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 <string>
using namespace std;
typedef long long ll;
ll a[210],bs[210];
int main(){
    int t; cin >> t;
    while(t){
        t--;
        int i,j,n,sz = 0;
        cin >> n;
        for(i=0;i<n;i++){
            cin >> a[i];
        }
        string s; cin >> s;
        for(i=n - 1;i>=0;i--){
            if(s[i]=='1'){
                for(j=0;j<sz;j++){
                    a[i] = min(a[i],a[i]^bs[j]);
                }
                if(a[i]!=0){
                    cout << 1 << endl;
                    break;
                }
            }else{
                for(j=0;j<sz;j++){
                    a[i] = min(a[i],a[i]^bs[j]);
                }
                if(a[i]!=0){
                    bs[sz] = a[i];
                    sz++;
                }
            }
            if(i==0){
                cout << 0 << endl;
            }
        }
    }
}