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 ll long long

const int N = 205, M = 60;
int T, n;
ll a[N];
char s[N];
struct wish{
	ll a[M];
	void insert(ll x){
		for(int i=M; i--;) if(x>>i&1){
			if(!a[i]){ a[i]=x; break;}
			else x^=a[i];
		}
	}
	bool exist(ll x){
		for(int i=M; i--;) if(x>>i&1) x^=a[i];
		return !x;
	}
	void reset(){ memset(a, 0, sizeof a);}
} x;
int main() {
	scanf("%d", &T);
	while(T--){
		scanf("%d", &n);
		for(int i=1; i<=n; ++i) scanf("%lld", a+i);
		scanf("%s", s+1);
		bool o=0;
		x.reset();
		for(int i=n; i; --i)
			if(s[i]=='0') x.insert(a[i]);
			else if(!x.exist(a[i])) o=1;
		puts(o?"1":"0");
	}
	return 0;
}