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 <iostream>
#include <cstdio>
#include <cstring>
#define MN 220

typedef long long ll;

ll d[64], a[MN];
char s[MN];

bool ins(ll x)
{
	for(int i = 62; i >= 0; i--)
	{
		if((x >> i) & 1)
		{
			if(!d[i]) {d[i] = x; return 1;}
			x ^= d[i];
		}
	}
	return 0;
}

int main()
{
	int T; scanf("%d", &T);
	while(T--)
	{
		memset(d, 0, sizeof(d));
		int n; scanf("%d", &n);
		for(int i = 1; i <= n; i++) scanf("%lld", &a[i]);
		scanf("%s", s + 1);
		bool ok = 0;
		for(int i = n; i >= 1; i--)
		{
			if(s[i] == '0') ins(a[i]);
			else if(ins(a[i])) {ok = 1; break;}
		}
		printf("%d\n", ok);
	}
}