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 ;

#define int long long

vector<int> basis;

bool ok(int x){
	for(int i = 0 ; i < 60 ; i++){
		if((x & 1LL << i) == 0) continue ;
		if(basis[i] == 0){
			return  false;
		}
		x ^= basis[i] ;
	}
	return  true;
}

void insert(int x){
	for(int i = 0 ; i < 60 ; i++){
		if((x & 1LL << i) == 0) continue ;
		if(basis[i] == 0){
			basis[i] = x ;
			return  ;
		}
		x ^= basis[i] ;
	}
	return  ;
}

int32_t main(){
	int t ;
	cin >> t ;
	while(t--){
		basis.clear() ;
		basis.resize(60) ;
		int n ; 
		cin >> n ;
		int a[n] ;
		for(int i = 0 ; i < n ; i++){
			cin >> a[i] ;
		}
		string s ; 
		cin >> s ;
		bool found = true ;
		for(int i = n - 1 ; i >= 0 ; i--){
			if(s[i] == '0') insert(a[i]) ;
			else{
				found &= ok(a[i]) ;
			}
		}
		cout << 1 - found << '\n' ;
	}
	return 0 ;
}