Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
import math
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
input_line = input().split()

N = int(input_line[0])
M = int(input_line[1])
counter = 0 
if N != 0:
    counter += combinations_count(N,2) 
if M != 0:
    counter += combinations_count(M,2)
        
print(counter)


Fixed submission:
import math
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
input_line = input().split()

N = int(input_line[0])
M = int(input_line[1])
counter = 0 
if N > 1:
    counter += combinations_count(N,2) 
if M > 1:
    counter += combinations_count(M,2)
        
print(counter)

Buggy python submission (verdict: Runtime Error):
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
import math
input_line = input().split()

N = int(input_line[0])
M = int(input_line[1])
counter = 0 
counter += combinations_count(N,2) 
counter += combinations_count(M,2)
        
print(counter)



Fixed submission:
import math
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
input_line = input().split()

N = int(input_line[0])
M = int(input_line[1])
counter = 0 
if N > 1:
    counter += combinations_count(N,2) 
if M > 1:
    counter += combinations_count(M,2)
        
print(counter)

Buggy python submission (verdict: Runtime Error):
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
import math
input_line = input().split()

N = int(input_line[0])
M = int(input_line[1])
counter = 0 
counter += combinations_count(N,2) 
counter += combinations_count(M,2)
        
print(counter)



Fixed submission:
import math
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
input_line = input().split()

N = int(input_line[0])
M = int(input_line[1])
counter = 0 
if N > 1:
    counter += combinations_count(N,2) 
if M > 1:
    counter += combinations_count(M,2)
        
print(counter)

Buggy python submission (verdict: Runtime Error):
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
import math
input_line = input().split()

N = int(input_line[0])
M = int(input_line[1])
counter = 0 

counter = math.factorial(N) / math.factorial(N - 2)* math.factorial(2) + math.factorial(M) / math.factorial(M - 2)* math.factorial(2)
        
print(combinations_count(N,2)+ combinations_count(M,2))



Fixed submission:
import math
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
input_line = input().split()

N = int(input_line[0])
M = int(input_line[1])
counter = 0 
if N > 1:
    counter += combinations_count(N,2) 
if M > 1:
    counter += combinations_count(M,2)
        
print(counter)
Buggy python submission (verdict: Runtime Error):
N, A, B = map(int, input().split()) 
ans = N // (A + B) * A
rem = N % (A + B)
ans += min(rem, A)
print(ans)


Fixed submission:
input_line = input()

if input_line == "AAA" or input_line == "BBB":
    print("No")
else:
    print("Yes")
Buggy python submission (verdict: Runtime Error):
input_line = input()

num_array = input_line.split()
ans = num_array[0] * num_array[1] %2

if ans = "0":
  print("Even")
else:
  print("Odd")

Fixed submission:
a,b = input().split()

c = int(a)*int(b)%2

if c==1:
    print("Odd")
else:
    print("Even")
Buggy python submission (verdict: Runtime Error):
a,b = input().split()

c = a+b
number = int(c)
w = False

for i in range(number/2):
    if i*i == number:
        print("Yes")
        w = True
        break
if w == False:
    print("No")

Fixed submission:
a,b = input().split()

c = a+b
w = False

for i in range(int(c)):
    if i*i == int(c):
        print("Yes")
        w = True
        break
if w == False:
    print("No")
Buggy python submission (verdict: Runtime Error):
H, W, D = map(int, input().split())
M = [(-1, -1)]*(H*W+1)
A = []
for i in range(H):
  As = list(map(int, input().split()))
  for j in range(W):
    a = As[j]
    M[a] = (i, j)
  A.append(As)
#print(M)
Dist = [0]*(H*W+1)
for k in range(0, H*W-D+1):
  i, j = M[k]
  x, y = M[k+D]
  Dist[k+D] = Dist[k]+abs(x-i)+abs(y-j)
Q = int(input())
for i in range(Q):
  L, R = map(int, input().split())
  r = Dist[R]-Dist[L]
  print(r)

Fixed submission:
n = int(input())
print(n//3)
Buggy python submission (verdict: Runtime Error):
from math import *

H, W, A, B = list(map(int, input().split()))
p = 1000000007

ft = [1]
ift = [-1] * (H + W + 1)
for i in range(1, H + W + 1):
    ft.append(ft[i-1] * i % p)

def ifac(a):
    if ift[a] != -1: return ift[a]
    res = 1
    x = ft[a]
    for i in range(ceil(log2(p-2))):
        if ((p - 2) >> i) & 1:
            res *= x % p
        x *= x % p
    ift[a] = res
    return res

def com(a, b):
    return (ft[a] * ifac(b) * ifac(a-b)) % p

ans = 0
for i in range(H-A):
    ans += com(B+i-1, i) * com(W-B+H-i-2, H-i-1)
    ans %= p

print(ans)


