Harryxun/sft_time huggingface dataset:
### BUGGY CODE ###

# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline

def f(i,d):
    """
    i 桁の n で、r(n)-n = d
    """
    n = i-1
    m = 0
    res = []
    while n>m:
        x = 10**n-10**m
        if m:
            res.append(tuple((x*k,v) for k,v in d2.items()))
        else:
            res.append(tuple((x*k,v) for k,v in d1.items()))
        n -= 1
        m += 1
    
    def sums(lsts):
        dic = {0:1}
        for lst in lsts:
            ndic = {}
            for k1,v1 in dic.items():
                for k2,v2 in lst:
                    k = k1+k2
                    v = v1*v2
                    if k in ndic: ndic[k] += v
                    else: ndic[k] = v
            dic = ndic
        
        return dic.items()
    
    L = len(res)
    #print(res[L//2:])
    s1 = sums(res[:L//2])
    s2 = sorted(sums(res[L//2:]))
    
    #print(s1)
    #print(s2)
    #print(d)

    v = 0
    from bisect import bisect_left
    for k1,v1 in s1:
        idx = bisect_left(s2,(d-k1,0))
        if idx < len(s2) and s2[idx][0] == d-k1:
            #print(k1,v1,idx,s2[idx])
            v += v1*s2[idx][1]
    return v*(1 if i%2==0 else 10)


d, = map(int,read().split())

ans = 0

from collections import Counter

d1 = Counter()
for i in range(10):
    for j in range(1,10):
        d1[i-j] += 1
        
d2 = Counter()
for i in range(10):
    for j in range(10):
        d2[i-j] += 1

for i in range(2,19):
#for i in range(2,19):
    r = f(i,d)    
    #print(r,i)
    ans += r

print(ans)


### FIXED CODE ###

# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline

def f(i,d):
    """
    i 桁の n で、r(n)-n = d
    """
    n = i-1
    m = 0
    res = []
    while n>m:
        x = 10**n-10**m
        if m:
            res.append(tuple((x*k,v) for k,v in d2.items()))
        else:
            res.append(tuple((x*k,v) for k,v in d1.items()))
        n -= 1
        m += 1
    
    def sums(lsts):
        dic = {0:1}
        for lst in lsts:
            ndic = {}
            for k1,v1 in dic.items():
                for k2,v2 in lst:
                    k = k1+k2
                    v = v1*v2
                    if k in ndic: ndic[k] += v
                    else: ndic[k] = v
            dic = ndic
        
        return dic.items()
    
    L = len(res)
    #print(res[L//2:])
    s1 = sums(res[:L//2])
    s2 = sorted(sums(res[L//2:]))
    
    #print(s1)
    #print(s2)
    #print(d)

    v = 0
    from bisect import bisect_left
    for k1,v1 in s1:
        idx = bisect_left(s2,(d-k1,0))
        if idx < len(s2) and s2[idx][0] == d-k1:
            #print(k1,v1,idx,s2[idx])
            v += v1*s2[idx][1]
    return v*(1 if i%2==0 else 10)


d, = map(int,read().split())

ans = 0

from collections import Counter

d1 = Counter()
for i in range(10):
    for j in range(1,10):
        d1[i-j] += 1
        
d2 = Counter()
for i in range(10):
    for j in range(10):
        d2[i-j] += 1

for i in range(2,18):
#for i in range(2,19):
    r = f(i,d)    
    #print(r,i)
    ans += r
if d%(10**9-10**8)==0:
    r = d//(10**9-10**8)
    ans += d2[r]*(10**7)*9

print(ans)
### BUGGY CODE ###

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

count = 0
for i in range(N):
  count_ = 0
  judge = i+1
  for j in range(judge,N):
    if H[i] >= H[j]:
      count_ += 1
    else:
      break;
    H[i] = H[j]
  if count_ > count:
    count = count_

print(count)

### FIXED CODE ###

N = int(input())
H = [int(e) for e in input().split()]
count_max = 0
i = 0
while i < N:
  judge = True
  count = 0
  tmp = i
  for j in range(tmp,N):
    if j < N-1:
      if H[j] >= H[j+1]:
        count += 1
      else:
        break;

