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 rep(i,n) for((i)=1;(i)<=(n);(i)++)
using namespace std;
int n,i,j,t;
long long a[65],b[205];
string s;
bool ins(long long x){
	int i;
	for(i=63;i>=0;i--)if((x>>i)&1){
		if(a[i]){
			x^=a[i];
			continue;
		}
		a[i]=x;
		return 1;
	}
	return 0;
}
int main(){
	cin>>t;
	while(t--){
		memset(a,0,sizeof(a));
		cin>>n;
		rep(i,n)cin>>b[i];
		cin>>s;
		for(i=n;i>=1;i--){
			if(ins(b[i])&&s[i-1]=='1') break;
		}
		cout<<(!!i)<<endl;
	}
	return 0;
}