Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Time Limit Exceeded):
import math
from functools import reduce
import itertools



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


a = int(input())
ans = 0
nums = []
for i in range(1, a+1):
    nums.append(i)

for balls in itertools.product(nums, repeat=3):
    ans += int(gcd(gcd(balls[0], balls[1]), balls[2]))

print(ans)


Fixed submission:
from math import gcd

a = int(input())

ans = 0
for i in range(1, a+1):
    for k in range(1, a+1):
        for j in range(1, a+1):
            ans += gcd(gcd(i,k),j)


print(ans)

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



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


a = int(input())
ans = 0
nums = []
for i in range(1, a+1):
    nums.append(i)

for balls in itertools.product(nums, repeat=3):
    ans += int(gcd(balls[0], balls[1], balls[2]))

print(ans)


Fixed submission:
from math import gcd

a = int(input())

ans = 0
for i in range(1, a+1):
    for k in range(1, a+1):
        for j in range(1, a+1):
            ans += gcd(gcd(i,k),j)


print(ans)

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

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

a = int(input())

ans = 0
for i in range(1, a+1):
    for k in range(1, a+1):
        for j in range(1, a+1):
            ans += int(gcd(i, k, j))
            # print(math.gcd(i, k ,j))

print(ans)

Fixed submission:
from math import gcd

a = int(input())

ans = 0
for i in range(1, a+1):
    for k in range(1, a+1):
        for j in range(1, a+1):
            ans += gcd(gcd(i,k),j)


print(ans)

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

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

a = int(input())

ans = 0
for i in range(1, a+1):
    for k in range(1, a+1):
        for j in range(1, a+1):
            ans += int(gcd(i, k, j))
            # print(math.gcd(i, k ,j))

print(ans)

Fixed submission:
from math import gcd

a = int(input())

ans = 0
for i in range(1, a+1):
    for k in range(1, a+1):
        for j in range(1, a+1):
            ans += gcd(gcd(i,k),j)


print(ans)
Buggy python submission (verdict: Runtime Error):
s = input()

if s[2] == a[3] and s[4] == s[5]:
    print("Yes")
else:
    print("No")


Fixed submission:
s = input()

if s[2] == s[3] and s[4] == s[5]:
    print("Yes")
else:
    print("No")
Buggy python submission (verdict: Runtime Error):
import collections
from collections import defaultdict
from math import factorial
n = int(input())
l = list(map(int, input().split()))

dict = defaultdict(int)
for i in l:
    dict[i]+=1



for j in l:
    ans = 0
    k = dict.copy()
    k[j] -= 1
    # print(k)
    for v in k.values():
        if v > 1:
            ans += int(factorial(v) / factorial(2) / factorial(v - 2))
    print(ans)


Fixed submission:
import collections
from collections import defaultdict

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

dict = defaultdict(int)
for i in l:
    dict[i]+=1

ans = 0
for v in dict.values():
    ans += int((v*(v-1)) // 2)

for k in l:
    print(ans - (dict[k] - 1))

Buggy python submission (verdict: Runtime Error):
from math import factorial
n = int(input())
l = list(map(int, input().split()))

dict = defaultdict(int)
for i in l:
    dict[i]+=1



for j in l:
    ans = 0
    k = dict.copy()
    k[j] -= 1
    # print(k)
    for v in k.values():
        if v > 1:
            ans += int(factorial(v) / factorial(2) / factorial(v - 2))
    print(ans)


Fixed submission:
import collections
from collections import defaultdict

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

dict = defaultdict(int)
for i in l:
    dict[i]+=1

ans = 0
for v in dict.values():
    ans += int((v*(v-1)) // 2)

for k in l:
    print(ans - (dict[k] - 1))

Buggy python submission (verdict: Runtime Error):
from math import factorial
n = int(input())
l = list(map(int, input().split()))

dict = {}
for i in l:
    if i not in dict:
        dict[i] = 1
    else:
        dict[i] += 1

for j in l:
    ans = 0
    k = dict.copy()
    k[j] -= 1
    for v in k.values():
        if v > 1:
            ans += int(factorial(v) / factorial(2) / factorial(v - 2))
    print(ans)