  #print(count)
  if count_max < count:
    count_max = count
  if judge == True:
    i += count + 1

print(count_max)
### BUGGY CODE ###

import math
n=int(input())
a=list(map(int,input().split()))
mxa=max(a)

def get_sieve_of_eratosthenes(mxa):
    fact = [0]*(mxa+1)
    limit = int(math.sqrt(mxa))
    for i in range(2,mxa+1):
        if fact[i]!=0:
            continue
        else:
            fact[i]=i
            for j in range(i, mxa+1, i):
                if fact[j]==0:
                    fact[j]=i
    for i in range(2,mxa+1):
        if fact[i]==0:
            fact[i]=i

    return fact

fact = get_sieve_of_eratosthenes(mxa)

lst=[0]*(len(fact))
for i in range(n):
    divisor = set()
    while a[i]!=1:
        divisor.add(fact[a[i]])
        a[i]//=fact[a[i]]
    for d in divisor:
        lst[d]+=1

pair=True
st=True

for i in lst:
    if i>=2:
        pair=False
    if i==n:
        st=False
if pair:
    print("pairwise coprime")
elif st:
    print("setwise coprime")
else:
    print("not coprime")


### FIXED CODE ###

import math
n=int(input())
a=list(map(int,input().split()))
mxa=max(a)

def get_sieve_of_eratosthenes(mxa):
    fact = [0]*(mxa+1)
    limit = int(math.sqrt(mxa))
    for i in range(2,limit+1):
        if fact[i]!=0:
            continue
        else:
            fact[i]=i
            for j in range(i, mxa+1, i):
                if fact[j]==0:
                    fact[j]=i
    for i in range(2,mxa+1):
        if fact[i]==0:
            fact[i]=i

    return fact

fact = get_sieve_of_eratosthenes(mxa)

lst=[0]*(len(fact))
for i in range(n):
    divisor = set()
    while a[i]!=1:
        divisor.add(fact[a[i]])
        a[i]//=fact[a[i]]
    for d in divisor:
        lst[d]+=1

pair=True
st=True

for i in lst:
    if i>=2:
        pair=False
    if i==n:
        st=False
if pair:
    print("pairwise coprime")
elif st:
    print("setwise coprime")
else:
    print("not coprime")
### BUGGY CODE ###

import numpy as np
S = input()
mod = 10 ** 9 + 7

n = len(S)
dp = np.zeros((n, 13))
a = S[-1]
now, pre = 10, 1
x_ = dp[0]
l = [1, 10, 9, 12, 3, 4]
l = [[i * l_ % 13 for i in range(1, 10)] for l_ in l]
li = 1
if a == "?":
    x_[0:10] = 1
else:
    x_[int(a)] = 1
for s, x in zip(S[-2::-1], dp[1:]):
    if s == "?":
        x += x_
        for v in l[li]:
            x[v:] += x_[:-v]
            x[:v] += x_[-v:]
    else:
        if s == "0":
            x += x_
        else:
            v = l[li][int(s) - 1]
            x[v:] += x_[:-v]
            x[:v] += x_[-v:]
    x %= mod
    li += 1
    li %= 6
    x_ = x
print(int(dp[-1][5]))

### FIXED CODE ###

#!python3

LI = lambda: list(map(int, input().split()))

# input
S = input()

MOD = 10 ** 9 + 7


def main():
    n = len(S)
    m = 5
    w = []
    p = 1
    for i in range(n):
        s = S[-1 - i]
        if s == "?":
            w.append(p)
        else:
            m = (m - int(s) * p) % 13
        p = p * 10 % 13

    n = len(w)
    l1 = [0] * 13
    l1[0] = 1
    for i in range(1, n + 1):
        l2 = [0] * 13
        for j in range(10):
            x = w[i - 1] * j % 13
            for k in range(13):
                t = (x + k) % 13
                l2[t] += l1[k]
        l1 = [y % MOD for y in l2]
    
    ans = l1[m]
    print(ans)


if __name__ == "__main__":
    main()
### BUGGY CODE ###

ni = lambda: int(input())
nm = lambda: map(int, input().split())
nl = lambda: list(map(int, input().split()))

n, m = nm()

a = sorted(nl())

pos = 0

changer = []

for i in range(m):
    b, c = nm()
    changer.append((c, b))

changer = sorted(changer)


for i in range(m):
    pos = 0

    c = changer[i]
    for j in range(c[1]):
        while pos < n:
            if a[pos] < c[0]:
                a[pos] = c[0]
                a = sorted(a)
                break
            pos += 1

print(sum(a))


