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;
ll b[110],T,n,a[210],ans;
string s;
int que(ll x){
	for (int i=60;i>=0;i--)if (x&((1ll)<<i))x^=b[i];
	return (x!=0);
}
void add(ll x){for (int i=60;i>=0;i--){if (x&((1ll)<<i)){if (b[i]==0){b[i]=x;return ;}x^=b[i];}}}
int main(){
	cin>>T;
	while (T--){
		cin>>n;ans=0;
		memset(b,0,sizeof(b));
		for (int i=1;i<=n;i++)cin>>a[i];
		cin>>s;
		for (int i=n;i>=1;i--){
			if (s[i-1]=='0')add(a[i]);
			else ans=ans|que(a[i]);
		}
		cout<<ans<<endl;
	}
	return 0;
}