Fixed submission:
def main():
    s = list(map(int, input().split()))
    fives = 0
    sevens = 0
    for item in s:
        if item == 5: fives += 1
        if item == 7: sevens += 1
    if fives == 2 and sevens == 1:
        print('YES')
    else:
        print('NO')

if __name__ == '__main__':
    main()
Buggy python submission (verdict: Time Limit Exceeded):
from math import *

p = 1000000007

def make_ft(max):
    ft = [0] * (max+1)
    x = 1
    ft[0] = 1
    # ft[i] == i!
    for i in range(1, max+1):
        x *= i
        x %= p
        ft[i] = x
    return ft

# i!^-1 == i!^(p-2) (mod p)
def make_ift(max, ft):
    ift = [0] * (max+1)
    ift[0] = 1
    for i in range(1, max+1):
        invf = 1
        x = ft[i]
        for j in range(ceil(log2(p-2))):
            # x == i!^2^j
            if ((p - 2) >> j) & 1:
                invf *= x
                invf %= p
            x *= x
            x %= p
        ift[i] = invf
    return ift

def combination(a, b, ft, ift):
    res = ft[a] * ift[b] * ift[a-b]
    res %= p
    return res

def main():
    H, W, A, B = list(map(int, input().split()))

    ft = make_ft(H+W)
    ift = make_ift(H+W, ft)
    ans = 0
    for i in range(H-A):
        ans += combination(B+i-1, i, ft, ift) * combination(W-B+H-i-2, H-i-1, ft, ift)
        ans %= p

    print(ans)

if __name__ == '__main__':
    main()


Fixed submission:
H, W, A, B = list(map(int, input().split()))
p = 1000000007

fac = [1] * (H + W + 1)
x = 1
for i in range(1, H + W + 1):
    x *= i
    x %= p
    fac[i] = x

ifac = [1] * (H + W + 1)
x = fac[H + W]
q = p - 2

while q > 0:
    if q & 1:
        ifac[H + W] *= x % p
    x *= x % p
    q >>= 1

for i in range(H + W - 1, 0, -1):
    ifac[i] = ifac[i + 1] * (i + 1) % p

def com(a, b):
    return (fac[a] * ifac[b] * ifac[a-b]) % p

ans = 0

for i in range(H-A):
    ans += com(B+i-1, i) * com(W-B+H-i-2, H-i-1)
    ans %= p

print(ans)

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

p = 1000000007
ft = []
ift = []

def make_ft(max):
    x = 1
    ft.append(x)
    # ft[i] == i!
    for i in range(1, max+1):
        x *= i
        x %= p
        ft.append(x)
    return

# i!^-1 == i!^(p+2) (mod p)
def make_ift(max):
    ift.append(1)
    for i in range(1, max+1):
        invf = 1
        x = ft[i]
        for j in range(ceil(log2(p-2))):
            # x == i!^2^j
            if ((p - 2) >> j) & 1:
                invf *= x
                invf %= p
            x *= x
            x %= p
        ift.append(invf)
    return

def combination(a, b):
    res = ft[a] * ift[b] * ift[a-b]
    res %= p
    return res

def main():
    H, W, A, B = list(map(int, input().split()))

    make_ft(H+W)
    make_ift(H+W)
    ans = 0
    for i in range(H-A):
        ans += combination(B+i-1, i) * combination(W-B+H-i-2, H-i-1)
        ans %= p

    print(ans)

if __name__ == '__main__':
    main()


Fixed submission:
H, W, A, B = list(map(int, input().split()))
p = 1000000007

fac = [1] * (H + W + 1)
x = 1
for i in range(1, H + W + 1):
    x *= i
    x %= p
    fac[i] = x

ifac = [1] * (H + W + 1)
x = fac[H + W]
q = p - 2

while q > 0:
    if q & 1:
        ifac[H + W] *= x % p
    x *= x % p
    q >>= 1

for i in range(H + W - 1, 0, -1):
    ifac[i] = ifac[i + 1] * (i + 1) % p

def com(a, b):
    return (fac[a] * ifac[b] * ifac[a-b]) % p

ans = 0

for i in range(H-A):
    ans += com(B+i-1, i) * com(W-B+H-i-2, H-i-1)
    ans %= p

print(ans)
Buggy python submission (verdict: Runtime Error):
K = int(input())
S = input()
SS = (int(len(S)))
if S <= 0:
  print(s)
else:
print(S[:SS-K])+print('.',K)

