Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
n,m=map(int, input().split())
def is_prime(N):
    is_prime=[True]*(N+1)
    is_prime[0:2]=False,False
    for i in range(int(N**0.5)+1):
        if is_prime[i]==False:
            continue
        for j in range(i*2,N+1,i):
            is_prime[j]=False
    return is_prime
def primes(N):
    prime=is_prime(N)
    return [i for i in range(N+1) if prime[i]]
def prime_factorization(n):
    ps=primes(int(n**0.5))
    r=[]
    for i,p in enumerate(ps):
        num=0
        while(True):
            x,y=divmod(n,p)
            if y!=0:
                break
            n=x
            num+=1
        if num>0:
            r.append((p,num))
    if n>1:
        r.append((n,1))
    return r

f=prime_factorization(m)
from scipy.special import perm, comb
ans=1
mod=10**9+7
for p in f:
    ans*=comb(p[1]+n-1,n-1,exact=True)
    ans%=mod
print(ans)


Fixed submission:
n,m=map(int, input().split())
def is_prime(N):
    is_prime=[True]*(N+1)
    is_prime[0:2]=False,False
    for i in range(int(N**0.5)+1):
        if is_prime[i]==False:
            continue
        for j in range(i*2,N+1,i):
            is_prime[j]=False
    return is_prime
def primes(N):
    prime=is_prime(N)
    return [i for i in range(N+1) if prime[i]]
def prime_factorization(n):
    ps=primes(int(n**0.5))
    r=[]
    for i,p in enumerate(ps):
        num=0
        while(True):
            x,y=divmod(n,p)
            if y!=0:
                break
            n=x
            num+=1
        if num>0:
            r.append((p,num))
    if n>1:
        r.append((n,1))
    return r
mod=10**9+7
def add(a,b):
    return (a+b)%mod
def sub(a,b):
    return (a-b)%mod
def mul(a,b):
    return ((a%mod)*(b%mod))%mod
def pow(x,y):
    if y==0:
        return 1
    elif y==1:
        return x%mod
    elif y%2==0:
        return pow(x,y//2)**2 % mod
    else:
        return pow(x,y//2)**2 * x % mod
def div(a,b):
    return mul(a,pow(b,mod-2))
def fac(n):
    a=1
    for i in range(2,n+1):
        a=mul(a,i)
    return a

f=prime_factorization(m)
ans=1
for p in f:
    ans=mul(ans,fac(p[1]+n-1))
    ans=div(ans,fac(p[1]))
    ans=div(ans,fac(n-1))
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
n,m,q=map(int, input().split())
lr=[list(map(int,input().split())) for i in range(m)]
pq=[list(map(int,input().split())) for i in range(q)]

import numpy as np
a=np.zeros((n+1,n+1),dtype=int)
for i in range(m):
    a[lr[i][0]:,lr[i][1]:]+=1
for i in range(q):
    print(a[pq[i][1],pq[i][1]]-a[pq[i][0]-1,pq[i][1]])

Fixed submission:
n,m,q=map(int, input().split())
lr=[list(map(int,input().split())) for i in range(m)]
pq=[list(map(int,input().split())) for i in range(q)]

a=[[0]*(n+1) for i in range(n+1)]
for i in range(m):
    a[lr[i][0]][lr[i][1]]+=1
for i in range(1,n+1):
    for j in range(1,n+1):
        a[i][j]+=a[i-1][j]
for i in range(1,n+1):
    for j in range(1,n+1):
        a[i][j]+=a[i][j-1]
for i in range(q):
    print(a[pq[i][1]][pq[i][1]]-a[pq[i][0]-1][pq[i][1]])
Buggy python submission (verdict: Time Limit Exceeded):
s=input()
dp=[[0]*4 for i in range(len(s)+1)]
dp[0][0]=1
mod=10**9+7
from copy import deepcopy
def dp_next(dp,i,j,mod):
    dp[i+1][j+1]=(dp[i+1][j+1]+dp[i][j])%mod
for i in range(len(s)):
    if s[i]=='?':
        for j in range(4):
            dp[i+1][j]=dp[i][j]*3
        for j in range(3):
            dp_next(dp,i,j,mod)
        continue
    dp[i+1]=deepcopy(dp[i])
    if s[i]=='A':
        dp_next(dp,i,0,mod)
    elif s[i]=='B':
        dp_next(dp,i,1,mod)
    elif s[i]=='C':
        dp_next(dp,i,2,mod)
print(dp[-1][3])

