Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
l=[]
for i in range(300):
  l.append(i**2)
l=set(l)
for i in range(1,n+1):
  ct=0
  for j1 in range(1,int(n**0.5)+2):
    for j2 in range(1,int(n**0.5)+2):
      a=j1+j2
      b=i-j1**2-j2**2-j1*j2
      for k in range(len(l)):
        if a**2+4*b in l:
          k=int((a**2+4*b)**0.5)
          if (a+k)%2==0:
            j3=(-a+k)//2
            if j3>0:
              ct+=1
              break
  print(ct)

Fixed submission:
n=int(input())
l=[]
for i in range(300):
  l.append(i**2)
l=set(l)
for i in range(1,n+1):
  ct=0
  for j1 in range(1,int(n**0.5)+2):
    for j2 in range(1,int(n**0.5)+2):
      a=j1+j2
      b=i-j1**2-j2**2-j1*j2
      if a**2+4*b in l:
        k=int((a**2+4*b)**0.5)
        if (a+k)%2==0:
          j3=(-a+k)//2
          if j3>0:
            ct+=1
  print(ct)

Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
l=[]
for i in range(500):
  l.append(i**2)
l=set(l)
for i in range(1,n+1):
  ct=0
  for j1 in range(1,int(n**0.5)+2):
    for j2 in range(1,int(n**0.5)+2):
      a=j1+j2
      b=i-j1**2-j2**2-j1*j2
      for k in range(len(l)):
        if a**2+4*b in l:
          k=int((a**2+4*b)**0.5)
          if (a+k)%2==0:
            j3=(-a+k)//2
            if j3>0:
              ct+=1
              break
  print(ct)

Fixed submission:
n=int(input())
l=[]
for i in range(300):
  l.append(i**2)
l=set(l)
for i in range(1,n+1):
  ct=0
  for j1 in range(1,int(n**0.5)+2):
    for j2 in range(1,int(n**0.5)+2):
      a=j1+j2
      b=i-j1**2-j2**2-j1*j2
      if a**2+4*b in l:
        k=int((a**2+4*b)**0.5)
        if (a+k)%2==0:
          j3=(-a+k)//2
          if j3>0:
            ct+=1
  print(ct)

Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
l=[]
for i in range(1000):
  l.append(i**2)
ans=[0]*n
for i in range(1,n+1):
  ct=0
  for j1 in range(1,int(n**0.5)+2):
    for j2 in range(1,int(n**0.5)+2):
      a=j1+j2
      b=i-j1**2-j2**2-j1*j2
      for k in range(len(l)):
        if l[k]==a**2+4*b:
          if (a+k)%2==0:
            j3=(-a+k)//2
            if j3>0:
              ct+=1
  print(ct)

Fixed submission:
n=int(input())
l=[]
for i in range(300):
  l.append(i**2)
l=set(l)
for i in range(1,n+1):
  ct=0
  for j1 in range(1,int(n**0.5)+2):
    for j2 in range(1,int(n**0.5)+2):
      a=j1+j2
      b=i-j1**2-j2**2-j1*j2
      if a**2+4*b in l:
        k=int((a**2+4*b)**0.5)
        if (a+k)%2==0:
          j3=(-a+k)//2
          if j3>0:
            ct+=1
  print(ct)
Buggy python submission (verdict: Time Limit Exceeded):
t=int(input())
l=[list(map(int,input().split())) for i in range(t)]
for i in range(t):
  ans=[]
  for j1 in range(70):
    for j2 in range(70):
      for j3 in range(70):
        x=(2**j1)*(3**j2)*(5**j3)
        ans.append(l[i][1]*j1+l[i][2]*j2+l[i][3]*j3+l[i][4]+l[i][4]*(abs(x-l[i][0])))
  print(min(ans))

