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;
const int N=207;
int t,n; long long a[N],w[N]; char s[N];
inline void ins(long long u){
	for(int i=61;i>=0;i--){
		if(u&(1ll<<i)){
			if(!w[i]){
				w[i]=u; return;
			}
			u^=w[i];
		}
	}
}
inline bool check(long long u){
	for(int i=61;i>=0;i--) if((u^w[i])<u) u^=w[i];
	if(u==0) return 0; return 1;
}
int main(){
	cin>>t;
	while(t--){
		memset(w,0,sizeof(w));
		cin>>n; bool fl=0;
		for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
		scanf("%s",s+1);
		for(int i=n;i>=1;i--){
			if(s[i]=='0') ins(a[i]);
			else fl|=check(a[i]);
		}
		if(fl) puts("1"); else puts("0");
	}
	return 0;
}