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=200,C=62;

int n;
char s[N+9];
LL a[N+9];
int id[C+9];

bool Insert(int x){
  for (int i=C-1;i>=0;--i)
	if (a[x]>>i&1){
	  if (!id[i]) {id[i]=x;return 1;}
	  a[x]^=a[id[i]];
	}
  return 0;
}

void work(){
  scanf("%d",&n);
  for (int i=1;i<=n;++i)
	scanf("%lld",&a[i]);
  scanf("%s",s+1);
  for (int i=0;i<C;++i) id[i]=0;
  for (int i=n;i>=1;--i)
    if (Insert(i)&&s[i]-'0') {puts("1");return;}
  puts("0");
}

int main(){
  int T;
  scanf("%d",&T);
  for (;T--;) work();
  return 0;
}