Fixed submission:
import math
import sys
from functools import lru_cache
sys.setrecursionlimit(10**6)
t=int(input())
for i in range(t):
  n,a,b,c,d=map(int,input().split())
  @lru_cache(maxsize=None)
  def f(n):
    if n==0:
      return 0
    if n==1:
      return d
    else:
      x=n*d
      
      q,r=divmod(n,2)
      if r==0:
        x=min(x,f(q)+a)
      else:
        x=min(x,f(q)+a+d,f(q+1)+a+d)
      
      q,r=divmod(n,3)
      if r==0:
        x=min(x,f(q)+b)
      elif r==1:
        x=min(x,f(q)+b+d,f(q+1)+b+d*2)
      else:
        x=min(x,f(q)+b+d*2,f(q+1)+b+d)
      
      q,r=divmod(n,5)
      if r==0:
        x=min(x,f(q)+c)
      elif r==1:
        x=min(x,f(q)+c+d,f(q+1)+c+d*4)
      elif r==2:
        x=min(x,f(q)+c+d*2,f(q+1)+c+d*3)
      elif r==3:
        x=min(x,f(q)+c+d*3,f(q+1)+c+d*2)
      else:
        x=min(x,f(q)+c+d*4,f(q+1)+c+d)
      
      return x
  
  print(f(n))
Buggy python submission (verdict: Time Limit Exceeded):
import sys
n=int(input())
s=[list(input()) for i in range(n)]
L1=[]
L2=[]
ct1=0;ct2=0
for i in range(n):
  ct3=0
  l=[0]
  for j in range(len(s[i])):
    if s[i][j]=='(':
      ct1+=1
      ct3+=1
      l.append(ct3)
    else:
      ct2+=1
      ct3-=1
      l.append(ct3)
  if l[-1]>=0:
    L1.append((min(l),l[-1]))
  else:
    L2.append((min(l)-l[-1],-l[-1]))
if ct1!=ct2:
  print('No')
  sys.exit()

L1.sort()
L1.reverse()
ct4=0
for i in range(len(L1)):
  if ct4+L1[i][0]<0:
    print('No')
    sys.exit()
  ct4+=L1[i][1]

L2.sort()
L2.reverse()
ct5=0
for i in range(len(L2)):
  if ct5+L2[i][0]<0:
    print('No')
    sys.exit()
  ct5+=L2[i][1]

print('Yes')

Fixed submission:
import sys
n=int(input())
s=[list(input()) for i in range(n)]
L1=[]
L2=[]
ct1=0;ct2=0
for i in range(n):
  ct3=0
  l=[0]
  for j in range(len(s[i])):
    if s[i][j]=='(':
      ct1+=1
      ct3+=1
      l.append(ct3)
    else:
      ct2+=1
      ct3-=1
      l.append(ct3)
  if l[-1]>=0:
    L1.append((min(l),l[-1]))
  else:
    L2.append((min(l)-l[-1],-l[-1]))
if ct1!=ct2:
  print('No')
  sys.exit()

L1.sort()
L1.reverse()
ct4=0
for i in range(len(L1)):
  if ct4+L1[i][0]<0:
    print('No')
    sys.exit()
  ct4+=L1[i][1]

L2.sort()
L2.reverse()
ct5=0
for i in range(len(L2)):
  if ct5+L2[i][0]<0:
    print('No')
    sys.exit()
  ct5+=L2[i][1]

print('Yes')
Buggy python submission (verdict: Time Limit Exceeded):
n,s=map(int,input().split())
a=list(map(int,input().split()))
mod=998244353
dp=[[[0]*3 for i in range(s+1)] for j in range(n+1)]
dp[0][0][0]=1
for i in range(n):
  for j in range(s+1):
    if j>=a[i]:
      x=dp[i][j-a[i]][0]+dp[i][j-a[i]][1]+dp[i][j][0]+dp[i][j][1]
      dp[i+1][j][1]=x%mod
      dp[i+1][j][2]=(x+dp[i][j][2])%mod
    else:
      dp[i+1][j][0]=dp[i][j][0]%mod
      dp[i+1][j][1]=(dp[i][j][0]+dp[i][j][1])%mod
      dp[i+1][j][2]=(dp[i][j][0]+dp[i][j][1]+dp[i][j][2])%mod
print(dp[n][s][2])

