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 <cstdio>
#include <algorithm>
using namespace std;

typedef long long ll;

ll b[64];
bool insert(ll x) {
	for(int i=63;i>=0;i--) {
		if( (x >> i) & 1 ) {
			if( b[i] ) x ^= b[i];
			else {
				b[i] = x;
				return true;
			}
		}
	}
	return false;
}


char s[205]; ll A[205];

void solve() {
	int N; scanf("%d", &N);
	for(int i=1;i<=N;i++) scanf("%lld", &A[i]);
	scanf("%s", s + 1);
	
	for(int i=0;i<64;i++) b[i] = 0;
	for(int i=N;i>=1;i--) {
		if( s[i] == '0' ) insert(A[i]);
		else if( insert(A[i]) ) {
			puts("1");
			return ;
		}
	}
	puts("0");
}

int main() {
	int T; scanf("%d", &T);
	while( T-- ) solve();
}