Fixed submission:
import collections
from collections import defaultdict

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

dict = defaultdict(int)
for i in l:
    dict[i]+=1

ans = 0
for v in dict.values():
    ans += int((v*(v-1)) // 2)

for k in l:
    print(ans - (dict[k] - 1))

Buggy python submission (verdict: Runtime Error):
from math import factorial
n = int(input())
l = list(map(int, input().split()))

dict = {}
for i in l:
    if i not in dict:
        dict[i] = 1
    else:
        dict[i] += 1



for j in l:
    ans = 0
    k = dict.copy()
    k[j] -= 1
    # print(k)
    for v in k.values():
        if v > 1:
            ans += int(factorial(v) / factorial(2) / factorial(v - 2))
    print(ans)


Fixed submission:
import collections
from collections import defaultdict

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

dict = defaultdict(int)
for i in l:
    dict[i]+=1

ans = 0
for v in dict.values():
    ans += int((v*(v-1)) // 2)

for k in l:
    print(ans - (dict[k] - 1))
Buggy python submission (verdict: Runtime Error):
import math
from decimal import Decimal
a, b, c = map(int, input().split())

if Decimal(c).sqrt() - (Decimal(a).sqrt() + Decimal((b).sqrt())) > 0:
    print("Yes")
else:
    print("No")

Fixed submission:
from decimal import Decimal
a, b, c = map(int, input().split())

if Decimal(a).sqrt() + Decimal(b).sqrt() < Decimal(c).sqrt():
    print("Yes")
else:
    print("No")
Buggy python submission (verdict: Runtime Error):
m = int(input())


if m%2 != 0
    print(m//2 + 1)
else:
    print(m//2)


Fixed submission:
m = int(input())

if m%2 != 0:
    print(m//2 + 1)
else:
    print(m//2)
Buggy python submission (verdict: Time Limit Exceeded):
dict = {}
for i in range(int(input())):
    a = input()
    if dict.get(a):
        dict[a] += 1
    else:
        dict[a] = 1



ans = [key for key, value in dict.items() if value == max(dict.values())]
ans.sort()
for i in ans:
    print(i)


Fixed submission:
dict = {}
for i in range(int(input())):
    a = input()
    if dict.get(a):
        dict[a] += 1
    else:
        dict[a] = 1

max_v = max(dict.values())


ans = [key for key, value in dict.items() if value == max_v]
ans.sort()
for i in ans:
    print(i)
Buggy python submission (verdict: Time Limit Exceeded):
N, B = map(int, input().split())
ana = []
dp = [0] * (N+2)

for i in range(B):
    ana.append(int(input()))

mod = 1000000007

dp[N] = 1
for i in reversed(range(N)):
    if i in ana:
        dp[i] = 0
        ana.pop(len(ana)-1)
        continue
    dp[i] = dp[i + 1] + dp[i + 2]
print(dp[0] % mod)

Fixed submission:
N, B = map(int, input().split())
ana = []
dp = [0] * (N+2)

for i in range(B):
    ana.append(int(input()))

mod = 1000000007

dp[N] = 1
for i in reversed(range(N)):
    if len(ana) >= 1 and i == ana[-1]:
        dp[i] = 0
        if len(ana) != 0:
            ana.pop(-1)
        continue
    dp[i] = dp[i + 1] + dp[i + 2]
print(dp[0] % mod)

Buggy python submission (verdict: Time Limit Exceeded):
N, B = map(int, input().split())
ana = []
dp = [0] * (N+2)

for i in range(B):
    ana.append(int(input()))

mod = 1000000007

dp[N] = 1
for i in reversed(range(N)):
    if i in ana:
        dp[i] = 0
        continue
    dp[i] = dp[i + 1] + dp[i + 2]
print(dp[0] % mod)



Fixed submission:
N, B = map(int, input().split())
ana = []
dp = [0] * (N+2)

for i in range(B):
    ana.append(int(input()))

mod = 1000000007

dp[N] = 1
for i in reversed(range(N)):
    if len(ana) >= 1 and i == ana[-1]:
        dp[i] = 0
        if len(ana) != 0:
            ana.pop(-1)
        continue
    dp[i] = dp[i + 1] + dp[i + 2]
print(dp[0] % mod)
Buggy python submission (verdict: Runtime Error):
a = int(input())
b = int(input())

ans = a - b + 1
print(ans)