Fixed submission:
n,s=map(int,input().split())
a=list(map(int,input().split()))
mod=998244353
dp0=[[0 for i in range(s+1)] for j in range(n+1)]
dp1=[[0 for i in range(s+1)] for j in range(n+1)]
dp2=[[0 for i in range(s+1)] for j in range(n+1)]
dp0[0][0]=1
for i in range(n):
  for j in range(s+1):
    if j>=a[i]:
      dp1[i+1][j]=(dp0[i][j-a[i]]+dp1[i][j-a[i]]+dp0[i][j]+dp1[i][j])%mod
      dp2[i+1][j]=(dp0[i][j-a[i]]+dp1[i][j-a[i]]+dp0[i][j]+dp1[i][j]+dp2[i][j])%mod
    else:
      dp0[i+1][j]=dp0[i][j]%mod
      dp1[i+1][j]=(dp0[i][j]+dp1[i][j])%mod
      dp2[i+1][j]=(dp0[i][j]+dp1[i][j]+dp2[i][j])%mod
print(dp2[n][s])

Buggy python submission (verdict: Time Limit Exceeded):
n,s=map(int,input().split())
a=list(map(int,input().split()))
mod=998244353
dp=[[[0]*3 for i in range(s+1)] for j in range(n+1)]
dp[0][0][0]=1
for i in range(n):
  for j in range(s+1):
    if j>=a[i]:
      dp[i+1][j][1]=(dp[i][j-a[i]][0]+dp[i][j-a[i]][1]+dp[i][j][0]+dp[i][j][1])%mod
      dp[i+1][j][2]=(dp[i][j-a[i]][0]+dp[i][j-a[i]][1]+dp[i][j][0]+dp[i][j][1]+dp[i][j][2])%mod
    else:
      dp[i+1][j][0]=dp[i][j][0]%mod
      dp[i+1][j][1]=(dp[i][j][1]+dp[i][j][0])%mod
      dp[i+1][j][2]=(dp[i][j][2]+dp[i][j][1]+dp[i][j][0])%mod
print(dp[n][s][2])

Fixed submission:
n,s=map(int,input().split())
a=list(map(int,input().split()))
mod=998244353
dp0=[[0 for i in range(s+1)] for j in range(n+1)]
dp1=[[0 for i in range(s+1)] for j in range(n+1)]
dp2=[[0 for i in range(s+1)] for j in range(n+1)]
dp0[0][0]=1
for i in range(n):
  for j in range(s+1):
    if j>=a[i]:
      dp1[i+1][j]=(dp0[i][j-a[i]]+dp1[i][j-a[i]]+dp0[i][j]+dp1[i][j])%mod
      dp2[i+1][j]=(dp0[i][j-a[i]]+dp1[i][j-a[i]]+dp0[i][j]+dp1[i][j]+dp2[i][j])%mod
    else:
      dp0[i+1][j]=dp0[i][j]%mod
      dp1[i+1][j]=(dp0[i][j]+dp1[i][j])%mod
      dp2[i+1][j]=(dp0[i][j]+dp1[i][j]+dp2[i][j])%mod
print(dp2[n][s])
Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
s=list(input())
q=int(input())
c=[chr(i) for i in range(97, 97+26)]
l=[input().split() for i in range(q)]
L=[]
for i in range(q):
  if l[i][0]=='2':
    L.append([int(l[i][1]),int(l[i][2])])

a=[[0 for i in range(n)] for i in range(26)]
b=[]
for i in range(n):
  a[c.index(s[i])][i]=1
for i in range(26):
  x=[0]
  for j in range(n):
    x.append(x[-1]+a[i][j])
  b.append(x)

L2=[[0 for i in range(26)] for i in range(len(L))]
for i in range(len(L)):
  for j in range(26):
    L2[i][j]=b[j][L[i][1]]-b[j][L[i][0]-1]

j2=0
for i in range(q):
  if l[i][0]=='1':
    for j in range(len(L)):
      if L[j][0]<=int(l[i][1])<=L[j][1]:
        L2[j][c.index(l[i][2])]+=1
        L2[j][c.index(s[int(l[i][1])-1])]-=1
    s[int(l[i][1])-1]=l[i][2]
  else:
    ans=0
    for i in range(26):
      if L2[j2][i]!=0:
        ans+=1
    print(ans)
    j2+=1