### FIXED CODE ###

ni = lambda: int(input())
nm = lambda: map(int, input().split())
nl = lambda: list(map(int, input().split()))

n, m = nm()

a = sorted(nl())

pos = 0

changer = []

for i in range(m):
    b, c = nm()
    changer.append((c, b))

changer = sorted(changer)[::-1]


for i in range(m):

    c = changer[i]
    for j in range(c[1]):
        while pos < n:
            if a[pos] < c[0]:
                a[pos] = c[0]
                break
            pos += 1
    if pos >= n:
        break

print(sum(a))
### BUGGY CODE ###

def f(L):
    X=0
    T=1
    for x in L[::-1]:
        X+=T*x
        T*=2
    return X

N=int(input())
X=input()
Zero="0"*N

X=list(map(int,X))

H=X.count(1)
Z=f(X)
G=1<<N

A=[]
for i in range(N):
    G>>=1
    
    if X[i]==0:
        J=H+1
    else:
        J=H-1
        
    Y=Z^G

    if Y==0:
        A.append(0)
        continue
    
    I=1
    Y=Y%J
    try:
        while True:
            Y=Y%bin(Y).count("1")
            I+=1
    except ZeroDivisionError:
        A.append(I)

print("\n".join(map(str,A)))


### FIXED CODE ###

N=int(input())
X=input()
Y=int(X,2)

J=X.count("1")

A=[0]*N
A[-1]=1
for i in range(2,N+1):
    A[-i]=(A[-(i-1)]*2)%(J+1)

B=[0]*N
if J>1:
    B[-1]=1
    for j in range(2,N+1):
        B[-j]=(B[-(j-1)]*2)%(J-1)


H=[0]*N

Q,R=divmod(Y,J+1)
if J>1:
    S,T=divmod(Y,J-1)
else:
    S=T=0

for i in range(N):
    if X[i]=="0":
        U=(R+A[i])%(J+1)
    else:
        if J==1:
            continue
        U=(T-B[i])%(J-1)
        
        
    I=1
    while U>0:
        U=U%bin(U).count("1")
        I+=1
    H[i]=I

print("\n".join(map(str,H)))
### BUGGY CODE ###

import itertools
N=int(input())
L=list(map(int,input().split()))

p=itertools.permutations(L,3)
total=0
for e in p:
    a=e[0]
    b=e[1]
    c=e[2]
    if(a < b + c and b <c + a and c < a + b):
        total+=1
print(total//6)

### FIXED CODE ###

import sys
from bisect import bisect_left
N=int(input())
L=list(map(int,input().split()))
L.sort()
total = 0
for i in range(N):
  for j in range(i + 1, N):
    a = L[i] + L[j]
    total += max(bisect_left(L, a) - j - 1, 0)

print(total)
### BUGGY CODE ###

K = int(input())
S = input()
N = len(S)
MOD = 10**9 + 7

fct = [1]
invfct = [1]
for i in range(1, K+N+1):
    fct.append(fct[i-1] * i % MOD)
    invfct.append(pow(fct[i], MOD-2, MOD))

def cmb(n, k):
    return fct[n] * invfct[k] * invfct[n-k]

ans = 0
for i in range(K+1):
    temp = pow(25, i, MOD)
    temp *= cmb(i+N-1, N-1)
    temp *= pow(26, K-i, MOD)
    ans += temp
    ans %= MOD
print(ans)