Fixed submission:
s=input()
import numpy as np
dp=np.zeros((len(s)+1,4),dtype=np.int64)
dp[0][0]=1
mod=10**9+7
for i in range(len(s)):
    if s[i]=='?':
        dp[i+1]=dp[i]*3
        dp[i+1][1:]+=dp[i][:3]
        dp[i+1]%=mod
    else:
        dp[i+1]=dp[i]
        j=ord(s[i])-ord('A')
        dp[i+1][j+1]=(dp[i+1][j+1]+dp[i][j])%mod
print(dp[-1][3])
Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
A=list(map(int,input().split()))
r=0
from collections import defaultdict
d=defaultdict(int)
d[A[0]]=1
for i in range(1,N):
    d2=defaultdict(int)
    for a in d.keys():
        if a&A[i]==0:
            r+=d[a]
            d2[a+A[i]]+=d[a]
    d2[A[i]]+=1
    d=d2
print(r+N)

Fixed submission:
N=int(input())
A=list(map(int,input().split()))
r=0
from collections import defaultdict
d=defaultdict(int)
d[A[0]]=1
for i in range(1,N):
    d2=defaultdict(int)
    for a in d.keys():
        if a&A[i]==0:
            r+=d[a]
            d2[a+A[i]]+=d[a]
    d2[A[i]]+=1
    d=d2
print(r+N)

Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
A=list(map(int,input().split()))
r=0
from collections import deque
q=deque([A[0]])
for i in range(1,N):
    q2=deque()
    for a in q:
        if a&A[i]==0:
            r+=1
            q2.append(a+A[i])
    q2.append(A[i])
    q=q2
print(r+N)

Fixed submission:
N=int(input())
A=list(map(int,input().split()))
r=0
from collections import defaultdict
d=defaultdict(int)
d[A[0]]=1
for i in range(1,N):
    d2=defaultdict(int)
    for a in d.keys():
        if a&A[i]==0:
            r+=d[a]
            d2[a+A[i]]+=d[a]
    d2[A[i]]+=1
    d=d2
print(r+N)
Buggy python submission (verdict: Time Limit Exceeded):
s=input()
K=int(input())
d=['zzzzz']
for i in range(len(s)):
    for j in range(i+1,len(s)+1):
        for k in range(len(d)):
            if s[i:j] not in d and s[i:j]<d[k]:
                d.insert(k,s[i:j])
                if len(d)>5:
                    d.pop()
                break
print(d[K-1])

Fixed submission:
s=input()
K=int(input())
d=['zzzzz']
for i in range(len(s)):
    for j in range(i+1,i+6):
        for k in range(len(d)):
            if s[i:j] not in d and s[i:j]<d[k]:
                d.insert(k,s[i:j])
                if len(d)>5:
                    d.pop()
                break
print(d[K-1])
Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
S=[input() for i in range(N)]
r=0
for k in range(N):
    f=1
    for i in range(len(S)-1):
        for j in range(i+1,len(S)):
            if S[i-k][j]!=S[j-k][i]:
                f=0
                break
        if f==0:
            break
    if f:
        r+=N
print(r)

Fixed submission:
N=int(input())
S=[input() for i in range(N)]
St=list(map(''.join,zip(*S)))
r=0
for k in range(N):
    f=1
    for i in range(N):
        if S[i][k:]+S[i][:k]!=St[i+k-N]:
            f=0
            break
    if f:
        r+=N
print(r)
Buggy python submission (verdict: Time Limit Exceeded):
H,W=map(int, input().split())
S=[input() for i in range(H)]
s=[[0]*W for h in range(H)]
b=0
for h in range(H):
    for w in range(W):
        if S[h][w]=='#':
            s[h][w]=-1
            b+=1
q=[]
i=1
q.append((0,0))
import sys
while (H-1,W-1) not in q:
    q2=[]
    for h,w in q:
        s[h][w]=i
        if h>0 and s[h-1][w]==0:
            q2.append((h-1,w))
        if h<H-1 and s[h+1][w]==0:
            q2.append((h+1,w))
        if w>0 and s[h][w-1]==0:
            q2.append((h,w-1))
        if w<W-1 and s[h][w+1]==0:
            q2.append((h,w+1))
    if len(q)==0:
        break
    q=q2
    i+=1
if len(q)==0:
    print(-1)
else:
    print(H*W-i-b)

