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[205],bas[65];
char s[205];
bool add(long long x)
{
	for (int i=60;i>=0;i--)
	{
		if (x&(1LL<<i))
		x^=bas[i];
	}
	if (!x)
	return 1;
	for (int i=60;i>=0;i--)
	{
		if (x&(1LL<<i))
		{
			bas[i]=x;
			return 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);
		bool z=1;
		memset(bas,0,sizeof(bas));
		for (int i=n-1;i>=0;i--)
		{
			if (s[i]=='1')
			z&=add(a[i]);
			else
			add(a[i]);
		}
		printf("%d\n",!z);
	}
}