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<stdio.h>
#include<vector>
#define it register int
#define ct const int
#define il inline
using namespace std;
typedef long long ll;
#define rll register ll
#define cll const ll
const int N=1000005;
int n,T;
ll a[N];
char s[N];
vector<ll> v;
il ll Min(cll p,cll q){return p<q?p:q;}
int main(){ 
	scanf("%d",&T);it i;
	while(T--){
		scanf("%d",&n);
		for(i=1;i<=n;++i) scanf("%lld",&a[i]);
		scanf("%s",s+1),v.clear();it fl=0;
		for(i=n;i;--i){
			rll x=a[i];
			for(const ll &j : v) x=Min(x,x^j);
			if(s[i]=='0') v.push_back(x);
			if(s[i]=='1'&&x){fl=1;break;}
		}
		printf("%d\n",fl);
	}
	return 0;
}