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<cstdio>
#include<algorithm>
using namespace std;
long long w[220], P[61];
int n;
char p[220];
bool OK(int pv){
    long long x = w[pv];
    for(int i=60;i>=0;i--){
        if((x>>i)&1){
            if(!P[i]){
                if(p[pv]=='1')return false;
                P[i]=x;
                return true;
            }
            x^=P[i];
        }
    }
    return true;
}
void Solve(){
    int i;
    for(i=0;i<=60;i++)P[i]=0;
    scanf("%d",&n);
    for(i=0;i<n;i++)scanf("%lld",&w[i]);
    scanf("%s",p);
    for(i=n-1;i>=0;i--){
        if(!OK(i)){
            puts("1");
            return;
        }
    }
    puts("0");
}
int main(){
    int TC;
    scanf("%d",&TC);
    while(TC--){
        Solve();
    }
}