Fixed submission:
H,W=map(int, input().split())
S=[input() for i in range(H)]
s=[[0]*W for h in range(H)]
b=0
for h in range(H):
    for w in range(W):
        if S[h][w]=='#':
            s[h][w]=-1
            b+=1
q=[]
i=1
q.append((0,0))
s[0][0]=1
while (H-1,W-1) not in q:
    q2=[]
    i+=1
    for h,w in q:
        if h>0 and s[h-1][w]==0:
            q2.append((h-1,w))
            s[h-1][w]=i
        if h<H-1 and s[h+1][w]==0:
            q2.append((h+1,w))
            s[h+1][w]=i
        if w>0 and s[h][w-1]==0:
            q2.append((h,w-1))
            s[h][w-1]=i
        if w<W-1 and s[h][w+1]==0:
            q2.append((h,w+1))
            s[h][w+1]=i
    q=q2
    if len(q)==0:
        break
if len(q)==0:
    print(-1)
else:
    print(H*W-i-b)

Buggy python submission (verdict: Time Limit Exceeded):
H,W=map(int, input().split())
S=[input() for i in range(H)]
s=[[0]*W for h in range(H)]
b=0
for h in range(H):
    for w in range(W):
        if S[h][w]=='#':
            s[h][w]=-1
            b+=1
q=[]
i=1
q.append((0,0))
while (H-1,W-1) not in q:
    q2=[]
    for h,w in q:
        s[h][w]=i
        if h>0 and s[h-1][w]==0:
            q2.append((h-1,w))
        if h<H-1 and s[h+1][w]==0:
            q2.append((h+1,w))
        if w>0 and s[h][w-1]==0:
            q2.append((h,w-1))
        if w<W-1 and s[h][w+1]==0:
            q2.append((h,w+1))
    q=q2
    i+=1
print(H*W-i-b)

Fixed submission:
H,W=map(int, input().split())
S=[input() for i in range(H)]
s=[[0]*W for h in range(H)]
b=0
for h in range(H):
    for w in range(W):
        if S[h][w]=='#':
            s[h][w]=-1
            b+=1
q=[]
i=1
q.append((0,0))
s[0][0]=1
while (H-1,W-1) not in q:
    q2=[]
    i+=1
    for h,w in q:
        if h>0 and s[h-1][w]==0:
            q2.append((h-1,w))
            s[h-1][w]=i
        if h<H-1 and s[h+1][w]==0:
            q2.append((h+1,w))
            s[h+1][w]=i
        if w>0 and s[h][w-1]==0:
            q2.append((h,w-1))
            s[h][w-1]=i
        if w<W-1 and s[h][w+1]==0:
            q2.append((h,w+1))
            s[h][w+1]=i
    q=q2
    if len(q)==0:
        break
if len(q)==0:
    print(-1)
else:
    print(H*W-i-b)
Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
A=[list(map(int,input().split())) for i in range(N)]
r=0
for i,aa in enumerate(A):
    for j,a in enumerate(aa[i+1:]):
        f=1
        j+=i+1
        for k in range(N):
            if k==i or k==j:
                continue
            if a>A[i][k]+A[k][j]:
                f=r=-1
                break
            if a==A[i][k]+A[k][j]:
                f=0
                break
        if f==1:
            r+=a
        elif f==-1:
            break
    if r<0:
        break
print(r)