Fixed submission:
n=int(input())
s=list(input())
q=int(input())
c=[chr(i) for i in range(97, 97+26)]
l=[input().split() for i in range(q)]

def segfunc(x,y):
  return x+y

def init(init_val,c):
  for i in range(n):
    seg[c][i+num-1]=init_val[i]
  for i in range(num-2,-1,-1):
    seg[c][i]=segfunc(seg[c][2*i+1],seg[c][2*i+2])

def update(k,x,c):
  k+=num-1
  seg[c][k]+=x
  while k:
    k=(k-1)//2
    seg[c][k]=segfunc(seg[c][k*2+1],seg[c][k*2+2])

def query(p,q,c):
  if q<=p:
    return ide_ele
  p+=num-1
  q+=num-2
  res=ide_ele
  while q-p>1:
    if p&1==0:
      res=segfunc(res,seg[c][p])
    if q&1==1:
      res=segfunc(res,seg[c][q])
      q-=1
    p=p//2
    q=(q-1)//2
  if p==q:
    res=segfunc(res,seg[c][p])
  else:
    res=segfunc(segfunc(res,seg[c][p]),seg[c][q])
  return res

ide_ele=0

num=2**(n-1).bit_length()
seg=[[ide_ele]*2*num for i in range(26)]

L=[[0 for i in range(n)] for j in range(26)]
for i in range(n):
  L[c.index(s[i])][i]+=1

for i in range(26):
  init(L[i],i)

for i in range(q):
  if l[i][0]=='1':
    update(int(l[i][1])-1,1,c.index(l[i][2]))
    update(int(l[i][1])-1,-1,c.index(s[int(l[i][1])-1]))
    s[int(l[i][1])-1]=l[i][2]
  else:
    ct=0
    for j in range(26):
      if query(int(l[i][1])-1,int(l[i][2]),j)!=0:
        ct+=1
    print(ct)
Buggy python submission (verdict: Time Limit Exceeded):
import bisect
n,k=map(int,input().split())
a=list(map(int,input().split()))
N=[];Z=[];P=[]
for i in range(n):
  if a[i]<0:
    N.append(a[i])
  elif a[i]==0:
    Z.append(a[i])
  else:
    P.append(a[i])

if k<=len(N)*len(P):
  for i in range(len(N)):
    N[i]*=-1
  N.sort()
  P.sort()
  L=0;R=10**18+1
  while R-L>1:
    x=(L+R)//2
    ct=0
    for j in range(len(N)):
      ct+=len(P)-bisect.bisect_left(P,(x+N[j]-1)//N[j])
    if ct<k:
      R=x
    else:
      L=x
  print(-L)

elif k<=len(N)*len(P)+(len(Z)*(len(Z)-1))//2+len(Z)*(len(N)+len(P)):
  print(0)

else:
  y=len(N)*len(P)+(len(Z)*(len(Z)-1))//2+len(Z)*(len(N)+len(P))
  for i in range(len(N)):
    N[i]*=-1
  N.sort()
  P.sort()
  L=0;R=10**18+1
  while R-L>1:
    x=(L+R)//2
    ct=0
    for j in range(1,len(N)):
      ct+=bisect.bisect_right(N[0:j],x//N[j])
    for j in range(1,len(P)):
      ct+=bisect.bisect_right(P[0:j],x//P[j])
    if ct<k-y:
      L=x
    else:
      R=x
  print(R)

Fixed submission:
import bisect
n,k=map(int,input().split())
a=list(map(int,input().split()))
N=[];Z=[];P=[]
for i in range(n):
  if a[i]<0:
    N.append(a[i])
  elif a[i]==0:
    Z.append(a[i])
  else:
    P.append(a[i])

if k<=len(N)*len(P):
  for i in range(len(N)):
    N[i]*=-1
  N.sort()
  P.sort()
  Nr=list(reversed(N))
  L=0;R=10**18+1
  while R-L>1:
    x=(L+R)//2
    ct=0
    ct2=0
    for j in range(len(Nr)):
      if ct2!=len(P):
        while Nr[j]*P[ct2]<x:
          ct2+=1
          if ct2==len(P):
            break
      ct+=len(P)-ct2
    if ct<k:
      R=x
    else:
      L=x
  print(-L)

elif k<=len(N)*len(P)+(len(Z)*(len(Z)-1))//2+len(Z)*(len(N)+len(P)):
  print(0)