### FIXED CODE ###

K = int(input())
S = input()
N = len(S)
MOD = 10**9 + 7

fct = [1]
invfct = [1]
pow25 = [1]
pow26 = [1]
for i in range(1, K+N+1):
    fct.append(fct[i-1] * i % MOD)
    invfct.append(pow(fct[i], MOD-2, MOD))
    pow25.append(pow25[i-1] * 25 % MOD)
    pow26.append(pow26[i-1] * 26 % MOD)

def cmb(n, k):
    return fct[n] * invfct[k] * invfct[n-k]

ans = 0
for i in range(K+1):
    temp = pow25[i]
    temp *= cmb(i+N-1, N-1)
    temp *= pow26[K-i]
    ans += temp
    ans %= MOD
print(ans)
### BUGGY CODE ###

def solve(n, t, ab_list):
    ab_list_s = sorted(ab_list, key=lambda x: x[0])
    res = 0
    dp = [0] * t
    for i in range(n):
        for s in range(t - 1, -1, -1):
            if dp[s] > 0 or s == 0:
                u = s + ab_list_s[i][0]
                r = dp[s] + ab_list_s[i][1]
                if u >= t:
                    res = max(res, r)
                else:
                    dp[u] = max(dp[u], r)
    return max(res, max(dp))


def main():
    n, t = map(int, input().split())
    ab_list = []
    for _ in range(n):
        a, b = map(int, input().split())
        ab_list.append([a, b])
    res = solve(n, t, ab_list)
    print(res)


def test():
    assert solve(2, 60, [[10, 10], [100, 100]]) == 110
    assert solve(3, 60, [[10, 10], [10, 20], [10, 30]]) == 60
    assert solve(3, 60, [[30, 10], [30, 20], [30, 30]]) == 50


if __name__ == "__main__":
    test()
    main()


### FIXED CODE ###

def solve(n, t, ab_list):
    ab_list_s = sorted(ab_list, key=lambda x: x[0])
    res = 0
    dp = [0] * t
    for i in range(n):
        for s in range(t - 1, -1, -1):
            if dp[s] > 0 or s == 0:
                u = s + ab_list_s[i][0]
                r = dp[s] + ab_list_s[i][1]
                if u >= t:
                    res = max(res, r)
                else:
                    dp[u] = max(dp[u], r)
    return max(res, max(dp))


def main():
    n, t = map(int, input().split())
    ab_list = []
    for _ in range(n):
        a, b = map(int, input().split())
        ab_list.append([a, b])
    res = solve(n, t, ab_list)
    print(res)


def test():
    assert solve(2, 60, [[10, 10], [100, 100]]) == 110
    assert solve(3, 60, [[10, 10], [10, 20], [10, 30]]) == 60
    assert solve(3, 60, [[30, 10], [30, 20], [30, 30]]) == 50


if __name__ == "__main__":
    # test()
    main()
### BUGGY CODE ###

import sys
import heapq
n,m=map(int,sys.stdin.readline().split())
a=list(map(int,sys.stdin.readline().split()))
a.sort
for i in range(m):
    b,c=map(int,sys.stdin.readline().split())
    t=[c]*b
    a=list(heapq.merge(a,t))
print(sum(heapq.nlargest(n,a)))

### FIXED CODE ###

n,m=map(int,input().split())
a=list(map(int,input().split()))
bc=[list(map(int,input().split())) for i in range(m)]
bc.sort(key=lambda x:x[1],reverse=True)
for b,c in bc:
    a.extend([c]*b)
    if len(a)>2*n:
        break
a.sort(reverse=True)
print(sum(a[:n]))
### BUGGY CODE ###

N,K = map(int,input().split())
*A, = map(int,input().split())

M = len(bin(K))-2

B = [[0]*N for _ in [0]*M]
B[0] = [a-1 for a in A]
for i in range(1,M):
    for j in range(N):
        B[i][j] = B[i-1][B[i-1][j]]

k = K
a = 0
while k>0:
    if k%2==1:
        a = B[0][a]
        k -= 1
        continue
    j = 1
    while k%(2**(j+1))==0:
        j += 1
    a = B[j][a]
    k -= 2**j
print(a+1)

### FIXED CODE ###

N,K = map(int,input().split())
*A, = map(int,input().split())

