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:
//Created Time:2020年06月07日 星期日 19时59分48秒
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define N 202
#define ll long long

using namespace std;

char s[N];
ll a[N], d[N];

bool ins(ll x){
	for(int i = 60; ~i && x; --i){
		if(!(x & (1ll << i))) continue;
		if(!d[i]) return d[i] = x, true;
		else x ^= d[i];
	}
	return false;
}

int main(){
	int t; cin >> t;
	while(t--){
		int n; bool ans = false;
		scanf("%d", &n);
		memset(d, 0, sizeof d);
		for(int i = 1; i <= n; ++i)
			scanf("%lld", a + i);
		scanf("%s", s + 1);
		for(int i = n; i; --i){
			bool flag = ins(a[i]);
			if(flag && s[i] == '1'){
				ans = true;
				break;
			}
		}
		if(ans) puts("1");
		else puts("0");
	}
	return 0;
}