else:
  y=len(N)*len(P)+(len(Z)*(len(Z)-1))//2+len(Z)*(len(N)+len(P))
  for i in range(len(N)):
    N[i]*=-1
  N.sort()
  P.sort()
  L=0;R=10**18+1
  Nr=list(reversed(N))
  Pr=list(reversed(P))
  while R-L>1:
    x=(L+R)//2
    ct=0
    ct2=0
    for j in range(len(Nr)):
      if ct2!=len(N):
        while Nr[j]*N[ct2]<=x:
          ct2+=1
          if ct2==len(N):
            break
      ct+=min(ct2,len(N)-1-j)
    ct3=0
    for j in range(len(Pr)):
      if ct3!=len(P):
        while Pr[j]*P[ct3]<=x:
          ct3+=1
          if ct3==len(P):
            break
      ct+=min(ct3,len(P)-1-j)
    if ct<k-y:
      L=x
    else:
      R=x
  print(R)
Buggy python submission (verdict: Runtime Error):
import sys
n=list(input())
N=len(n)
k=int(input())
dp=[[0 for i in range(len(n))] for j in range(k)]
ans=0
x=int(n[0])

if k==1:
  ans+=(N-1)*9
  ans+=x
  print(ans)
  sys.exit()

elif k==2:
  ans+=(N-1)*(N-2)*81//2
  ans+=(x-1)*(N-1)*9
  n2=n[1:N+1]
  N2=len(n2)
  x=int(n2[0])
  ans+=(N2-1)*9
  ans+=x
  print(ans)
  sys.exit()

else:
  ans+=(N-1)*(N-2)*(N-3)*729//6
  ans+=(x-1)*(N-1)*(N-2)*81//2
  n=n[1:N+1]
  N=len(n)
  x=int(n[0])
  ans2=0
  ans2+=(N-1)*(N-2)*81//2
  ans2+=(x-1)*(N-1)*9
  n2=n[1:N+1]
  N2=len(n2)
  x=int(n2[0])
  ans2+=(N2-1)*9
  ans2+=x
  ans+=ans2
  print(ans)
  sys.exit()

Fixed submission:
import sys
n=list(input())
N=len(n)
k=int(input())
x=int(n[0])
if N<k:
  print(0)
  sys.exit()

def s1(m):
  N=len(m)
  x=int(m[0])
  if N>1 and x==0:
    m2=m[1:N+1]
    return s1(m2)
  elif x==0:
    return 0
  else:
    ans=0
    ans+=(N-1)*9
    ans+=x
    return ans

def s2(m):
  N=len(m)
  x=int(m[0])
  if N>1 and x==0:
    m2=m[1:N+1]
    return s2(m2)
  elif x==0:
    return 0
  else:
    ans=0
    ans+=((N-1)*(N-2))*81//2
    ans+=((x-1)*(N-1))*9
    m2=m[1:N+1]
    ans+=s1(m2)
    return ans
  
def s3(m):
  N=len(m)
  x=int(m[0])
  if N>1 and x==0:
    m2=m[1:N+1]
    return s3(m2)
  elif x==0:
    return 0
  else:
    ans=0
    ans+=((N-1)*(N-2)*(N-3)*729)//6
    ans+=((x-1)*(N-1)*(N-2)*81)//2
    m2=m[1:N+1]
    ans+=s2(m2)
    return ans

if k==1:
  print(s1(n))
  sys.exit()

if k==2:
  print(s2(n))
  sys.exit()

if k==3:
  print(s3(n))
  sys.exit()
Buggy python submission (verdict: Runtime Error):
def cmb(n,r,mod):
  if r<0 or r>n:
    return 0
  r=min(r,n-r)
  return g1[n]*g2[r]*g2[n-r]%mod
 
r1,c1,r2,c2=map(int,input().split())
mod=10**9+7

g1=[1,1]
g2=[1,1]
inverse=[0,1]
 
for i in range(2,10**6+1):
  g1.append((g1[-1]*i)%mod)
  inverse.append((-inverse[mod%i]*(mod//i))%mod)
  g2.append((g2[-1]*inverse[-1])%mod)

def g(r,c):
  ans=0
  for i in range(1,c+1):
    ans+=cmb(r+i-1,i,mod)
  return ans

print((g(r2+1,c2+1)-g(r2+1,c1)-g(r1,c2+1)+g(r1,c1)+mod)%mod)