Fixed submission:
K = int(input())
S = input()
SS = (int(len(S)))
if SS-K <= 0:
  print(S)
else:
  print((S[:K-SS])+('.'*3))
Buggy python submission (verdict: Runtime Error):
import numpy as np
stdin = open(0)

N,K = map(int,input().split())
A = np.array(stdin.read().split(), np.int64)
A = np.sort(A)

maxA = max(np.abs(A))


z = A[A==0]
p = A[A>0]
n = A[A<0]


def check(x):
    ret = 0
    if x >= 0:
        ret += N*len(z)
    ret += np.searchsorted(A,x//p,side='right').sum()
    ret += (N-np.searchsorted(A,x/n)).sum()
    ret -= len([a for a in A if a*a <= x])
    return ret//2;
        

ub = maxA*maxA
lb = -ub-1
while ub-lb > 1:
    mid = (ub+lb)>>1
    if check(mid) < K:
        lb = mid
    else:
        ub = mid
print(ub)

Fixed submission:
import numpy as np
import math
stdin = open(0)

N,K = map(int,input().split())
A = np.array([int(Ai) for Ai in input().split()])
A = np.sort(A)

maxA = max(np.abs(A))

z = A[A==0]
p = A[A>0]
n = A[A<0]

def check(x):
    ret = 0
    if x >= 0:
        ret += N*len(z)
    ret += np.searchsorted(A,x//p,side='right').sum()
    ret += (N - np.searchsorted(A, (-x - 1) // (-n), side='right')).sum()
#     ret += (N-np.searchsorted(A,np.ceil(x/n))).sum()
    ret -= np.count_nonzero(A*A<=x)
    return ret//2;

ub = maxA*maxA
lb = -ub-1
while ub-lb > 1:
    mid = (ub+lb)>>1
    if check(mid) < K:
        lb = mid
    else:
        ub = mid
print(ub)
Buggy python submission (verdict: Runtime Error):
def main(n, a):
  for x in a:
    if(x == 0):
      print(0)
      return
   
  ans = a[0]
  for i in range(1, n):
    ans = ans * a[i]
    if(ans > 1000000000000000000):
      print(-1)
      return
  print(ans)
 
if(__name__ == '__main__'):
  n = int(input())
  a = map(int, input().split())
  main(n, a)

Fixed submission:
def main(n, a):
  a = list(a)
  for x in a:
    if(x == 0):
      print(0)
      return
   
  ans = a[0]
  for i in range(1, n):
    ans = ans * a[i]
    if(ans > 1000000000000000000):
      print(-1)
      return
  print(ans)
 
if(__name__ == '__main__'):
  n = int(input())
  a = map(int, input().split())
  main(n, a)

Buggy python submission (verdict: Runtime Error):

def main(n, a):
  for x in a:
    if(x == 0):
      print(0)
      return
   
  ans = a[0]
  for i in range(1, n):
    ans = ans * a[i]
    if(ans > 1000000000000000000):
      print(-1)
      return
  print(ans)

if(__name__ == '__main__') {
  n = int(input())
  a = map(int, input().split())
  main(n, a)
  	

Fixed submission:
def main(n, a):
  a = list(a)
  for x in a:
    if(x == 0):
      print(0)
      return
   
  ans = a[0]
  for i in range(1, n):
    ans = ans * a[i]
    if(ans > 1000000000000000000):
      print(-1)
      return
  print(ans)
 
if(__name__ == '__main__'):
  n = int(input())
  a = map(int, input().split())
  main(n, a)
Buggy python submission (verdict: Runtime Error):
a = input(α)
b = a.isupper()
print(b)
if b == True:
    print("A")
else:
    print("a")


Fixed submission:
a = input()
b = a.isupper()
if b == True:
    print("A")
else:
    print("a")
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = [int(x) for x in input().split()]
ans = 0
for i in range(N):
    flag = 0
    for j in range(N):
        if i!=j and A[i]%A[j] == 0:
            #print("i=%d,j=%d,A[j]=%d"%(i,j,A[j]))
            flag +=1
            break
    if flag == 0:
        ans += 1
print(ans)