Fixed submission:

l = [int(x) for x in input().split( )]

ans = l[0] - l[1] + 1
print(ans)
Buggy python submission (verdict: Runtime Error):
if abs(a-c) <= d:
    print('Yes')
elif abs(a-b) <= d and abs(b-c) <= d:
    print('Yes')
else:
    print('No')

Fixed submission:
a, b, c, d = map(int, input().split())
if (abs(a-b) <= d and abs(b-c) <= d) or abs(a-c) <= d:
    print('Yes')
else:
    print('No')
Buggy python submission (verdict: Runtime Error):
h,w,k=map(int,input().split())
c=[[] for i in range(h)]
for i in range(h):
  S=input()
  for j in range(w):
    c[i].append(S[j])
b1=2**h
b2=2**w
cnt=0
tori=0
for i in range(b1):
  s=(str(bin(i))[2:]).zfill(h)
  for j in range(b2):
    d=[]
    d=copy.deepcopy(c)
    cnt=0
    t=(str(bin(j))[2:]).zfill(w)
    for l in range(h):
      if s[l]=='1':
        for unchi in range(w):
          d[l][unchi]='r'
    for m in range(w):
      if t[m]=='1':
        for unchi in range(h):
          d[unchi][m]='r'
    for ch in range(h):
      cnt+=d[ch].count('#')
    if cnt==k:
      tori+=1
print(tori)

      

Fixed submission:
import copy
h,w,k=map(int,input().split())
c=[[] for i in range(h)]
for i in range(h):
  S=input()
  for j in range(w):
    c[i].append(S[j])
b1=2**h
b2=2**w
cnt=0
tori=0
for i in range(b1):
  s=(str(bin(i))[2:]).zfill(h)
  for j in range(b2):
    d=[]
    d=copy.deepcopy(c)
    cnt=0
    t=(str(bin(j))[2:]).zfill(w)
    for l in range(h):
      if s[l]=='1':
        for unchi in range(w):
          d[l][unchi]='r'
    for m in range(w):
      if t[m]=='1':
        for unchi in range(h):
          d[unchi][m]='r'
    for ch in range(h):
      cnt+=d[ch].count('#')
    if cnt==k:
      tori+=1
print(tori)
Buggy python submission (verdict: Time Limit Exceeded):
import sys
x=int(input())
a=0
while True:
  for i in range(-64,64):
    if a**5-i**5==x:
      print(a,i)
      sys.exit()
  a+=1

Fixed submission:
import sys
x=int(input())
a=0
while True:
  for i in range(-64,a):
    if a**5-i**5==x:
      print(a,i)
      sys.exit()
  a+=1
Buggy python submission (verdict: Runtime Error):
import sys
s=input()
l=len(s)
if l==1:
  print('No')
  sys.exit()
for i in range(0,l,2):
  if s[i]=='h':
    if s[i+1]!='i':
      print('No')
      sys.exit()
  else:
    print('No')
    sys.exit()
print('Yes')


Fixed submission:
import sys
s=input()
l=len(s)
if l%2==1:
  print('No')
  sys.exit()
for i in range(0,l,2):
  if s[i]=='h':
    if s[i+1]!='i':
      print('No')
      sys.exit()
  else:
    print('No')
    sys.exit()
print('Yes')

Buggy python submission (verdict: Runtime Error):
import sys
s=input()
l=len(s)
for i in range(0,l,2):
  if s[i]=='h':
    if s[i+1]!='i':
      print('No')
      sys.exit()
  else:
    print('No')
    sys.exit()
print('Yes')

Fixed submission:
import sys
s=input()
l=len(s)
if l%2==1:
  print('No')
  sys.exit()
for i in range(0,l,2):
  if s[i]=='h':
    if s[i+1]!='i':
      print('No')
      sys.exit()
  else:
    print('No')
    sys.exit()
print('Yes')
Buggy python submission (verdict: Runtime Error):
a,b,m=map(int,input().split())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
lst=[]
for i in range(m):
  x,y,c=map(int,input().split())
  lst.append([x,y,c])
v=min(A)+min(B)
for i in range(m):
  V=a[A[i][0]-1]+B[lst[i][1]-1]-lst[i][2]
  if v>V:
    v=V
print(v)
  
