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;

const int MX = 200, MB = 60;

long long a[MX], base[MB];
char s[MX + 1];

int main() {
	int T;
	ignore = scanf("%d", &T);
	while (T--) {
		int n;
		ignore = scanf("%d", &n);
		for (int i = 0; i < n; i++) ignore = scanf("%lld", a + i);
		ignore = scanf("%s", s);
		
		fill(base, base + MB, 0);
		
		int ans = 0;
		for (int i = n - 1; i >= 0; i--) {
			bool added = false;
			long long val = a[i];
			for (int j = 0; j < MB; j++) {
				if (((val >> j) & 1) == 0) continue;
				
				if (base[j] == 0) {
					base[j] = val;
					added = true;
					break;
				}
				
				val ^= base[j];
			}
			
			if (s[i] == '1' && added) {
				ans = 1;
			}
		}
		
		printf("%d\n", ans);
	}
	
	return 0;
}