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;

long long a[210];
char s[210];

long long bit[70];

void insert(long long x) {
	for (int i = 0; i < 60; i++) {
		if (x >> i & 1) {
			if (!bit[i]) {
				bit[i] = x;
				return ;
			}
			x ^= bit[i];
		}
	}
}

bool check(long long x) {
	for (int i = 0; i < 60; i++) {
		if (x >> i & 1) {
			x ^= bit[i];
		}
	}
	return x == 0;
}

int main () {
	int T; scanf("%d", &T);
	while (T--) {
		int n; scanf("%d", &n);
		for (int i = 0; i < n; i++) {
			scanf("%lld", &a[i]);
		}
		scanf("%s", s);
		memset(bit, 0, sizeof(bit));
		for (int i = n - 1; i >= 0; i--) {
			if (s[i] == '0') insert(a[i]);
			else {
				if (!check(a[i])) {
					printf("1\n");
					goto END;
				}
			}
		}
		printf("0\n");
		END:;
	}
	return 0;
}