M = len(bin(K))-2

B = [[0]*N for _ in [0]*M]
B[0] = [a-1 for a in A]
for i in range(1,M):
    for j in range(N):
        B[i][j] = B[i-1][B[i-1][j]]

k = K
a = 0
while k>0:
    if k%2==1:
        a = B[0][a]
        k -= 1
        continue
    j = 1
    while k%(2**(j+1))==0:
        j += 1
    a = B[j][a]
    k -= 2**j
print(a+1)
### BUGGY CODE ###

import bisect
import collections

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

s.sort()

while len(s) > 1:#最も体力のあるのが攻撃を受ける
    temp = s.pop()
    for j in s:
        damege = (temp//j)*j
    if temp != 0 and temp != damege:
        index = bisect.bisect_left(s,temp-damege)
        s.insert(index,temp-damege)

print(s[0])


### FIXED CODE ###

import math

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

tmp = a[0]
for i in range(1,len(a)):
    tmp = math.gcd(tmp,a[i])
print(tmp)
### BUGGY CODE ###

import sys
def main():
    input = sys.stdin.readline
    H,W = map(int, input().split())
    A = [list(map(int, input().split())) for _ in range(H)]
    B = [list(map(int, input().split())) for _ in range(H)]

    S = (80+80)*80
    dp = [[[0]*(S+1) for _ in range(W)] for __ in range(H)]
    dp[0][0][abs(A[0][0] - B[0][0])] = 1
    for i in range(H):
        for j in range(W):
            for s in range(S+1):
                if i < H-1:
                    ni = i + 1
                    nj = j
                    t = abs(A[ni][nj] - B[ni][nj])
                    ns = s + t
                    if ns <= S:
                        dp[ni][nj][ns] |= dp[i][j][s]
                    ns = abs(s - t)
                    dp[ni][nj][ns] |= dp[i][j][s]
                if j < W-1:
                    ni = i
                    nj = j + 1
                    t = abs(A[ni][nj] - B[ni][nj])
                    ns = s + t
                    if ns <= S:
                        dp[ni][nj][ns] |= dp[i][j][s]
                    ns = abs(s - t)
                    dp[ni][nj][ns] |= dp[i][j][s]
    for s in range(S+1):
        if dp[H-1][W-1][s]:
            print(s)
            break

if __name__ == '__main__':
    main()

### FIXED CODE ###

import sys
def main():
    input = sys.stdin.readline
    H,W = map(int, input().split())
    A = [list(map(int, input().split())) for _ in range(H)]
    B = [list(map(int, input().split())) for _ in range(H)]
    C = [[abs(A[i][j] - B[i][j]) for j in range(W)] for i in range(H)]

    M = 160*80
    dp = [[0 for _ in range(W)] for __ in range(H)]
    dp[0][0] = 1 << (C[0][0] + M)
    for i in range(H):
        for j in range(W):
            for ni,nj in [(i,j+1),(i+1,j)]:
                if ni >= H or nj >= W: continue
                t = C[ni][nj]
                dp[ni][nj] |= dp[i][j] << t
                dp[ni][nj] |= dp[i][j] >> t
    
    a = dp[H-1][W-1]
    ans = 0
    while True:
        if a & (1 << (M+ans)) or a & (1 >> (M-ans)): break
        ans += 1
    print(ans)

if __name__ == '__main__':
    main()
### BUGGY CODE ###

import sys,math,collections,itertools,copy
input = sys.stdin.readline

H,W=list(map(int,input().split()))
s = []
dot_cnt = 0
for _ in range(H):
    a = input().rstrip()
    dot_cnt += a.count('.')
    s.append(list(a))

num_lis = [[float('inf')]*W for _ in range(H)]

#--#
for ih in range(H):
    for iw in range(W):
        if s[ih][iw]=='#':
            num_lis[ih][iw]=0
        else:
            if iw-1>=0:
                num_lis[ih][iw] = min(num_lis[ih][iw-1]+1,num_lis[ih][iw])
                
    for iw in range(W-1,-1,-1):
        
        if s[ih][iw]=='#':
            num_lis[ih][iw]=0
        else:
            if iw+1<=W-1:
                num_lis[ih][iw] = min(num_lis[ih][iw+1]+1,num_lis[ih][iw])

