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;
typedef pair<int,int>pii;
const int mn=200+10;
const ll inf=0x3f3f3f3f3f3f3f3f;
const ll mod=1e9+7;
ll basis[64];
ll a[mn];
bool add(ll x){
    for(int i=60;i>=0;i--)if((x>>i)&1){
        if(basis[i])x^=basis[i];
        else{
            basis[i]=x;
            return 1;
        }
    }
    return 0;
}
int main(){
    cin.tie(0);
    cin.sync_with_stdio(0);
    int tc;
    cin>>tc;
    while(tc--){
        memset(basis,0,sizeof(basis));
        int n;
        cin>>n;
        for(int i=0;i<n;i++)cin>>a[i];
        string s;
        cin>>s;
        bool f=0;
        for(int i=n-1;i>=0;i--){
            if(s[i]-'0'){
                if(add(a[i])){
                    f=1;
                }
            }
            else add(a[i]);
        }
        printf("%d\n",(int)f);
    }
}