Problem: There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):

* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.



Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.

Determine whether x becomes 0 at the end of the game when the two persons play optimally.

Solve T test cases for each input file.

Constraints

* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.

Input

Input is given from Standard Input in the following format. The first line is as follows:


T


Then, T test cases follow. Each test case is given in the following format:


N
A_1 A_2 \cdots A_N
S


Output

For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.

Example

Input

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000


Output

1
0
0

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
#define LL long long 
int n;
LL a[66], x[222], b[66];
char s[222];
void insert(LL x, LL *a){
    for(int i = 60;i >= 0; i--){
        if(x >> i & 1){
            if(!a[i]){
                a[i] = x; 
                break;
            }
            else x ^= a[i];
        }
    }
}
bool check(LL x){
    for(int i = 60;i >= 0; i--){
        if(x >> i & 1)x ^= a[i];
    }
    return x != 0;
}
int main(){
    int T;
    cin>>T;
    while(T--){
        scanf("%d", &n);
        memset(a, 0, sizeof a);
        memset(b, 0, sizeof b);
        for(int i = 1;i <= n; i++)scanf("%lld", &x[i]);
        scanf("%s", s + 1);
        bool fl = 0;
        for(int i = n;i >= 1; i--){
            if(s[i] == '0')insert(x[i], a);
            else fl |= check(x[i]);
        }
        printf("%d\n", fl);
    }
    return 0;
}