_keta1 = search(s, str(keta1), 0)
  if first_keta1 == -1 or first_keta1 >= n-2:
    continue
  for keta2 in range(10):
    first_keta2 = search(s, str(keta2), first_keta1 + 1)
    if first_keta2 == -1 or first_keta2 >= n-1:
      continue
    for keta3 in range(10):
      first_keta3 = search(s, str(keta3), first_keta2 + 1)
      if first_keta3 != -1:
        total += 1
print(total)

Buggy submission (verdict: Runtime Error):
from collections import Counter as cnt
n = int(input())
s = list(input())

count = cnt(s)
num_rest = []
for i in range(n):
  count[s[i]] -= 1
  rest = 0
  for value in count.values():
    if value != 0:
      rest += 1
  num_rest.append(rest)
#print(num_rest)

checked = {}
total = 0
for i in range(n-2):
  if s[i] not in checked:
    checked(s[i]) = {}
  elif len(checked[s[i]].keys()) == 10:
    continue
  else:
    for j in range(i+1, n-1):
      if s[j] not in checked[s[i]]:
        checked[s[i]][s[j]] == True
        total += num_rest[j]
print(total)
Problem p03006 (python)

Fixed submission:
from collections import defaultdict as dd
from itertools import combinations
from sys import exit
n = int(input())
if n == 1:
    print(1)
    exit()

Points = []
for i in range(n):
    Points.append(list(map(int, input().split())))

Vector = dd(lambda: 0)
for point1, point2 in combinations(Points, 2):
    if point1[0] > point2[0]:
        x_v = point1[0] - point2[0]
        y_v = point1[1] - point2[1]
    elif point1[0] == point2[0] and point1[1] >= point2[1]:
        x_v = point1[0] - point2[0]
        y_v = point1[1] - point2[1]
    else:
        x_v = point2[0] - point1[0]
        y_v = point2[1] - point1[1]
    Vector[(x_v, y_v)] += 1
#print(Vector)

print(max(n - max(Vector.values()), 1))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict as dd
from itertools import combinations
from sys import exit
n = int(input())
if n == 1:
    print(1)

Points = []
for i in range(n):
    Points.append(list(map(int, input().split())))

Vector = dd(lambda: 0)
for point1, point2 in combinations(Points, 2):
    if point1[0] >= point2[0]:
        x_v = point1[0] - point2[0]
        y_v = point1[1] - point2[1]
    else:
        x_v = point2[0] - point1[0]
        y_v = point2[1] - point1[1]
    Vector[(x_v, y_v)] += 1

print(max(n - max(Vector.values()), 1))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict as dd
from itertools import combinations
n = int(input())
Points = []
for i in range(n):
    Points.append(list(map(int, input().split())))

Vector = dd(lambda: 0)
for point1, point2 in combinations(Points, 2):
    if point1[0] >= point2[0]:
        x_v = point1[0] - point2[0]
        y_v = point1[1] - point2[1]
    else:
        x_v = point2[0] - point1[0]
        y_v = point2[1] - point1[1]
    Vector[(x_v, y_v)] += 1

print(max(n - max(Vector.values()), 0))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict as dd
from itertools import combinations
n = int(input())
Points = []
for i in range(n):
    Points.append(list(map(int, input().split())))

Vector = dd(lambda: 0)
for point1, point2 in combinations(Points, 2):
    if point1[0] >= point2[0]:
        x_v = point1[0] - point2[0]
        y_v = point1[1] - point2[1]
    else:
        x_v = point2[0] - point1[0]
        y_v = point2[1] - point1[1]
    Vector[(x_v, y_v)] += 1

print(n - max(Vector.values()))
Problem p03044 (python)

Fixed submission:
import numpy as np
from scipy.sparse.csgraph import shortest_path
import heapq
n = int(input())
edge = [[] for i in range(n)]
for i in range(n-1):
    u, v, w = map(int, input().split())
    u -= 1
    v -= 1
    edge[u].append([w, v])
    edge[v].append([w, u])

def dijkstra_heap(s):
    #始点sから各頂点への最短距離
    d = [float("inf")] * n
    used = [True] * n #True:未確定
    d[s] = 0
    used[s] = False
    edgelist = []
    for e in edge[s]:
        heapq.heappush(edgelist,e)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        #まだ使われてない頂点の中から最小の距離のものを探す
        if not used[minedge[1]]:
            continue
        v = minedge[1]
        d[v] = minedge[0]
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,[e[0]+d[v],e[1]])
    return d

