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;
typedef long long ll;
const int N=210;

ll gi() {
	ll x=0,o=1;char ch=getchar();
	while(!isdigit(ch)&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	return x*o;
}

int n;
ll a[N],p[70];
char s[N];

void insert(ll v) {
	for(int i=60;~i;i--)
		if(v>>i&1) {
			if(!p[i]) { p[i]=v;break; }
			v^=p[i];
		}
}

bool in(ll v) {
	for(int i=60;~i;i--)
		if(v>>i&1) {
			if(!p[i]) return 0;
			v^=p[i];
		}
	return 1;
}

int main() {
	int T=gi();
	while(T--) {
		cin>>n;
		for(int i=1;i<=n;i++) a[i]=gi();
		scanf("%s",s+1);
		memset(p,0,sizeof(p));
		int ans=0;
		for(int i=n;i;i--) {
			if(s[i]=='0') {
				insert(a[i]);
			}
			else {
				if(!in(a[i])) { ans=1;break; }
			}
		}
		cout<<ans<<'\n';
	}
	return 0;
}