  

Fixed submission:
a,b,m=map(int,input().split())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
lst=[]
for i in range(m):
  x,y,c=map(int,input().split())
  lst.append([x,y,c])
v=min(A)+min(B)
for i in range(m):
  V=A[lst[i][0]-1]+B[lst[i][1]-1]-lst[i][2]
  if v>V:
    v=V
print(v)
Buggy python submission (verdict: Time Limit Exceeded):
n,a,b=map(int,input().split())

cmba=1
cmbb=1
p=(10**9)+7
lst=[]
num=pow(2,n,p)-1
for i in range(1,b+1):
  cmbb*=(n-i+1)*(pow(i,p-2,p))%p
  cmba=cmbb
  if i==a:
    lst.append(cmba)
    
num=num-lst[0]-cmbb
num=num%p

print(num)

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

cmba=1
cmbb=1
p=(10**9)+7
lst=[]
num=pow(2,n,p)-1
for i in range(1,b+1):
  cmbb*=((n-i+1)*(pow(i,p-2,p)))%p
  if cmbb>p:
    cmbb=cmbb%p
  cmba=cmbb
  if i==a:
    lst.append(cmba)
    
num=num-lst[0]-cmbb
num=num%p

print(num)

Buggy python submission (verdict: Time Limit Exceeded):
n,a,b=map(int,input().split())

def modpow(a,m,n):
    b=bin(n)
    bi=[]
    for i in range(len(b)-2):
        c=str(b)[len(b)-1-i]
        c=int(c)
        bi.append(c)
    pre_pow=[a%m]
    num=a
    for j in range(len(b)-1):
        num*=num
        num=num%m
        pre_pow.append(num)
    ans=1
    for k in range(len(b)-2):
        if bi[k]!=0:
            ans*=pre_pow[k]
    return(ans%m)

cmba=1
cmbb=1
p=(10**9)+7
lst=[]
num=modpow(2,p,n)-1
for i in range(1,b+1):
  cmbb*=((n-i+1)%p)*(modpow(i,p,p-2)%p)%p
  cmba=cmbb
  if i==a:
    lst.append(cmba)
    
num=num-lst[0]-cmbb
num=num%p

print(num)

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

cmba=1
cmbb=1
p=(10**9)+7
lst=[]
num=pow(2,n,p)-1
for i in range(1,b+1):
  cmbb*=((n-i+1)*(pow(i,p-2,p)))%p
  if cmbb>p:
    cmbb=cmbb%p
  cmba=cmbb
  if i==a:
    lst.append(cmba)
    
num=num-lst[0]-cmbb
num=num%p

print(num)
Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
p=list(map(int,input().split()))
m=0
for i in range(n-k+1):
  if sum(p[i:i+k])>m:
    m=sum(p[i:i+k])
print((m+k)/2)
    


Fixed submission:
n,k=map(int,input().split())
p=list(map(int,input().split()))
a=[0]*n
a[0]=p[0]
for i in range(n-1):
  a[i+1]=a[i]+p[i+1]
m=a[k-1]
for j in range(n-k):
  if a[j+k]-a[j]>m:
    m=a[j+k]-a[j]
print((m+k)/2)

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
p=list(map(int,input().split()))
m=0
l=0
for i in range(n-k+1):
  if sum(p[i:i+k])>m:
    m=sum(p[i:i+k])
    l=(m+k)/2
print(l)
    


Fixed submission:
n,k=map(int,input().split())
p=list(map(int,input().split()))
a=[0]*n
a[0]=p[0]
for i in range(n-1):
  a[i+1]=a[i]+p[i+1]
m=a[k-1]
for j in range(n-k):
  if a[j+k]-a[j]>m:
    m=a[j+k]-a[j]
print((m+k)/2)
Buggy python submission (verdict: Time Limit Exceeded):
import fractions
from functools import reduce
n=int(input())
a=list(map(int,input().split()))
def lcm_base(x,y):
    return (x*y)//fractions.gcd(x,y)
def lcm(*numbers):
    return reduce(lcm_base,numbers,1)
num=lcm(*a)
m=1
for i in range(n):
  m*=a[i]
l=0
for i in range(n):
  l+=num//a[i]
  l=l%((10**9)+7)
print(l)
  