Fixed submission:
def cmb(n,r,mod):
  if r<0 or r>n:
    return 0
  r=min(r,n-r)
  return g1[n]*g2[r]*g2[n-r]%mod
 
r1,c1,r2,c2=map(int,input().split())
mod=10**9+7

g1=[1,1]
g2=[1,1]
inverse=[0,1]
 
for i in range(2,2*10**6+2):
  g1.append((g1[-1]*i)%mod)
  inverse.append((-inverse[mod%i]*(mod//i))%mod)
  g2.append((g2[-1]*inverse[-1])%mod)

def g(r,c):
  ans=0
  for i in range(1,c+1):
    ans+=cmb(r+i-1,i,mod)
  return ans

print((g(r2+1,c2+1)-g(r2+1,c1)-g(r1,c2+1)+g(r1,c1)+mod)%mod)
Buggy python submission (verdict: Runtime Error):
n=int(input())
c=list(map(int,input().split()))
mod=10**9+7
c.sort()
c.reverse()
ans=0
x=pow(2,n-2,mod)
for i in range(n):
  ans+=c[i]*(i+2)*x
  ans%=mod
ans*=pow(2,n,mod)
ans%=mod
print(ans)

Fixed submission:
import sys
n=int(input())
c=list(map(int,input().split()))
mod=10**9+7
if n==1:
  print(c[0]*2%mod)
  sys.exit()
c.sort()
c.reverse()
ans=0
x=pow(2,n-2,mod)
for i in range(n):
  ans+=c[i]*(i+2)*x
  ans%=mod
ans*=pow(2,n,mod)
ans%=mod
print(ans)
Buggy python submission (verdict: Runtime Error):
import sys
n=int(input())
if n==2 or n==5:
  print(-1)
  sys.exit()
if n%3==0:
  a=[]
  b=[]
  for j in range(n//3):
    a.append('a')
    a.append('a')
    a.append('.')
    b.append('.')
    b.append('.')
    b.append('a')
  for i in range(n):
    if i%3==0:
      print(''.join(a))
    else:
      print(''.join(b))
  sys.exit()

elif n%4==0:
  a=[]
  b=[]
  c=[]
  d=[]
  for j in range(n//4):
    a.append('a')
    a.append('a')
    a.append('c')
    a.append('d')
    b.append('b')
    b.append('b')
    b.append('c')
    b.append('d')
    c.append('e')
    c.append('f')
    c.append('g')
    c.append('g')
    d.append('e')
    d.append('f')
    d.append('h')
    d.append('h')
  for i in range(n):
    if i%4==0:
      print(''.join(a))
    elif i%4==1:
      print(''.join(b))
    elif i%4==2:
      print(''.join(c))
    elif i%4==3:
      print(''.join(d))
  sys.exit()

for i in range(n//3):
   if (n-i*3)%4==0:
     x=i
     y=(n-i*3)//4
     break

ans=[]
for i in range(n):
  ans1=['.']*n
  ans.append(ans1)

for i in range(x):
  ans[i*3][i*3]='a'
  ans[i*3][i*3+1]='b'
  ans[i*3][i*3+2]='b'
  ans[i*3+1][i*3]='a'
  ans[i*3+1][i*3+2]='a'
  ans[i*3+2][i*3]='b'
  ans[i*3+2][i*3+1]='b'
  ans[i*3+2][i*3+2]='a'
for i in range(y):
  ans[x*3+i*4][x*3+i*3+i*4]='a'
  ans[x*3+i*4][x*3+i*3+i*4+1]='b'
  ans[x*3+i*4][x*3+i*3+i*4+2]='c'
  ans[x*3+i*4][x*3+i*3+i*4+3]='c'
  
  ans[x*3+i*4+1][x*3+i*3+i*4]='a'
  ans[x*3+i*4+1][x*3+i*3+i*4+1]='b'
  ans[x*3+i*4+1][x*3+i*3+i*4+2]='d'
  ans[x*3+i*4+1][x*3+i*3+i*4+3]='d'
  
  ans[x*3+i*4+2][x*3+i*3+i*4]='e'
  ans[x*3+i*4+2][x*3+i*3+i*4+1]='e'
  ans[x*3+i*4+2][x*3+i*3+i*4+2]='g'
  ans[x*3+i*4+2][x*3+i*3+i*4+3]='h'
  
  ans[x*3+i*4+3][x*3+i*3+i*4]='f'
  ans[x*3+i*4+3][x*3+i*3+i*4+1]='f'
  ans[x*3+i*4+3][x*3+i*3+i*4+2]='g'
  ans[x*3+i*4+3][x*3+i*3+i*4+3]='h'

for i in range(n):
  print(''.join(ans[i]))

