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>
#define SIZE 205
#define MX 62
using namespace std;
typedef long long int ll;
typedef pair <int,int> P;

ll A[SIZE];
char S[SIZE];
ll bit[MX];
void solve()
{
	int n;
	scanf("%d",&n);
	for(int i=0;i<n;i++) scanf("%lld",&A[i]);
	scanf("%s",&S);
	memset(bit,-1,sizeof(bit));
	for(int i=n-1;i>=0;i--)
	{
		int f=-1;
		for(int j=MX-1;j>=0;j--)
		{
			if(A[i]>>j&1)
			{
				if(bit[j]==-1)
				{
					f=j;
					break;
				}
				A[i]^=bit[j];
			}
		}
		if(S[i]=='1'&&f!=-1)
		{
			puts("1");
			return;
		}
		if(f!=-1) bit[f]=A[i];
	}
	puts("0");
}
int main()
{
	int T;
	scanf("%d",&T);
	while(T--) solve();
}