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[202];
long long v[202];
char s[202];

int main()
{
	int T;
	scanf("%d", &T);
	while(T--)
	{
		int n;
		scanf("%d", &n);
		for(int i = 1; i <= n; i++)
		{
			scanf("%lld", &a[i]); 
		}
		scanf("%s", s + 1);
		
		memset(v, 0, sizeof(v));
		
		int ans = 0;
		for(int i = n; i >= 1; i--)
		{
			if(s[i] == '0')
			{
				for(int j = 61; j >= 0; j--)
					if(a[i] & (1ll << j))
					{
						if(v[j] == 0)
						{
							v[j] = a[i];
							break;
						}
						else
							a[i] ^= v[j];
					}
			}
			else
			{
				for(int j = 61; j >= 0; j--)
					if(a[i] & (1ll << j))
					{
						if(v[j] == 0)
						{
							ans = 1;
							break;
						}
						else
							a[i] ^= v[j];
					}
				if(ans == 1)
					break;
			}
		}
		printf("%d\n", ans);
	}
	return 0;
}