#--#
for iw in range(W):
    for ih in range(H):
        if s[ih][iw]=='#':
            num_lis[ih][iw]=0
        else:
            if ih-1>=0:
                num_lis[ih][iw] = min(num_lis[ih-1][iw]+1,num_lis[ih][iw])
                
    for ih in range(H-1,-1,-1):
        if s[ih][iw]=='#':
            num_lis[ih][iw]=0
        else:
            if ih+1<=H-1:
                num_lis[ih][iw] = min(num_lis[ih+1][iw]+1,num_lis[ih][iw])

maxOpe = 0
for iw in range(W):
    for ih in range(H):
        maxOpe = max(maxOpe,num_lis[ih][iw])
print(maxOpe)


### FIXED CODE ###

import sys,math,collections,itertools,copy
input = sys.stdin.readline

H,W=list(map(int,input().split()))
s = []
dot_cnt = 0
for _ in range(H):
    a = input().rstrip()
    dot_cnt += a.count('.')
    s.append(list(a))

num_lis = [[float('inf')]*W for _ in range(H)]

#--#
for ih in range(H):
    for iw in range(W):
        if s[ih][iw]=='#':
            num_lis[ih][iw]=0
        else:
            if iw-1>=0:
                num_lis[ih][iw] = min(num_lis[ih][iw-1]+1,num_lis[ih][iw])
                
    for iw in range(W-1,-1,-1):
        
        if s[ih][iw]=='#':
            num_lis[ih][iw]=0
        else:
            if iw+1<=W-1:
                num_lis[ih][iw] = min(num_lis[ih][iw+1]+1,num_lis[ih][iw])

#--#
for iw in range(W):
    for ih in range(H):
        if s[ih][iw]=='#':
            num_lis[ih][iw]=0
        else:
            if ih-1>=0:
                num_lis[ih][iw] = min(num_lis[ih-1][iw]+1,num_lis[ih][iw])
                
    for ih in range(H-1,-1,-1):
        if s[ih][iw]=='#':
            num_lis[ih][iw]=0
        else:
            if ih+1<=H-1:
                num_lis[ih][iw] = min(num_lis[ih+1][iw]+1,num_lis[ih][iw])

maxOpe = 0
for iw in range(W):
    for ih in range(H):
        maxOpe = max(maxOpe,num_lis[ih][iw])
print(maxOpe)
### BUGGY CODE ###

N, M = map(int, input().split())
ab_s = [list(map(int, input().split())) for _ in range(M)]
bridges = [0] * N
ab_s = sorted(ab_s, key=lambda x: x[1])
for ab in ab_s:
  if sum(bridges[ab[0]:ab[1]]) == 0:
    bridges[ab[1]-1] = 1
print(sum(bridges))


### FIXED CODE ###

N, M = map(int, input().split())
ab_s = [list(map(int, input().split())) for _ in range(M)]
bridges = [0] * N
ab_s = sorted(ab_s, key=lambda x: x[1])
for ab in ab_s:
    if bridges[ab[1]-1] - bridges[ab[0]-1] == 0:
        for i in range(ab[1]-1, N):
            bridges[i] += 1
print(bridges[-1])
### BUGGY CODE ###

def dp_fn():
  N, W = map(int, input().split())
  WV = (map(int, input().split()) for _ in range(N))
  
  DP = {0:0}
  
  for w, v in WV:
    CP = {}
    for i in DP.keys():
      if i + w <= W:
        CP[i+w] = max(DP[i] + v, DP[i])
    for i in CP.keys():
      DP[i] = CP[i]
  return max(DP.values())
  
print(dp_fn())

### FIXED CODE ###

import sys
input = sys.stdin.readline

def dp_fn():
  N, W = map(int, input().split())
  WV = (map(int, input().split()) for _ in range(N))
  
  DP = {0:0}
  
  for w, v in WV:
    keys = sorted(DP.keys(), reverse=True)
    for i in keys:
      j = DP[i]
      if j+w <= W:
        if i+v in DP:
          DP[i+v] = min(DP[i+v], j+w)
        else:
          DP[i+v] = j+w
  return max(DP.keys())
  
print(dp_fn())
### BUGGY CODE ###

# coding: utf-8
import sys

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

# 逆から、人1が多かったらその時点で駄目、人0が人1の数を覆い尽くす必要がある
T = ir()

def solve():
    N = ir()
    A = lr()
    S = sr()
    dp = [None] * (N+1)
    dp[N] = {0}
    for i in range(N-1, -1, -1):
        if S[i] == '0':
            dp[i] = dp[i+1].copy()
            for element in dp[i+1]:
                dp[i].add(element ^ A[i])
        elif S[i] == '1':
            if A[i] not in dp[i+1]:
                return 1
            else:
                dp[i] = dp[i+1]
    return 0
    
for _ in range(T):
    print(solve())