Fixed submission:
N = int(input())
A = [int(x) for x in input().split()]
D = set() #重複
S = set() #初出
for i in range(N):
    if A[i] in S:
        D.add(A[i])
    else:
        S.add(A[i])
#print(D,S)
M = max(S)
#print(M)
X = [1 for i in range(M+1)] #i番目が数字iに対応、条件を満たせば1、満たさなければ0にする。
#print(X)
for a in S:
    if a in D:
        X[a]=0 #aが重複していれば、aは条件を満たす数字ではない。
    for i in range(2*a,M+1,a):
        X[i]=0 #aはおｋ、2a以上のaの倍数は条件を満たさない。
        
ans = 0
for i in range(N):
    if X[A[i]]==1: #数字A(i)に対応するX[i]の箇所を参照して、条件を満たしていれば+1する
        ans += 1
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = [int(x) for x in input().split()]
ans = 0
for i in range(N):
    flag = 0
    for j in range(N):
        if i!=j and A[i]%A[j] == 0:
            #print("i=%d,j=%d,A[j]=%d"%(i,j,A[j]))
            flag +=1
    if flag == 0:
        ans += 1
print(ans)

Fixed submission:
N = int(input())
A = [int(x) for x in input().split()]
D = set() #重複
S = set() #初出
for i in range(N):
    if A[i] in S:
        D.add(A[i])
    else:
        S.add(A[i])
#print(D,S)
M = max(S)
#print(M)
X = [1 for i in range(M+1)] #i番目が数字iに対応、条件を満たせば1、満たさなければ0にする。
#print(X)
for a in S:
    if a in D:
        X[a]=0 #aが重複していれば、aは条件を満たす数字ではない。
    for i in range(2*a,M+1,a):
        X[i]=0 #aはおｋ、2a以上のaの倍数は条件を満たさない。
        
ans = 0
for i in range(N):
    if X[A[i]]==1: #数字A(i)に対応するX[i]の箇所を参照して、条件を満たしていれば+1する
        ans += 1
print(ans)
Buggy python submission (verdict: Runtime Error):
N = int(input()) #1行目のNを取得する
s_char = list(input().split())
s = [int(n) for n in s_char]
ans = 1

for num in s:
    if len(str(ans))+len(str(num))>20:
        #print('e')
        ans = -1
        break
    ans *= num
    if ans > 10**18:
        ans = -1
        break

for num in s:
    if num == 0:
        ans = 0
        
print(ans)

Fixed submission:
s = input().split()
print(int(s[0])*int(s[1]))

Buggy python submission (verdict: Runtime Error):
N = int(input()) #1行目のNを取得する
s_char = list(input().split())
s = [int(n) for n in s_char]
ans = 1

for num in s:
    if len(str(ans))+len(str(num))>20:
        #print('e')
        ans = -1
        break
    ans *= num
    if ans > 10**18:
        ans = -1
        break

for num in s:
    if num ==0:
        ans =0
        
print(ans)

Fixed submission:
s = input().split()
print(int(s[0])*int(s[1]))
Buggy python submission (verdict: Runtime Error):
s = input().split()
 
num = int(s[0])
 
#num
 
num2 = int(s[1]*100)
 
#num2
ans = num*num2//100

print(ans)

Fixed submission:
s = input().split()
 
num = int(s[0])
 
#num
 
num2 = int(s[1].replace('.', ''))
 
#num2
ans = (num*num2)//100
 
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N, K = map(int, input().split())
H = [int(N) for N in input().split()]
for i in range(0, K):
    if H[H.index(max(H))] == 0:
        break
    H[H.index(max(H))] = 0
print(sum(filter(lambda x: x != 0, H)))


Fixed submission:
N, K = map(int, input().split())
H = [int(N) for N in input().split()]
H.sort(reverse=True)
if N <= K:
    print(0)
else:
    for i in range(0, K):
        H[i] = 0
    print(sum(H))

Buggy python submission (verdict: Time Limit Exceeded):
N, K = map(int, input().split())
H = [int(N) for N in input().split()]
for i in range(0, K):
    H[H.index(max(H))] = 0
print(sum(filter(lambda x: x != 0, H)))


Fixed submission:
N, K = map(int, input().split())
H = [int(N) for N in input().split()]
H.sort(reverse=True)
if N <= K:
    print(0)
else:
    for i in range(0, K):
        H[i] = 0
    print(sum(H))