  
  
  
  
  


Fixed submission:
import fractions
from functools import reduce
n=int(input())
a=list(map(int,input().split()))
p=10**9+7
def lcm_base(x,y):
    return (x*y)//fractions.gcd(x,y)
def lcm(*numbers):
    return reduce(lcm_base,numbers,1)
num=lcm(*a)
l=0
for i in range(n):
  l+=num*pow(a[i],p-2,p)
print(l%p)
Buggy python submission (verdict: Runtime Error):
n=int(input())
lst=[]
for i in range(n):
  s,t=input().split()
  T=int(t)
  lst.append([s,t])
x=input()
for j in range(n):
  if lst[j][0]==x:
    k=j
    break
totl=0
for j in range(k+1,n):
  totl+=lst[j][1]
print(totl)

Fixed submission:
n=int(input())
lst=[]
for i in range(n):
  s,t=input().split()
  T=int(t)
  lst.append([s,T])
x=input()
for j in range(n):
  if lst[j][0]==x:
    k=j
    break
totl=0
for j in range(k+1,n):
  totl+=lst[j][1]
print(totl)
Buggy python submission (verdict: Runtime Error):
n=int(input())
s=input()
lst=['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','X','Y','Z']
S=list(s)
for i in range(len(list(s))):
  idx=lst.index(S[i])
  S[i]=lst[(idx+n)%len(lst)]
t=''.join(S)
print(t)
  


Fixed submission:
n=int(input())
s=input()
lst=['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z']
S=list(s)
for i in range(len(S)):
  idx=lst.index(S[i])
  S[i]=lst[(idx+n)%(len(lst))]
t=''.join(S)
print(t)

Buggy python submission (verdict: Runtime Error):
n=int(input())
s=input()
lst=['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','X','Y','Z']
S=list(s)
for i in range(len(s)):
  idx=lst.index(S[i])
  S[i]=lst[(idx+n)%len(lst)]
t=''.join(S)
print(t)
  


Fixed submission:
n=int(input())
s=input()
lst=['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z']
S=list(s)
for i in range(len(S)):
  idx=lst.index(S[i])
  S[i]=lst[(idx+n)%(len(lst))]
t=''.join(S)
print(t)

Buggy python submission (verdict: Runtime Error):
n=int(input())
s=input()
lst=['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','X','Y','Z']
S=list(s)
for i in range(n):
  idx=lst.index(S[i])
  S[i]=lst[(idx+n)%len(lst)]
t=''.join(S)
print(t)
  

Fixed submission:
n=int(input())
s=input()
lst=['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z']
S=list(s)
for i in range(len(S)):
  idx=lst.index(S[i])
  S[i]=lst[(idx+n)%(len(lst))]
t=''.join(S)
print(t)
Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
l=list(map(int,input().split()))
l.sort(reverse=True)
cnt=0
for i in range(n-2):
  for j in range(i+1,n-1):
    for k in range(j+1,n):
      if l[i]<l[j]+l[k]:
        cnt+=1
      else:
        break
print(cnt)
      

Fixed submission:
import bisect
n=int(input())
l=list(map(int,input().split()))
l.sort()
cnt=0
for i in range(n-2):
  a=l[i]
  for j in range(i+1,n-1):
    b=l[j]
    k=bisect.bisect_left(l,a+b)
    cnt+=(k-j-1)
print(cnt)
Buggy python submission (verdict: Runtime Error):
n=int(input())
A=list(map(int,input().split()))
a=[]
for i in range(n):
  a.append([i+1])
for j in range(n):
  a[j].append(A[j])
a.sort(key=lambda x:x[1])
lst=[]
for k in range(n):
  lst.append(a[k][0])
print(''.join(lst))
  


