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;
typedef long long ll;
const int N = 100000 + 10;
ll a[61];
void add(ll x){
    for(int i=60;i>=0;i--) if(x>>i&1){
        if(a[i]) x ^= a[i];
        else{
            a[i] = x; break;
        }
    }
}
bool check(ll x){
    for(int i=60;i>=0;i--) if(x>>i&1) x ^= a[i];
    return x==0;
}
ll x[N];
char s[N];
int main(){
    ios::sync_with_stdio(0);
    int T; cin>>T;
    while(T--){
        memset(a,0,sizeof(a));
        int n; cin>>n;
        for(int i=1;i<=n;i++) cin>>x[i];
        cin>>(s+1);
        int ok = 1;
        for(int i=n;i>=1;i--){
            if(s[i]=='0') add(x[i]);
            else ok &= check(x[i]);
        }
        cout<<!ok<<endl;
    }
}