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;
typedef long double ld;
const int N=500005,M=1000000007;
int n,i,j,t;
long long a[N],f[66];
char c[N];
int main()
{
	scanf("%d",&t);
	while(t--)
	{
		scanf("%d",&n);
		for(i=1;i<=n;++i)
			scanf("%lld",&a[i]);
		scanf("%s",c+1);
		memset(f,0,sizeof(f));
		for(i=n;i>=1;--i)
			if(c[i]=='0')
			{
				long long x=a[i];
				for(j=62;j>=0;--j)
					if((x>>j)&1)
						if(!f[j])
						{
							f[j]=x;
							break;
						}
						else
							x^=f[j];
			}
			else
			{
				long long x=a[i];
				for(j=62;j>=0;--j)
					if((x>>j)&1)
						x^=f[j];
				if(x)
					break;
			}
		if(i<=0)
			puts("0");
		else
			puts("1");
	}
}