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 <cstdio>
#include <cstring>
#define debug(...) fprintf(stderr,__VA_ARGS__)
using namespace std; 
typedef long long ll;
const int maxN=200+5;
int T;
int N;
ll A[maxN];
ll base[64];
char S[maxN];
void ins(ll x) {
	for(int i=62;~i;--i) if(x>>i&1) {
		if(base[i]) x^=base[i];
		else {
			for(int j=i+1;j<63;++j) if(base[j]>>i&1) {
				base[j]^=x;
			}
			for(int j=i-1;~j;--j) if(x>>j&1) {
				x^=base[j];
			}
			base[i]=x;
			break;
		}
	}
}
bool sol() {
	memset(base,0,sizeof(base));
	for(int i=N;i>=1;--i) {
		if(S[i]=='0') {
			ins(A[i]);
		}
		else {
			for(int j=62;~j;--j) if(A[i]>>j&1) {
				if(!base[j]) return 1;
				A[i]^=base[j];
			}
		}
	}
	return 0;
}
int main() {
	scanf("%d",&T);
	for(int kase=1;kase<=T;++kase) {
		scanf("%d",&N);
		for(int i=1;i<=N;++i) scanf("%lld",&A[i]);
		scanf("%s",S+1);
		printf("%d\n",sol());
	}
	return 0;
}