Fixed submission:
N=int(input())
A=[list(map(int,input().split())) for i in range(N)]
r=0
for i,aa in enumerate(A):
    for j,a in enumerate(aa[i+1:]):
        f=1
        j+=i+1
        for k in range(N):
            if k==i or k==j:
                continue
            if a>A[i][k]+A[k][j]:
                f=r=-1
                break
            if a==A[i][k]+A[k][j]:
                f=0
                break
        if f==1:
            r+=a
        elif f==-1:
            break
    if r<0:
        break
print(r)
Buggy python submission (verdict: Runtime Error):
N=int(input())
edge=[list(map(int,input().split())) for i in range(N-1)]
inf=10**15
c=[[] for i in range(N)]
for i,j,w in edge:
    c[i-1].append((j-1,w))
    c[j-1].append((i-1,w))
Q,K=map(int, input().split())
d=[inf]*N
d[K-1]=0
v=[0]*N
def dfs(p,v,d):
    for n,w in c[p]:
        if v[n]==0:
            d[n]=min(d[n],d[p]+w)
            v[n]=1
            dfs(n,v,d)
dfs(K-1,v,d)
xy=[list(map(int,input().split())) for i in range(Q)]
for x,y in xy:
    print(d[x-1]+d[y-1])

Fixed submission:
N=int(input())
edge=[list(map(int,input().split())) for i in range(N-1)]
inf=10**15
c=[[] for i in range(N)]
for i,j,w in edge:
    c[i-1].append((j-1,w))
    c[j-1].append((i-1,w))
Q,K=map(int, input().split())
d=[inf]*N
d[K-1]=0
v=[0]*N
import sys
sys.setrecursionlimit(10**5+9)
def dfs(p,v,d):
    for n,w in c[p]:
        if v[n]==0:
            d[n]=min(d[n],d[p]+w)
            v[n]=1
            dfs(n,v,d)
dfs(K-1,v,d)
xy=[list(map(int,input().split())) for i in range(Q)]
for x,y in xy:
    print(d[x-1]+d[y-1])

Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
edge=[list(map(int,input().split())) for i in range(N-1)]
INF=10**15
c=[[INF]*N for i in range(N)]
for i,j,w in edge:
    c[i-1][j-1]=w
    c[j-1][i-1]=w
Q,K=map(int, input().split())
xy=[list(map(int,input().split())) for i in range(Q)]
from heapq import heappop,heappush
def dij(c,N,start):
    d=[INF]*N
    d[start]=0
    prev=[-1]*N
    q=[]
    heappush(q,(0,start))
    while len(q)>0:
        u=heappop(q)[1]
        for v in range(N):
            if c[u][v]<INF:
                temp=d[u]+c[u][v]
                if d[v]>temp:
                    d[v]=temp
                    prev[v]=u
                    heappush(q,(d[v],v))
    return d
d=dij(c,N,K-1)
for x,y in xy:
    print(d[x-1]+d[y-1])

Fixed submission:
N=int(input())
edge=[list(map(int,input().split())) for i in range(N-1)]
inf=10**15
c=[[] for i in range(N)]
for i,j,w in edge:
    c[i-1].append((j-1,w))
    c[j-1].append((i-1,w))
Q,K=map(int, input().split())
d=[inf]*N
d[K-1]=0
v=[0]*N
import sys
sys.setrecursionlimit(10**5+9)
def dfs(p,v,d):
    for n,w in c[p]:
        if v[n]==0:
            d[n]=min(d[n],d[p]+w)
            v[n]=1
            dfs(n,v,d)
dfs(K-1,v,d)
xy=[list(map(int,input().split())) for i in range(Q)]
for x,y in xy:
    print(d[x-1]+d[y-1])
Buggy python submission (verdict: Runtime Error):
N,K=map(int,input().split())
A=list(map(int,input().split()))
from fractions import gcd
g=A[0]
for a in A[1:]:
    g=gcd(g,a)
print(['IMPOSSIBLE','POSSIBLE'][(g==1 or K%g==0) and max(A)>=K]

Fixed submission:
N,K=map(int,input().split())
A=list(map(int,input().split()))
from fractions import gcd
g=A[0]
for a in A[1:]:
    g=gcd(g,a)
print(['IMPOSSIBLE','POSSIBLE'][(g==1 or K%g==0) and max(A)>=K])

Buggy python submission (verdict: Runtime Error):
N,K=map(int,input().split())
A=list(map(int,input().split()))
from fractions import gcd
g=A[0]
for a in A[1:]:
    g=gcd(g,a)
print(['IMPOSSIBLE','POSSIBLE'][((g==1 or K%g==0) and max(A)>=K)