Buggy python submission (verdict: Time Limit Exceeded):
N, K = map(int, input().split())
H = [int(N) for N in input().split()]
for i in range(0, K):
    max_index = H.index(max(H))
    H[max_index] = 0
print(sum(int(i) for i in H))

Fixed submission:
N, K = map(int, input().split())
H = [int(N) for N in input().split()]
H.sort(reverse=True)
if N <= K:
    print(0)
else:
    for i in range(0, K):
        H[i] = 0
    print(sum(H))
Buggy python submission (verdict: Runtime Error):
ｓ

Fixed submission:
s = input()
t = input()
ans = 0

for i in range(3):
    if s[i] == t[i]:
        ans = ans + 1
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
X = int(input())


def get_result(X):
    a = 0
    while True:
        a5 = a ** 5
        c = a5 - X
        if c < 0:
            c = -c
            b = 0
            while True:
                b5 = b ** 5
                if b5 == c:
                    return a, -b
                if b5 > c:
                    break
                b += 1
        a += 1


a, b = get_result(X)
print(a, b)

Fixed submission:
X = int(input())


def is_ok(A, B, X):
    return A ** 5 - B ** 5 == X


def spiral():
    i = 1
    p = [0, 0]
    yield p
    while True:
        for j in range(i):
            p[0] += 1
            yield p
        for j in range(i):
            p[1] -= 1
            yield p
        i += 1
        for j in range(i):
            p[0] -= 1
            yield p
        for j in range(i):
            p[1] += 1
            yield p
        i += 1


for a, b in spiral():
    if is_ok(a, b, X):
        print(a, b)
        break
Buggy python submission (verdict: Runtime Error):
N = int(input())

result_list = [
    ["a"],
    ["aa", "ab"],
    ["aaa", "aab", "aba", "abb", "abc"]
]

for s in result_list[N - 1]:
    print(s)

Fixed submission:
N = int(input())
#N = 4
def to_str(n):
    s = [chr(i + 97) for i in reversed(n)]
    s = "".join(s)
    return s
n = [0] * N
n_max = list(reversed(list(range(N))))

s = to_str(n)
print(s)
while True:
    for j in range(N-1):
        #if n[j] < n[j+1]+1:
        if n[j] < max(n[j+1:]) + 1:
            n[j] += 1
            for k in range(j):
                n[k] = 0
            s = to_str(n)
            print(s)
            break
    if n == n_max:
        break
Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
p = list(map(int, input().split()))


def _condition(i, p):
    for j in range(i):
        if p[i] <= p[j]:
            pass
        else:
            return False
    return True


def _result(p):
    sum = 0
    for i in range(len(p)):
        sum += _condition(i, p)
    return sum


print(_result(p))

Fixed submission:
n = int(input())
p = list(map(int, input().split()))


def _result(p):
    sum = 0
    m = p[0]
    for i in range(0, len(p)):
        if p[i] > m:
            pass
        else:
            m = p[i]
            sum += 1
    return sum


print(_result(p))
Buggy python submission (verdict: Runtime Error):
import math

a, b = map(int, input().split())


def lcm(x, y):
    return (x * y) // math.gcd(x, y)


print(lcm(a, b))

Fixed submission:
# import math
import fractions

a, b = map(int, input().split())


def lcm(x, y):
    # return (x * y) // math.gcd(x, y)
    return (x * y) // fractions.gcd(x, y)


print(lcm(a, b))
Buggy python submission (verdict: Time Limit Exceeded):
N = list(map(int, input().split()))[0]
A = list(map(int, input().split()))
def get_result(ary):
    d_old = -1
    for i in range(0, len(ary)):
        left = sum(ary[:i])
        right = sum(ary[i:])
        d = abs(left - right)
        if d > d_old and d_old > -1:
            return d_old
        else:
            d_old = d
    return d_old
print(get_result(A))

Fixed submission:
import numpy as np
N = list(map(int, input().split()))[0]
A = np.array(list(map(int, input().split())))
def get_result(ary):
    cumsum_left = np.cumsum(ary)
    cumsum_right = np.cumsum(ary[::-1])
    d = np.abs(cumsum_left[:-1] - cumsum_right[::-1][1:])
    return np.min(d)
print(get_result(A))
Buggy python submission (verdict: Runtime Error):
N = int(input())
H = list(map(int, input().split()))


def move_number(number_list):
    n = len(number_list)
    result = 0
    for i in range(n - 1):
        if number_list[i + 1] <= number_list[i]:
            result += 1
        else:
            return result
    return result


def all_move_numbers(number_list):
    result = []
    n = len(number_list)
    for i in range(n - 1):
        _number_list = number_list[i:]
        result.append(move_number(_number_list))
    return result


def max_number(number_list):
    result = max(all_move_numbers(number_list))
    return result


print(max_number(H))

