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
using namespace std;

int A[200];
string s;

set<int> S;
bool sub(void){
	S.clear();
	int n;
	cin >> n;
	for(int i = 0; i < n; i++){
		cin >> A[i];
	}
	cin >> s;
	for(int i = n - 1; i >= 0; i--){
		int x = A[i];
//		cout << "process: ";
//		cout << x << endl;
		for(auto ptr = S.rbegin(); ptr != S.rend(); ptr++){
			if(x != 0 && __builtin_clzll(*ptr) == __builtin_clzll(x)){
//				cout << x << ' ' << *ptr << endl;
				x ^= *ptr;
			}
		}
		
//		cout << "round ";
//		cout << i << ' ' << x <<  endl;
//		for(auto j : S){
//			cout << j << ' ';
//		}
//		cout << endl;
		// cout << x << endl;
		if(x == 0){
			continue;
		}else{
			if(s[i] == '1'){
				return 1;
			}
			
			S.insert(x);
		}
	}
	return 0;
}

int32_t main(){
	int t;
	cin >> t;
	while(t--){
		bool res = sub();
		cout << res << endl;
	}
}