Path_from_0 = dijkstra_heap(0)
for i in range(n):
    print(Path_from_0[i] % 2)

Buggy submission (verdict: Runtime Error):
import numpy as np
from scipy.sparse.csgraph import shortest_path
import heapq
n = int(input())
edge = [[] for i in range(n)]
for i in range(n-1):
    u, v, w = map(int, input().split())
    u -= 1
    v -= 1
    edge[u].append([w, v])
    edge[v].append([w, u])

def dijkstra_heap(s):
    #始点sから各頂点への最短距離
    d = [float("inf")] * n
    used = [True] * n #True:未確定
    d[s] = 0
    used[s] = False
    edgelist = []
    for e in edge[s]:
        heapq.heappush(edgelist,e)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        #まだ使われてない頂点の中から最小の距離のものを探す
        if not used[minedge[1]]:
            continue
        v = minedge[1]
        d[v] = minedge[0]
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,[e[0]+d[v],e[1]])
    return d

Path_from_0 = dijkstra_heap(0)
for i in range(n):
    print(Path_from_0[i] % 2)

Buggy submission (verdict: Runtime Error):
import numpy as np
from scipy.sparse.csgraph import shortest_path
n = int(input())
Sides = [[0 for i in range(n)] for j in range(n)]
for i in range(n-1):
    u, v, w = map(int, input().split())
    u -= 1
    v -= 1
    Sides[u][v] = w
    Sides[v][u] = w

Path_from_0 = shortest_path(np.array(Sides), indices=0)
for i in range(n):
    print(int(Path_from_0[i]) % 2)
Problem p03087 (python)

Fixed submission:
n, q = map(int, input().split())
S = input()

Sev = [0] * n
for i in range(n-1):
  if S[i] == "A" and S[i+1] == "C":
    Sev[i] = 1

Simos = [0] * n
Simos[0] = Sev[0]
for i in range(1, n):
  Simos[i] = Simos[i-1] + Sev[i]
    
for i in range(q):
  l, r = map(int, input().split())
  l = l-1
  r = r-1
  r = r-1
  if l == 0:
    print(Simos[r])
  else:
    print(Simos[r] - Simos[l-1])

Buggy submission (verdict: Runtime Error):
n, q = map(int, input().split())
s = input()
for i in range(q):
  l, r = map(int, input().split())
  substring = s[1 - 1 : r]
  print(substring)
  sp = substring.replace('AC', '+')
  print(sp)
  print(sp.count("+"))
Problem p03273 (python)

Fixed submission:
h, w = map(int, input().split())

pic = [""] * h
for i in range(h):
  pic[i] = input()

row = [False] * h
col = [False] * w
for i in range(h):
  for j in range(w):
    if pic[i][j] == "#":
      row[i] = True
      col[j] = True

for i in range(h):
  if row[i] == True:
    for j in range(w):
      if col[j] == True:
        print(pic[i][j], end = "")
    print()

Buggy submission (verdict: Runtime Error):
h, w = [int(num) for num in input().split()]
lis = []
for i in range(h):
  lis.append([a for a in input()])

def h_remove():
  pop_list = []
  h_c = 0
  pop_flag = False
  global h, w, lis
  while h_c < h:
    if lis[h_c].count("#") == w  or  lis[h_c].count(".") == w:
      lis.pop(h_c)
      h -= 1
      pop_flag = True
    else:
      h_c += 1
  return pop_flag

def transpose(list):
  return [[arr_w[i] for arr_w in list] for i in range(len(list[0]))]

def w_remove():
  global h, w, lis
  lis = transpose(lis)
  h, w = w, h
  pop_flag = h_remove()
  lis = transpose(lis)
  h, w = w, h
  return pop_flag

lis = transpose(transpose(lis))

pop_h, pop_w = True, True
while (pop_h == True) or (pop_w == True):
  pop_h = h_remove()
  pop_w = w_remove()
print(lis)
Problem p03274 (python)

Fixed submission:

n,k=map(int,input().split())
x=sorted(list(map(int,input().split())))
print(min((min(abs(x[i])+abs(x[i+k-1]-x[i]),abs(x[i+k-1])+abs(x[i]-x[i+k-1]))) for i in range(n-k+1)))