Fixed submission:
N = int(input())
H = list(map(int, input().split()))


def decreasing(number_list):
    n = len(number_list) - 1
    result = ["F"] * n
    for i in range(n):
        if number_list[i + 1] <= number_list[i]:
            result[i] = "T"

    return result


print(max(map(len, "".join(decreasing(H)).split("F"))))
Buggy python submission (verdict: Runtime Error):
N = int(input())


def sum_ms(ps):
    n = len(ps)
    result = 0
    for j in range(n):
        i = j + 1
        result += i % ps[j]
    return result


ps = list(range(2, N + 1))
ps.append(1)
print(sum_ms(ps))

Fixed submission:
import decimal

N = decimal.Decimal(input())
print(N * (N - 1) / 2)

Buggy python submission (verdict: Runtime Error):
N = int(input())


def ms(ps):
    n = len(ps)
    result = []
    for j in range(n):
        i = j + 1
        result.append(i % ps[j])
    return result


ps = list(range(2, N + 1))
ps.append(1)
print(sum(ms(ps)))

Fixed submission:
import decimal

N = decimal.Decimal(input())
print(N * (N - 1) / 2)
Buggy python submission (verdict: Time Limit Exceeded):
from itertools import chain, combinations
import copy

n = int(input())
a = list(map(int, input().split()))


def powerset(iterable):
    s = list(iterable)
    return chain.from_iterable(combinations(s, r) for r in range(len(s) + 1))


def is_mono(a):
    if len(a) < 2:
        return True
    for i in range(len(a) - 1):
        if a[i + 1] < a[i]:
            return False
    return True


def can_mono(a):
    for i in range(len(a) - 2):
        if a[i + 1] < a[i] and a[i + 2] < a[i + 1]:
            return False
    for m in powerset(range(len(a))):
        b = copy.deepcopy(a)
        for i in m:
            b[i] -= 1
            if is_mono(b):
                return True
    return False


if can_mono(a):
    result = 'Yes'
else:
    result = 'No'
print("{}".format(result))

Fixed submission:
n = int(input())
a = list(map(int, input().split()))


def can_mono(a):
    len_a = len(a)
    for i in range(len_a - 2):
        if a[i + 1] < a[i] - 1:
            return False
        if a[i + 1] < a[i]:
            for j in range(i + 1, len_a - 1):
                if a[j + 1] < a[i + 1]:
                    return False
                if a[j + 1] > a[i + 1]:
                    break
                if a[j + 1] == a[i + 1]:
                    continue
    return True


if can_mono(a):
    result = 'Yes'
else:
    result = 'No'
print("{}".format(result))

Buggy python submission (verdict: Time Limit Exceeded):
from itertools import chain, combinations
import copy

n = int(input())
a = list(map(int, input().split()))


def powerset(iterable):
    s = list(iterable)
    return chain.from_iterable(combinations(s, r) for r in range(len(s) + 1))


def is_mono(a):
    if len(a) < 2:
        return True
    for i in range(len(a) - 1):
        if a[i + 1] < a[i]:
            return False
    return True


def can_mono(a):
    for m in powerset(range(len(a))):
        b = copy.deepcopy(a)
        for i in m:
            b[i] -= 1
            if is_mono(b):
                return True
    return False


if can_mono(a):
    result = 'Yes'
else:
    result = 'No'
print("{}".format(result))

Fixed submission:
n = int(input())
a = list(map(int, input().split()))


def can_mono(a):
    len_a = len(a)
    for i in range(len_a - 2):
        if a[i + 1] < a[i] - 1:
            return False
        if a[i + 1] < a[i]:
            for j in range(i + 1, len_a - 1):
                if a[j + 1] < a[i + 1]:
                    return False
                if a[j + 1] > a[i + 1]:
                    break
                if a[j + 1] == a[i + 1]:
                    continue
    return True


if can_mono(a):
    result = 'Yes'
else:
    result = 'No'
print("{}".format(result))
Buggy python submission (verdict: Runtime Error):
alpha = input()
if alpha.isupper() == True:
    print(aplha.lower())
else :
    print(alpha.upper())


Fixed submission:
alpha = input()
if alpha.isupper() == True:
    print("A")
else :
    print("a")