Fixed submission:
import sys
n=int(input())
if n==2:
  print(-1)
  sys.exit()
if n==3:
  print('aa.')
  print('..a')
  print('..a')
  sys.exit()

x=(n//4)-1
y=(n%4)+4

l=[[['a','a','b','c'],['d','d','b','c'],['b','c','a','a'],['b','c','d','d']],[['a','a','b','b','a'],['b','c','c','.','a'],['b','.','.','c','b'],['a','.','.','c','b'],['a','b','b','a','a']],[['a','a','b','c','.','.'],['d','d','b','c','.','.'],['.','.','a','a','b','c'],['.','.','d','d','b','c'],['b','c','.','.','a','a'],['b','c','.','.','d','d']],[['a','a','b','b','c','c','.'],['d','d','.','d','d','.','a'],['.','.','d','.','.','d','a'],['.','.','d','.','.','d','b'],['d','d','.','d','d','.','b'],['.','.','d','.','.','d','c'],['.','.','d','.','.','d','c']]]

if n<8:
  for i in range(n):
    print(''.join(l[n-4][i]))
  sys.exit()

ans=[]
for i in range(n):
  ans1=['.']*n
  ans.append(ans1)

for i in range(x):
  for j in range(4):
    for k in range(4):
      ans[i*4+j][i*4+k]=l[0][j][k]

for j in range(y):
  for k in range(y):
    ans[x*4+j][x*4+k]=l[y-4][j][k]

for i in range(n):
  print(''.join(ans[i]))
Buggy python submission (verdict: Time Limit Exceeded):
import collections
n,k=map(int,input().split())
a=list(map(int,input().split()))
m=[]
m2=[0]
for i in range(n):
  m.append(a[i])
for i in range(n):
  m2.append((m2[-1]+m[i]))
for i in range(n+1):
  m2[i]-=i
  m2[i]%=k

ans=0
dict={}
for i in range(1,n+1):
  x=m2[i]
  if i<=k-1:
    dict[i-1]=m2[i-1]
  else:
    dict[i-1]=m2[i-1]
    del dict[i-k]
  d=collections.Counter(dict.values())
  ans+=d[x]
print(ans)

Fixed submission:
import collections
n,k=map(int,input().split())
a=list(map(int,input().split()))
m=[]
m2=[0]
for i in range(n):
  m.append(a[i])
for i in range(n):
  m2.append((m2[-1]+m[i]))
for i in range(n+1):
  m2[i]-=i
  m2[i]%=k

ans=0
dict=collections.defaultdict(int)
for i in range(1,n+1):
  x=m2[i]
  if i<=k-1:
    dict[m2[i-1]]+=1
  else:
    dict[m2[i-1]]+=1
    dict[m2[i-k]]-=1
  ans+=dict[x]
print(ans)
Buggy python submission (verdict: Runtime Error):
m=int(input())
l=[list(map(int,input().split())) for i in range(m)]
ct=0;sum=0
for i in range(m):
  ct+=l[i][0]*l[i][1]
  sum+=l[i][1]
ans=sum-1
sct=str(ct)
if len(sct)>=2:
  for i in range(1,len(sct)):
    ans+=int(ct[0:i])
print(ans)

Fixed submission:
m=int(input())
l=[list(map(int,input().split())) for i in range(m)]
ct=0;sum=0
for i in range(m):
  ct+=l[i][0]*l[i][1]
  sum+=l[i][1]
print(sum-1+((ct-1)//9))
Buggy python submission (verdict: Time Limit Exceeded):
def dijkstra(s,n,w,cost):
    d = [float("inf")] * n
    used = [False] * n
    d[s] = 0
    
    while True:
        v = -1
        for i in range(n):
            if (not used[i]) and (v == -1):
               v = i
            elif (not used[i]) and d[i] < d[v]:
                v = i
        if v == -1:
               break
        used[v] = True
               
        for j in range(n):
               d[j] = min(d[j],d[v]+cost[v][j])
    return d

n,m = map(int,input().split())

cost = [[float("inf") for i in range(n)] for i in range(n)] 
for i in range(m):
    x,y,z = map(int,input().split())
    cost[x-1][y-1] = z
    cost[y-1][x-1] = z
for i in range(1,n):
    cost[i][i-1]=0
x=dijkstra(0,n,m,cost)[n-1]
if x==float("inf"):
  print(-1)
else:
  print(x)

