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>
#define ll long long
#define pii pair<ll ,int>
using namespace std;
const int inf = 0x3f3f3f3f;
const int maxn =504;
ll n,m,t;
ll a[maxn];
string s;
int main(){
    ios::sync_with_stdio(false);
//    #ifdef NK
//        freopen("in.txt","r",stdin);
//    #endif
    cin>>t;
    while(t--){
        vector<ll>b;
        cin>>n;
        for(int i=1;i<=n;i++)cin>>a[i];
        cin>>s;
        s="#"+s;
        int ok=1;
        for(int i=n;i;i--){
            ll v=a[i];
            for(ll x:b){
                v=min(v,v^x);
            }
            if(s[i]=='1'){

                if(v){
                    ok=0;
                    break;
                }
            }else{
                b.push_back(v);
            }

        }
        cout<<(ok?"0\n":"1\n");
    }

    return 0;
}