Buggy submission (verdict: Runtime Error):
n, k = map(int, input().split())
X = list(map(int, input().split()))

for i in range(n):
  if X[i] > 0:
    over_zero = i
    break
else:
  over_zero = n

min_cost = 10**8
#プラス側でトライ
if over_zero + k - 1 < n:
  min_cost = X[over_zero + k - 1]
#マイナス側でトライ
if over_zero - k >= 0:
  min_cost = min(X[over_zero - k], min_cost)
for i in range(0, k+1):
  #マイナスサーチ
  if over_zero - i >= 0:
    minus_cost = -(X[over_zero - i])
  else:
    continue
  #プラスサーチ
  if over_zero + k - i - 1 < n:
    plus_cost = (X[over_zero + k - i - 1])
  else:
    continue
  cost = plus_cost + minus_cost + min(plus_cost, minus_cost) 
  min_cost = min(cost, min_cost)

print(min_cost)
Problem p03283 (python)

Fixed submission:
n, m, q = map(int, input().split())
Arr = []
for i in range(n+1):
  Arr.append([0] * (n+1))
for i in range(m):
  l, r = map(int, input().split())
  Arr[l][r] += 1
#print(Arr)

B = []
for i in range(n+1):
  B_line = [0]
  for j in range(1, n+1):
    B_line.append(B_line[-1] + Arr[i][j])
  B.append(B_line)
#print(B)
  
for x in range(q):
  left, right = map(int, input().split())
  train_num = 0
  for i in range(left, right+1):
    train_num += B[i][right] - B[i][left-1]
  print(train_num)

Buggy submission (verdict: Runtime Error):
n, m, q = map(int, input().split())
import numpy as np
Arr = np.zeros((n+1)**2, dtype=np.int).reshape((n+1, n+1))
for i in range(m):
  l, r = map(int, input().split())
  Arr[l][r] += 1
#print(Arr)

A = np.array(Arr)
for i in range(q):
  left, right = map(int, input().split())
  train_num = np.sum(A[left:right+1, left:right+1], axis=None, dtype=np.int)
  print(train_num)

Buggy submission (verdict: Runtime Error):
n, m, q = map(int, input().split())
import numpy as np
Arr = np.zeros((n+1)**2, dtype=np.int).reshape((n+1, n+1))
for i in range(m):
  l, r = map(int, input().split())
  Arr[l][r] += 1
#print(Arr)

A = np.array(Arr)
for i in range(q):
  left, right = map(int, input().split())
  train_num = np.sum(A[left:right+1, left:right+1], axis=None, dtype=np.int)
  print(train_num)

Buggy submission (verdict: Runtime Error):
n, m, q = map(int, input().split())
import numpy as np
Arr = np.zeros((n+1)**2, dtype=np.int).reshape((n+1, n+1))
for i in range(m):
  l, r = map(int, input().split())
  Arr[l][r] += 1
#print(Arr)

A = np.array(Arr)
for i in range(q):
  left, right = map(int, input().split())
  train_num = np.sum(A[left:right+1, left:right+1], axis=None, dtype=np.int)
  print(train_num)
Problem p03503 (python)

Fixed submission:
n = int(input())
ans = 0

import numpy as np

F = [list(map(int, input().split())) for i in range(n)]
P = [list(map(int, input().split())) for i in range(n)]

Cands = [[]]
for i in range(10):
  temp = []
  for cand in Cands:
    temp.append(cand + [0])
    temp.append(cand + [1])
    Cands = temp
Cands = Cands[1:]

max_p = -10000000000
for cand in Cands:
  sum_p = 0
  for i in range(n):
    day_num = np.dot(cand, F[i])
    sum_p += P[i][day_num]
  max_p = max(sum_p, max_p)
print(max_p)

Buggy submission (verdict: Runtime Error):
n = int(input())
ans = 0

import numpy as np

F = [list(map(int, input().split())) for i in range(n)]
P = [list(map(int, input().split())) for i in range(n)]

Cands = [[]]
for i in range(10):
  temp = []
  for cand in Cands:
    temp.append(cand + [0])
    temp.append(cand + [1])
    Cands = temp
Cands = Cands[1:]

max_p = -10000000000
for cand in Cands:
  sum_p = 0
  for i in range(n):
    day_num = np.dot(cand, F[i])
    sum_p += P[i][day_num]
  max_p = max(sum_p, max_p)
print(max_p)
Problem p03607 (python)

Fixed submission:
n = int(input())
A = [0] * n
for i in range(n):
  A[i] = int(input())
from collections import Counter
C = Counter(A)
counter = 0
for val in C.values():
  counter += val % 2
print(counter)

Buggy submission (verdict: Runtime Error):
n = int(input())
list = [0] * 1000001

for i in range(n):
  num = int(input())
  if list[num - 1] == 0:
    list[num - 1] = 1
  else:
    list[num - 1] = 0

print(sum(list))