Fixed submission:
N,K=map(int,input().split())
A=list(map(int,input().split()))
from fractions import gcd
g=A[0]
for a in A[1:]:
    g=gcd(g,a)
print(['IMPOSSIBLE','POSSIBLE'][(g==1 or K%g==0) and max(A)>=K])
Buggy python submission (verdict: Time Limit Exceeded):
H,W,K=map(int,input().split())
A=[input() for i in range(H)]
for i,l in enumerate(A):
    if 'S' in l:
        S=((1,0,K),i,l.index('S'))
q=[S]
from heapq import heappop,heappush
n=((0,1),(0,-1),(1,0),(-1,0))
v=[[0]*W for i in range(H)]
v[S[1]][S[2]]=1
a=999
#M=[[999]*H for i in range(W)]
while q:
    (s,m,o),i,j=heappop(q)
    #M[i][j]=min(s,M[i][j])
    if i in (0,H-1) or j in (0,W-1):
        a=min(a,s)
    for x,y in n:
        if 0<=i+x<H and 0<=j+y<W:
            if v[i+x][j+y]:continue
            v[i+x][j+y]=1
            if A[i+x][j+y]=='.':
                if m<K:
                    heappush(q,((s,m+1,o),i+x,j+y))
                else:
                    heappush(q,((s+1,1,o-K),i+x,j+y))
            elif A[i+x][j+y]=='#':
                if m<K and o<K:
                    heappush(q,((s,m+1,o+1),i+x,j+y))
                else:
                    heappush(q,((s+1,1,o-K+1),i+x,j+y))
print(a)
#print(*M,sep='\n')

Fixed submission:
H,W,K=map(int,input().split())
A=[input() for i in range(H)]
for i,l in enumerate(A):
    if 'S' in l:
        S=(K,i,l.index('S'))
from collections import deque
q=deque([S])
X=[(S[1],S[2])]
n=((0,1),(0,-1),(1,0),(-1,0))
v=[[0]*W for i in range(H)]
v[S[1]][S[2]]=1
while q:
    m,i,j=q.popleft()
    for x,y in n:
        if 0<=i+x<H and 0<=j+y<W:
            if v[i+x][j+y]:continue
            v[i+x][j+y]=1
            if A[i+x][j+y]=='.' and m>0:
                q.append((m-1,i+x,j+y))
                X.append((i+x,j+y))
print(min([min(0--i//K,0--(H-i-1)//K,0--j//K,0--(W-j-1)//K) for i,j in X])+1)
Buggy python submission (verdict: Time Limit Exceeded):
N,Ma,Mb=map(int,input().split())
a,b,c=map(list,zip(*[list(map(int,input().split())) for i in range(N)]))
ma,mb=sum(a),sum(b)
MAX=5000
dp=[[[MAX]*(mb+1) for i in range(ma+1)] for j in range(N+1)]
dp[0][0][0]=0
for i in range(N):
    for j in range(ma):
        for k in range(mb):
            dp[i+1][j][k]=min(dp[i][j][k],dp[i+1][j][k])
            if j+a[i]<=ma and k+b[i]<=mb:
                dp[i+1][j+a[i]][k+b[i]]=min(dp[i+1][j+a[i]][k+b[i]],dp[i][j][k]+c[i])
ans=MAX
x=1
while x*Ma<=ma and x*Mb<=mb:
    ans=min(ans,dp[N][x*Ma][x*Mb])
    x+=1
print(ans if ans<MAX else -1)

Fixed submission:
N,Ma,Mb=map(int,input().split())
a,b,c=map(list,zip(*[list(map(int,input().split())) for i in range(N)]))
ma,mb=sum(a),sum(b)
MAX=5000
dp=[[[MAX]*(mb+1) for i in range(ma+1)] for j in range(N+1)]
dp[0][0][0]=0
for i in range(N):
    for j in range(ma):
        for k in range(mb):
            dp[i+1][j][k]=min(dp[i][j][k],dp[i+1][j][k])
            if j+a[i]<=ma and k+b[i]<=mb:
                dp[i+1][j+a[i]][k+b[i]]=min(dp[i+1][j+a[i]][k+b[i]],dp[i][j][k]+c[i])
ans=MAX
x=1
while x*Ma<=ma and x*Mb<=mb:
    ans=min(ans,dp[N][x*Ma][x*Mb])
    x+=1
print(ans if ans<MAX else -1)
Buggy python submission (verdict: Runtime Error):
import sys
def input(): return sys.stdin.readline().strip()
N=int(input())
A=[int(input()) for i in range(N-1)]
c=[[] for i in range(N)]
for i,a in enumerate(A):
    c[a-1].append(i+1)
import sys
sys.setrecursionlimit(10**5+9)
def f(i):
    if len(c[i])==0:
        return 0
    return max([e+i+1 for i,e in enumerate(sorted([f(j) for j in c[i]],reverse=True))])
print(f(0))