### FIXED CODE ###

# coding: utf-8
import sys

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

# 逆から, zero_cardsに数を貯めて行き、bitで0に出来るか
T = ir()
for _ in range(T):
    N = ir()
    A = lr()
    S = sr()
    zero_cards = []
    for a, person in zip(A[::-1], S[::-1]):
        for z in zero_cards:
            a = min(a, a^z)
        if a:
            if person == '1':
                print(1)
                break
            zero_cards.append(a)
    else:
        print(0)
### BUGGY CODE ###

n = input()
s = list(map(int, input().split()))
a = 1
flag0 = False
flag = True
for i in s:
  a*=i
  if a > 1000000000000000000:
    flag = False
  if i == 0:
    flag0 = True
if flag0:
  print(0)
elif flag:
  print(a)
else:
  print(-1)

### FIXED CODE ###

n = input()
s = list(map(int, input().split()))
a = 1
flag0 = False
flag = True
for i in s:
  a*=i
  if a > 1000000000000000000:
    flag = False
    break
for i in s:
  if i == 0:
    flag0 = True
if flag0:
  print(0)
elif flag:
  print(a)
else:
  print(-1)
### BUGGY CODE ###

import fractions

A, B = map(int, input().split())

f = fractions.gcd(A, B)

kouyakusuu = []
# print(f)
for i in range(2, f+1):
    # print(f, i)
    if f % i != 0:
        continue
    else:
        kouyakusuu.append(i)
        while f % i == 0:
            f = f / i
    if f == 1:
        break
# print(kouyakusuu)
print(len(kouyakusuu)+1)

### FIXED CODE ###

import fractions

A, B = map(int, input().split())

f = fractions.gcd(A, B)

kouyakusuu = []

if f % 2 == 0:
    kouyakusuu.append(2)
    while f % 2 == 0:
        f = f / 2

i = 3
while i*i <= f:
    if f % i == 0:
        kouyakusuu.append(i)
        while f % i == 0:
            f = f / i
    i += 2
if f != 1:
    kouyakusuu.append(f)
print(len(kouyakusuu)+1)
### BUGGY CODE ###

#K : XYZそれぞれは、0以上K以下
#S : X+Y+Zの合計値を示すS

K,S = map(int,input().split())

X=Y=Z=0
result = 0
while(X<=K):
    while(Y<=K):
        while(Z<=K):
            if X+Y+Z<S:
                pass
            elif X+Y+Z==S:
                result +=1
            else:
                break
            Z+=1
        Z=0
        Y+=1
    Y=0
    X+=1
print(result)

### FIXED CODE ###

#K : XYZそれぞれは、0以上K以下
#S : X+Y+Zの合計値を示すS

K,S = map(int,input().split())

X=Y=Z=0
result = 0
for x in range(K+1):
    for y in range ( K+1 ):
        if 0 <= S-X-Y <=K:
            result +=1
        # Z = S-X-Y
        # # print("XYZ",X,Y,Z)
        # if X+Y+Z == S:
        #     if  Z<=K :
        #         result+=1 
        Y+=1
    Y=0
    X+=1

print(result)
### BUGGY CODE ###

import math
from functools import reduce

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

k = int(input())
total = 0
for i in range(1,k+1):
    for j in range(1,k+1):
        for l in range(1, k+1):
            if i == j:
                total += math.gcd(i,l)
            elif j == l:
                total += math.gcd(j,i)
            elif l == i:
                total += math.gcd(l,j)
            else:
                total += gcd(i,j,l)
print(total)


### FIXED CODE ###

import math

k = int(input())
total = 0
for i in range(1,k+1):
    for j in range(1,k+1):
        sub_gcd = math.gcd(i,j)
        for l in range(1, k+1):
            total += math.gcd(sub_gcd, l)
print(total)