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 MAXN 207
#define MAXL 67
using namespace std;
long long b[MAXL],a[MAXN];
bool vi[MAXL];
void dodaj(long long x)
{
	for(long long i=59;i>=0;i--) if(x&(1LL<<i))
	{
		if(vi[i]) x^=b[i];
		else {vi[i]=true; b[i]=x; return;}
	}
}
bool proveri(long long x)
{
	for(long long i=59;i>=0;i--) if(x&(1LL<<i) && vi[i]) x^=b[i];
	return x!=0;
}
int main()
{
	int t; cin>>t;
	while(t--)
	{
		int n; cin>>n;
		string s;
		fill(vi,vi+MAXL,false);
		for(int i=0;i<n;i++) cin>>a[i];
		cin>>s;
		bool p1=false;
		for(int i=n-1;i>=0;i--)
		{
			if(s[i]=='0') dodaj(a[i]);
			else p1=p1||proveri(a[i]);
		}
		if(p1) printf("1\n");
		else printf("0\n");
	}
}