Fixed submission:
import sys
def input(): return sys.stdin.readline().strip()
N=int(input())
A=[int(input()) for i in range(N-1)]
c=[[] for i in range(N)]
for i,a in enumerate(A):
    c[a-1].append(i+1)
import sys
sys.setrecursionlimit(10**7)
def f(i):
    if len(c[i])==0:
        return 0
    return max([e+i+1 for i,e in enumerate(sorted([f(j) for j in c[i]],reverse=True))])
print(f(0))

Buggy python submission (verdict: Runtime Error):
import sys
def input(): return sys.stdin.readline().strip()
N=int(input())
A=[int(input()) for i in range(N-1)]
c=[[] for i in range(N)]
for i,a in enumerate(A):
    c[a-1].append(i+1)
import sys
sys.setrecursionlimit(10**5)
def f(i):
    if len(c[i])==0:
        return 0
    return max([e+i+1 for i,e in enumerate(sorted([f(j) for j in c[i]],reverse=True))])
print(f(0))

Fixed submission:
import sys
def input(): return sys.stdin.readline().strip()
N=int(input())
A=[int(input()) for i in range(N-1)]
c=[[] for i in range(N)]
for i,a in enumerate(A):
    c[a-1].append(i+1)
import sys
sys.setrecursionlimit(10**7)
def f(i):
    if len(c[i])==0:
        return 0
    return max([e+i+1 for i,e in enumerate(sorted([f(j) for j in c[i]],reverse=True))])
print(f(0))
Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
A=list(map(int,input().split()))
p=[None]*N
for i,a in enumerate(A):
    p[a-1]=i
ans=0
b={-1:1,N:1}
from bisect import bisect
for i in range(N):
    bs=sorted(b.keys())
    s=bisect(bs,p[i])
    ans+=(i+1)*(p[i]-bs[s-1])*(bs[s]-p[i])
    b[p[i]]=1
print(ans)

Fixed submission:
N=int(input())
A=list(map(int,input().split()))
p=[None]*N
for i,a in enumerate(A):
    p[a-1]=i
ans=0
l,r=[i for i in range(N)],[i for i in range(N)]
for i in range(N-1,-1,-1):
    left,right=l[p[i]],r[p[i]]
    ans+=(i+1)*(p[i]-left+1)*(right-p[i]+1)
    if left>0:
        r[left-1]=right
    if right<N-1:
        l[right+1]=left
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
A=list(map(int,input().split()))
p=[None]*N
for i,a in enumerate(A):
    p[a-1]=i
ans=0
b=[-1,N]
from bisect import bisect
for i in range(N):
    s=bisect(b,p[i])
    ans+=(i+1)*(p[i]-b[s-1])*(b[s]-p[i])
    b=b[:s]+[p[i]]+b[s:]
print(ans)

Fixed submission:
N=int(input())
A=list(map(int,input().split()))
p=[None]*N
for i,a in enumerate(A):
    p[a-1]=i
ans=0
l,r=[i for i in range(N)],[i for i in range(N)]
for i in range(N-1,-1,-1):
    left,right=l[p[i]],r[p[i]]
    ans+=(i+1)*(p[i]-left+1)*(right-p[i]+1)
    if left>0:
        r[left-1]=right
    if right<N-1:
        l[right+1]=left
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N,x=map(int,input().split())
a=list(map(int,input().split()))
c=[[None]*N for i in range(N)]
for j in range(N):
    for i in range(N):
        if j==0:
            c[j][i]=a[i]
        else:
            c[j][i]=min(c[j-1][i-1],a[i])
ans=2*10**12
for i in range(N):
    ans=min(ans,sum(c[i])+x*i)
print(ans)

