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>
typedef long long ll;
const int N=205;
int T,i,j,n;
ll a[N],b[65];
inline bool ins(ll x){
	for(j=59;j>=0;--j)if(x>>j&1){if(!b[j]){b[j]=x;return 1;}x^=b[j];}
	return 0;
}
char c[N];
int main(){
	for(scanf("%d",&T);T--;){
		memset(b,0,sizeof b);
		scanf("%d",&n);
		for(i=1;i<=n;++i)scanf("%lld",a+i);
		scanf("%s",c+1);
		for(i=n;i;--i)if(ins(a[i]) && c[i]=='1')break;
		puts(i?"1":"0");
	}
}