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 ll long long
using namespace std;
const int MAXN=271,B=61;
int t,n,flg;
ll x,k,a[MAXN],b[MAXN];
char s[MAXN];
bool ins (ll x) {
	for (int i=B;i>=0;i--) {
		if ((x&(1ll<<i))) {
			if (b[i]) {x^=b[i];}
			else {b[i]=x;break;} 
		}
	}
	if (x) {return 1;}
	else {return 0;}
}
int main () {
	scanf("%d",&t);
	for (int ii=1;ii<=t;ii++) {
		memset(b,0,sizeof(b));
		scanf("%d",&n);
		for (int i=1;i<=n;i++) {
			scanf("%lld",&a[i]);
		}
		scanf("%s",s+1);
		int flg=0;
		for (int i=n;i>=1;i--) {
			if (s[i]=='0') {
				ins(a[i]);
			} else {
				if (ins(a[i])) {flg=1;break;}
			}
		}
		printf("%d\n",flg);
	}
	return 0;
}