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;
using ll=long long;

int T,N;
ll A[200];
string S;

int main(){
	cin>>T;
	while(T--){
		cin>>N;
		for(int i=0;i<N;i++){
			cin>>A[i];
		}
		cin>>S;
		ll B[60];
		for(int i=0;i<60;i++){
			B[i]=0;
		}
		bool f=false;
		for(int i=N-1;i>=0;i--){
			if(S[i]=='1'){
				for(int j=59;j>=0;j--){
					if((A[i]>>j)&1){
						A[i]^=B[j];
					}
				}
				if(A[i]){
					f=true;
					break;
				}
			}
			else{
				for(int j=59;j>=0;j--){
					if((A[i]>>j)&1){
						if(B[j])A[i]^=B[j];
						else{
							B[j]=A[i];
							break;
						}
					}
				}
			}
		}
		cout<<f<<endl;
	}
}