Fixed submission:
import heapq
def dijkstra_heap(s):
    d = [float("inf")] * n
    used = [True] * n 
    d[s] = 0
    used[s] = False
    edgelist = []
    for e in edge[s]:
        heapq.heappush(edgelist,e)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        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


n,m = map(int,input().split())

edge = [[] for i in range(n)]
for i in range(m):
    x,y,z = map(int,input().split())
    edge[x-1].append([z,y-1])
    edge[y-1].append([z,x-1]) 
for i in range(1,n):
  edge[i].append([0,i-1])
x=dijkstra_heap(0)[n-1]
if x==float("inf"):
  print(-1)
else:
  print(x)
Buggy python submission (verdict: Time Limit Exceeded):
import heapq
n,k=map(int,input().split())
a=list(map(int,input().split()))
f=list(map(int,input().split()))
a.sort()
f.sort()
f.reverse()
l=[]
for i in range(n):
  l.append([-a[i]*f[i],-f[i],a[i]])
heapq.heapify(l)
for i in range(k):
  x=heapq.heappop(l)
  heapq.heappush(l,[-(max(x[2]-1,0))*(-x[1]),x[1],max(x[2]-1,0)])
l=list(l)
L=[]
for i in range(n):
  L.append(l[i][0])
print(-min(L))

Fixed submission:
import heapq
n,k=map(int,input().split())
a=list(map(int,input().split()))
f=list(map(int,input().split()))
a.sort()
f.sort()
f.reverse()
l=0;r=max(a)*max(f)
sum=sum(a)
while abs(l-r)>1:
  x=(l+r)//2
  ct=0
  for i in range(n):
    ct+=max(a[i]-(x//f[i]),0)
  if ct<=k:
    r=x
  else:
    l=x+1
x=l
ct=0
for i in range(n):
  ct+=max(a[i]-(x//f[i]),0)
if ct<=k:
  print(l)
else:
  print(r)
Buggy python submission (verdict: Time Limit Exceeded):
from operator import itemgetter
n,m=map(int,input().split())
l=[]
for i in range(m):
  l2=[]
  a,b=map(int,input().split())
  l2.append(a)
  x=list(map(int,input().split()))
  ct=0
  for i in range(n):
    if i+1 in x:
      ct+=2**i
  l2.append(ct)
  l.append(l2)

dp=[[999999999999 for i in range(2**n)] for j in range(m+1)]
dp[0][0]=0
for i in range(1,m+1):
  for j in range(2**n):
    dp[i][j|l[i-1][1]]=min(dp[i-1][j|l[i-1][1]],dp[i-1][j]+l[i-1][0],dp[i][j|l[i-1][1]])
  for j in range(2**n):
    dp[i][j]=min(dp[i][j],dp[i-1][j])

if dp[m][2**n-1]<10**11:
  print(dp[m][2**n-1])
else:
  print(-1)

Fixed submission:
from operator import itemgetter
n,m=map(int,input().split())
l=[]
for i in range(m):
  l2=[]
  a,b=map(int,input().split())
  l2.append(a)
  x=list(map(int,input().split()))
  ct=0
  for i in range(n):
    if i+1 in x:
      ct+=2**i
  l2.append(ct)
  l.append(l2)

dp=[[999999999999 for i in range(2**n)] for j in range(m+1)]
dp[0][0]=0
for i in range(1,m+1):
  for j in range(2**n):
    dp[i][j|l[i-1][1]]=min(dp[i-1][j|l[i-1][1]],dp[i-1][j]+l[i-1][0],dp[i][j|l[i-1][1]])
  for j in range(2**n):
    dp[i][j]=min(dp[i][j],dp[i-1][j])

if dp[m][2**n-1]<10**11:
  print(dp[m][2**n-1])
else:
  print(-1)