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 int long long
#define fr(i,a,b) for(int i(a),end##i(b);i<=end##i;i++)
#define fd(i,a,b) for(int i(a),end##i(b);i>=end##i;i--)
using namespace std;
const int maxn=500+5;
int a[maxn],s[maxn];
int n,T;
int p[200];
void insert(int x){
	fd(i,63,0){
		if((x>>i)&1){
			if(!p[i]){
				p[i]=x;
				return ;
			}
			else x^=p[i];
		}
	}
}
bool check(int x){
	fd(i,63,0){
		if((x>>i)&1)x^=p[i];
	}
	return !x;
}
signed main(){
	scanf("%lld",&T);
	while(T--){
		memset(p,0,sizeof(p));	
		scanf("%lld",&n);
		fr(i,1,n)scanf("%lld",&a[i]);
		fr(i,1,n)scanf("%1lld",&s[i]);
		fd(i,n,1){
			if(s[i]){
				if(!check(a[i]))goto NO;
			}
			else{
				insert(a[i]);	
			}
		}
		printf("0\n");
		continue;
		NO:;
		printf("1\n");
	}
	return 0;
}