Fixed submission:
N,x=map(int,input().split())
a=list(map(int,input().split()))
c=[[None]*N for i in range(N)]
for j in range(N):
    for i in range(N):
        if j==0:
            c[j][i]=a[i]
        else:
            c[j][i]=min(c[j-1][i-1],a[i])
ans=2*10**12
for i in range(N):
    ans=min(ans,sum(c[i])+x*i)
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
xy = [list(map(int, input().split())) for i in range(n)]
ans = 0
for i in range(n-1):
    for j in range(i+1, n):
        ans = max(ans, abs(xy[i][0]-xy[j][0])+abs(xy[i][1]-xy[j][1]))
print(ans)

Fixed submission:
n = int(input())
x = []
y = []
for i in range(n):
    l = list(map(int, input().split()))
    x.append(l[0]+l[1])
    y.append(l[0]-l[1])
print(max(max(x)-min(x), max(y)-min(y)))
Buggy python submission (verdict: Runtime Error):
import math

n = int(input())
l = [0] * n
y = int(math.sqrt(n-3))
if n <= 5:
    for i in range(n):
        print(0)
for i in range(1,y):
    for j in range(1, y):
        for k in range(1, y):
            x = i ** 2 + j ** 2 + k ** 2 + i*j + i*k + j*k
            if x % 1 == 0 and x <= n:
                l[x-1] += 1
for i in l:
    print(i)

Fixed submission:
import math
import sys

n = int(input())
l = [0] * n
if n < 6:
    for i in range(n):
        print(0)
    sys.exit()
y = int(math.sqrt(n-3))
if n <= 5:
    for i in range(n):
        print(0)
for i in range(1,y):
    for j in range(1, y):
        for k in range(1, y):
            x = i ** 2 + j ** 2 + k ** 2 + i*j + i*k + j*k
            if x % 1 == 0 and x <= n:
                l[x-1] += 1
for i in l:
    print(i)
Buggy python submission (verdict: Runtime Error):
import sympy

n = int(input())
ans = 0
for i in range(1, n + 1):
    ans += i * len(sympy.divisors(i))
print(ans)    

Fixed submission:
n = int(input())
ans = 0
for i in range(1, n+1):
    ans += (i+(n-n%i))*(n//i)//2
print(ans)
Buggy python submission (verdict: Runtime Error):
n = int(input())
a = list(map(int, input().split()))
q = int(input())
bc = [list(map(int, input().split())) for i in range(q)]
for f in bc:
    a = [f[1] if j == f[0] else j for j in a]
    print(sum(a))


Fixed submission:
a = input()
if a.isupper():
  print("A")
else:
  print("a")
Buggy python submission (verdict: Runtime Error):
n = int(input())
a = list(map(int, input().split()))
ans = a[0]
for i in range(1, n):
  ans = ans ^ a[i]
for i in range(n):
  print(ans ^ i,ende="")

Fixed submission:
n = int(input())
a = list(map(int, input().split()))
ans = 0
for i in range(n):
  ans = ans ^ a[i]
for i in range(n):
  print(ans ^ a[i],end=" ")
Buggy python submission (verdict: Time Limit Exceeded):
# coding: utf-8
a = int(input())
b = list(map(int, input().split()))
c = 1
for i in b:
  c = c * i
if c > 10 ** 18:
  print(-1)
else:
  print(c)

Fixed submission:
# coding: utf-8
a = int(input())
b = list(map(int, input().split()))
c = 1
if 0 in b:
    print(0)
else:
  while c < 10 ** 18 and len(b) != 0:
    c = c * b[0]
    del b[0]
  if c > 10 ** 18:
    print(-1)
  else:
    print(c)
Buggy python submission (verdict: Runtime Error):
from collections import Counter

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a
  
n = int(input())
print(len(Counter(n)))

Fixed submission:
# coding: utf-8
# Your code here!

from collections import Counter

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a
  
n = int(input())
x = Counter(prime_factorize(n))
x_keys = list(x.keys())
x_values = list(x.values())
ans = 0
for i in range(len(x_keys)):
    z = x_values[i]
    mai = 1
    while z - mai >= 0:
        z -= mai
        mai += 1
        ans += 1
print(ans)
Buggy python submission (verdict: Runtime Error):
a = int(input())
print(a.replace("?","D")

Fixed submission:
a = input()
print(a.replace("?","D"))