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;
long long n,T;
long long base[70];
long long a[210];
string b;
int main(){
	cin>>T;
	while(T--){
		cin>>n;
		for(long long i=1;i<=n;++i){
			cin>>a[i];
		}
		cin>>b;
		memset(base,0,sizeof(base));
		bool y=1;
		for(long long i=n;i>=1&&y;--i){
			if(b[i-1]=='0'){
				long long x=a[i];
				for(long long j=0;j<64;++j){
					if((x>>j)&1){
						if(!base[j]){
							base[j]=x;
							break;
						}
						else{
							x^=base[j];
						}
					}
				}	
			}
			else{
				long long x=a[i];
				for(long long j=0;j<64;++j){
					if((x>>j)&1){
						if(base[j]){
							x^=base[j];
						}
						else break;
					}
				}
				if(x){
					y=0;
				}
			}
		}
		cout<<(!y)<<'\n';
	}
	return 0;
}