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 <iostream>
#include <vector>
#include <set> 
#include <map>
#include <algorithm>
#include <cmath>
#include <iomanip>
using namespace std;
typedef long long int ll;
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int t;
    cin>>t;
    while(t--){
        int n;
        cin>>n;
        vector <ll> v(n);
        for(int i=0;i<n;i++)cin>>v[i];
        string s;
        cin>>s;
        int status=0;
        vector <ll> xors;
        for(int i=n-1;i>=0;i--){
            ll x=v[i];
            for(auto it:xors){
                x=min(x,x^it);
            }
            if(x==0)continue;
            if(s[i]=='0'){
                xors.push_back(x);
            }
            else {
                cout<<1<<endl;
                status=1;
                break;
            }
        }
        if(status==0)cout<<0<<endl;
    }
    return 0;
}