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:
//agc045_a.cpp
//Sun Jul  5 18:44:30 2020

#include <iostream>
#include <string>
#include <queue>
#include <map>
#include <unordered_map>
#include <vector>
#include <algorithm>
#include <math.h>
#include <set>
#define INTINF 2147483647
#define LLINF 9223372036854775807
#define MOD 1000000007
#define rep(i,n) for (int i=0;i<(n);++i)

using namespace std;
using ll=long long;
typedef pair<int,int> P;

int main(){
	int t;
	cin >> t;

	rep(i,t){
		int n;
		cin >> n;
		ll a[n];
		rep(j,n) cin >> a[j];
		string s;
		cin >> s;

		vector<ll> xors;
		int ans = 0;
		for (int j=n-1;j>=0;j--){
			ll x = a[j];
			rep(k,xors.size()){
				x = min(x,x^xors[k]);
			}
			if (x){
				if (s[j]=='0'){
					xors.push_back(x);
				}else {
					ans = 1;
					break;
				}
			}
		}
		cout << ans << endl;
	}

}