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>
using namespace std;

typedef long long ll;

int N;
ll A[202];
string s;

ll B[62];

void solve(){
	bool ret=true;
	for(int i=0;i<62;i++){
		B[i]=0;
	}
	for(int i=N-1;i>=0;i--){
		if(s[i]=='0'){
			for(int j=61;j>=0;j--){
				if((A[i]>>j)&1LL){
					if(B[j]==0){
						B[j]=A[i];
						break;
					}
					else A[i]^=B[j];
				}
			}
		}
		else {
			for(int j=61;j>=0;j--){
				if((A[i]>>j)&1LL){
					if(B[j]==0){
						ret=false;
						break;
					}
					else A[i]^=B[j];
				}
			}
		}
	}
	if(ret)puts("0");
	else puts("1");
}

int main(){
	int T;
	scanf("%d",&T);
	for(;T>0;T--){
		scanf("%d",&N);
		for(int i=0;i<N;i++)scanf("%lld",&A[i]);
		cin>>s;
		solve();
	}
}