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;
#define rep(i,n) for(int i=0; i<(n); i++)
using ll = long long;
int t, n, ok;
ll a[205];
char s[205];
int main(){
	scanf("%d", &t);
	rep(o,t){
		scanf("%d", &n);
		rep(i,n) scanf("%lld", a+i);
		scanf("\n%s", s);
		ok = 0;
		for(int i=n-1; i>=0; i--) if(a[i]){
			if(s[i] == '1'){
				ok = 1;
				break;
			}
			rep(k,64) if(a[i]>>k&1){
				for(int j=i-1; j>=0; j--) if(a[j]>>k&1) a[j] ^= a[i];
				break;
			}
		}
		printf("%d\n", ok);
	}
}