Buggy submission (verdict: Runtime Error):
n = int(input())
list = [0] * 100000

for i in range(n):
  num = int(input())
  if list[num - 1] == 0:
    list[num - 1] = 1
  else:
    list[num - 1] = 0

print(sum(list))
Problem p03673 (python)

Fixed submission:
n = int(input())
A = list(map(int, input().split()))
if n >= 2:
  for i in range(n, 0, -2):
    print(A[i-1], end=" ")
  for i in range(n % 2, n - 2, 2):
    print(A[i], end=" ")
  print(A[n-2])
if n == 1:
  print(*A)

Buggy submission (verdict: Runtime Error):
N=int(input())
A=list(map(int,input().split()))
print(*A[::-2],*A[N%2::2])

Buggy submission (verdict: Runtime Error):
n = int(input())
A = input().split()

if len(A) % 2:
  B = [A[-i][::-1] for i in range(1, len(A)-1, 2)] + A[1::2]
else:
  B = [A[-i][::-1] for i in range(1, len(A), 2)] + A[::2]
  b = "".join(B)
print(*b)
Problem p04044 (python)

Fixed submission:
n, l = map(int, input().split())
string_list = sorted([input() for i in range(n)])
print("".join(string_list))

Buggy submission (verdict: Runtime Error):
n, l = map(int, input().split())
string_list = sorted([input() for i in range(l)])
print("".join(string_list))

Buggy submission (verdict: Runtime Error):
n, l = map(int, input().split())
string_list = [input() for i in range(l)]
print("".join(sorted(string_list)))
Problem p03292 (python)

Fixed submission:
A = list(map(int, input().split()))
A.sort()
print(A[2] - A[0])

Buggy submission (verdict: Runtime Error):
A = list(map(int, input().split())).sorted
print(A[2] - A[0])

Buggy submission (verdict: Runtime Error):
A = list(map(int, input().split()).sorted
print(A[2] - A[0])

Buggy submission (verdict: Runtime Error):
N = int(input())
print(sum(list(map(int,input().split())))-N)
Problem p03378 (python)

Fixed submission:
N, M, X = map(int, input().split())
A = list(map(int, input().split()))
P = list(filter(lambda x: x < X, A))
Q = list(filter(lambda x: x > X, A))
print(min(len(P), len(Q)))

Buggy submission (verdict: Runtime Error):
N, M, X = map(int, input().split())
A = list(map(int, input().split()))
S = sum(s < X for s in A)
print(min(s, N-s))
Problem p03633 (python)

Fixed submission:
def gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    else:
        return gcd(b, a%b)

def lcm(a, b):
    return a // gcd(a, b) * b

N = input()
V = 1
for i in range(int(N)):
    T = input()
    V = lcm(V, int(T))

print(V)

Buggy submission (verdict: Runtime Error):
def gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    else:
        return int(gcd(b, a%b))

def lcm(a, b):
    return int(a / gcd(a, b) * b)

N = input()
V = 1
for i in range(int(N)):
    T = input()
    V = lcm(V, int(T))

print("%d" % V)

Buggy submission (verdict: Runtime Error):
def gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    else:
        return gcd(b, a%b)

def lcm(a, b):
    return a / gcd(a, b) * b

N = input()
V = 1
for i in range(int(N)):
    T = input()
    V = lcm(V, int(T))

print("%d" % V)

Buggy submission (verdict: Runtime Error):
def gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    else:
        return gcd(b, a%b)

def lcm(a, b):
    return a * b / gcd(a, b)

N = input()
V = 1
for i in range(int(N)):
    T = input()
    V = lcm(V, int(T))
    
print(int(V))

Buggy submission (verdict: Runtime Error):
def gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    else:
        return gcd(b, a%b);

def lcm(a, b):
    return a * b / gcd(a, b);

N = input()
V = 1
for i in range(int(N)):
    T = input()
    V = lcm(V, int(T));
print(int(V))

Buggy submission (verdict: Runtime Error):
def gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    else:
        return gcd(b, a%b);

def lcm(a, b):
    return int(a * b / gcd(a, b));

N = input()
V = 1
for i in range(int(N)):
    T = input()
    V = lcm(V, int(T));
print(V)

Buggy submission (verdict: Runtime Error):
def gcd(a, b):
    if b == 0:
        return a
    else:
        return gcd(b, a%b);

def lcm(a, b):
    return int(a * b / gcd(a, b));

N = input()
V = 1
for i in range(int(N)):
    T = input()
    V = lcm(V, int(T));
print(V)