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<cstring>
#include<cstdio>
#include<bitset>
#include<algorithm>
using namespace std;
typedef long long ll;
int n;
#define Maxn 205
bitset<Maxn> a[60];
bitset<Maxn> b[Maxn];
char S[Maxn];
ll A[Maxn];

int main(){
	int T;
	scanf("%d",&T);
	while(T--){
		scanf("%d",&n);
		for(int i=1;i<=n;++i)
		    for(int j=1;j<=n;++j)b[i][j]=0;
		for(int i=0;i<60;++i)
		    for(int j=1;j<=n;++j)a[i][j]=0; 
		for(int i=1;i<=n;++i){
			scanf("%lld",&A[i]);
			for(int j=0;j<60;++j)
			    if(A[i]&(1ll<<j))a[j][i]=1;
		}
		scanf("%s",S+1);
		for(int i=0;i<60;++i)
		    for(int j=n;j>=1;--j)
		        if(a[i][j]){
					if(!b[j][j]){
						b[j]=a[i];break;
					}
					else a[i]=a[i]^b[j];
		        }
		int last=n+1;
		bool flag=true;
		for(int i=n;i>=1;--i)
		    if(b[i][i]){
				if(S[i]=='1')flag=false;
		    }
	    if(flag)puts("0");
	    else puts("1");
	}
	return 0; 
}