Fixed submission:
n=int(input())
A=list(map(int,input().split()))
a=[]
for i in range(n):
  a.append([i+1,A[i]])
b=sorted(a,key=lambda x:x[1])
lst=[]
for k in range(n):
  lst.append(b[k][0])
print(*lst)
Buggy python submission (verdict: Runtime Error):
a,b=map(int,input().split())
if a<b:
  a,b=b,a
def gcd(m,n):
  while n!=0:
    m,n=n,m%n
  return m
def div(n):
  division=[]
  for i in range(1,int(n**0.5)+1):
    if n%i==0:
      division.append(i)
      if i!=(n//i):
        div.append(n//i)
  return division
lst=div(gcd(a,b))
cnt=1
for i in range((len(lst)+1)//2):
  if len(div(lst[i]))==2:
    cnt+=1
print(cnt)
    
    

Fixed submission:
a,b=map(int,input().split())
if a<b:
  a,b=b,a
def gcd(m,n):
  while n!=0:
    m,n=n,m%n
  return m
def div(l):
  division=[]
  for i in range(1,int(l**0.5)+1):
    if l%i==0:
      division.append(i)
      if i!=(l//i):
        division.append(l//i)
  return division
lst=div(gcd(a,b))
cnt=1
for i in range(len(lst)):
  if len(div(lst[i]))==2:
    cnt+=1
print(cnt)
Buggy python submission (verdict: Time Limit Exceeded):
n,k,q=map(int,input().split())
a=[]
for i in range(q):
  a.append(int(input()))
for j in range(n):
  if k-q+(a.count(j+1))>0:
    print('Yes')
  else:
    print('No')

Fixed submission:
import sys
n,k,q=map(int,input().split())
if k-q>0:
  for i in range(n):
    print('Yes')
  sys.exit()
a=[0]*n
for i in range(q):
  b=int(input())
  a[b-1]+=1
for j in range(n):
  if k-q+a[j]>0:
    print('Yes')
  else:
    print('No')
Buggy python submission (verdict: Runtime Error):
n=int(input())
h=list(map(int,input().split()))
cnt=0
lst=[]
for i in range(n-1):
  if h[i+1]<=h[i]:
    cnt+=1
    if i==n-1:
      lst.append(cnt)
  else:
    lst.append(cnt)
    cnt=0
print(max(lst))    

Fixed submission:
import sys
n=int(input())
h=list(map(int,input().split()))
cnt=0
lst=[]
if n==1:
  print(0)
  sys.exit()
for i in range(n-1):
  if h[i+1]<=h[i]:
    cnt+=1
    if i==(n-2):
      lst.append(cnt)
  else:
    lst.append(cnt)
    cnt=0
print(max(lst))
Buggy python submission (verdict: Runtime Error):
n=int(input())
v=list(map(int,input().split()))
V=v.sort()
cnt=(V[0]+V[1])/2
for i in range(2,n):
  cnt=(cnt+V[i])/2
print(cnt)

Fixed submission:
n=int(input())
v=list(map(int,input().split()))
v.sort()
cnt=(v[0]+v[1])/2
if n==2:
  print((v[0]+v[1])/2)
else:
  for i in range(2,n):
    cnt=(cnt+v[i])/2
  print(cnt)
Buggy python submission (verdict: Runtime Error):
k,x=map(int,input().split())
lst=[]
for i in range(1,2*k):
  lst.append(x-k+i)
lst_2=''.join(lst)
print(lst_2)


Fixed submission:
k,x=map(int,input().split())
lst=[]
for i in range(1,2*k):
  lst.append(x-k+i)
for j in range(len(lst)):
  print(lst[j])

Buggy python submission (verdict: Runtime Error):
k,x=map(int,input().split())
lst=[]
for i in range(1,2*k):
  lst.append(x-k+i)
lst_2=lst.split('')
print(lst_2)


Fixed submission:
k,x=map(int,input().split())
lst=[]
for i in range(1,2*k):
  lst.append(x-k+i)
for j in range(len(lst)):
  print(lst[j])

Buggy python submission (verdict: Runtime Error):
k,x=map(int,input().split())
lst=[]
for i in range(1,2*k):
  lst.append(x-k+i)
lst_2=''.split(lst)
print(lst_2)


Fixed submission:
k,x=map(int,input().split())
lst=[]
for i in range(1,2*k):
  lst.append(x-k+i)
for j in range(len(lst)):
  print(lst[j])

Buggy python submission (verdict: Runtime Error):
k,x=map(int,input().split())
lst=[]
for i in range(1,k):
  lst.append(x-k+i)
lst.append(x)
for j in range(1,k):
  lst.append(x+j)
print(''.join(lst))


Fixed submission:
k,x=map(int,input().split())
lst=[]
for i in range(1,2*k):
  lst.append(x-k+i)
for j in range(len(lst)):
  print(lst[j])

Buggy python submission (verdict: Runtime Error):
k,x=map(int,input().split())
lst=[x]
for i in range(1,k):
  lst.append(x-i)
  lst.append(x+i)
print(','.join(lst))


Fixed submission:
k,x=map(int,input().split())
lst=[]
for i in range(1,2*k):
  lst.append(x-k+i)
for j in range(len(lst)):
  print(lst[j])
Buggy python submission (verdict: Runtime Error):
n=int(input())
T=[]
for i in range(n):
  T.append(tuple(sorted(input().split())))
U=set(T)
cnt=[]
for j in range(len(U)):
  cnt.append(T.count(U[j]))
conb=[]
for k in range(len(U)):
  conb.append(cnt[k]*(cnt[k]-1)/2)
print(sum(conb))
  
  
  
  


Fixed submission:
n=int(input())
d={}
totl=0

for i in range(n):
  s=list(input())
  s.sort()
  t=''.join(s)
  
  if t in d:
    d[t]+=1
  else:
    d[t]=1

for t in d:
  totl+=d[t]*(d[t]-1)/2

print(int(totl))

Buggy python submission (verdict: Runtime Error):
n=int(input())
S=[]
for i in range(n):
  S.append(sorted(input().split()))
print(n-len(set(S)))
  
  

Fixed submission:
n=int(input())
d={}
totl=0

for i in range(n):
  s=list(input())
  s.sort()
  t=''.join(s)
  
  if t in d:
    d[t]+=1
  else:
    d[t]=1

for t in d:
  totl+=d[t]*(d[t]-1)/2

print(int(totl))
Buggy python submission (verdict: Runtime Error):
n=int(input())
cnt=0
J=0
for i in range(n):
  for j in range(5):
    if 10**j=<i<10**(j+1):
      J=j
      break
  if J%2==0:
    cnt+=1
print(cnt)
 
 


Fixed submission:
n=int(input())
cnt=0
for i in range(1,n+1):
  for j in range(6):
    if 10**j<=i<10**(j+1):
      J=j
      break
  if J%2==0:
    cnt+=1
print(cnt)

Buggy python submission (verdict: Runtime Error):
n=int(input())
cnt=0
for i in range(n):
  for j in range(5):
    if 10**j=<i<10**(j+1):
      J=j
      break
  if J%2==0:
    cnt+=1
print(cnt)
 
  
  

Fixed submission:
n=int(input())
cnt=0
for i in range(1,n+1):
  for j in range(6):
    if 10**j<=i<10**(j+1):
      J=j
      break
  if J%2==0:
    cnt+=1
print(cnt)
Buggy python submission (verdict: Runtime Error):
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
totl=0
for i in range(n-1):
  if a[i]+a[i+1]<b[i]:
    totl+=a[i]+a[i+1]
    a[i]=0
    a[i+1]=0
  else:
    totl+=b[i]
    if a[i]<b[i]:
      a[i]=0
      a[i+1]-=b[i]-a[i]
    else:
      a[i]-=b[i]
    

print(totl)
  


Fixed submission:
n=int(input())
p=list(map(int,input().split()))
cnt=0
for i in range(n):
  if p[i]!=i+1:
    cnt+=1
if cnt>2:
  print('NO')
else:
  print('YES')

Buggy python submission (verdict: Runtime Error):
n=int(input())
p=list(map(int,input().split()))
q=[]
for i in range(n-1):
  q.append(p[i+1]-p[i])
cnt=q.count(1)
if cnt=>3:
  print('NO')
else:
  print('YES')
  

Fixed submission:
n=int(input())
p=list(map(int,input().split()))
cnt=0
for i in range(n):
  if p[i]!=i+1:
    cnt+=1
if cnt>2:
  print('NO')
else:
  print('YES')