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 mod 1000000007
#define vi vector<int>
typedef long long int ll;

int main (void)
{
  //freopen("in.txt","r",stdin);
  //freopen("out.txt","w",stdout);
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t;
  cin >> t;
  while(t--){
  	//cout << "Case #" << c - t << ": ";
	int n,d = 61;
	cin >> n;
	vector<ll> base(d,0),a(n);
	for(int i = 0;i < n;i++) cin >> a[i];
	string s;
	cin >> s;
	bool flag = 0;
	for(int j = n - 1;j > -1;j--){
		if(s[j] - '0'){
			for(int i = 0;i < d;i++){
				if(a[j]&(1LL<<i)){
					if(!base[i]){
						flag = 1;
						break;
					}
					a[j] ^= base[i];
				}
			}
		}
		else{
			for(int i = 0;i < d;i++){
				if(a[j]&(1LL<<i)){
					if(!base[i]){
						base[i] = a[j];
						break;
					}
					a[j] ^= base[i];
				}
			}
		}
		if(flag) break;
	}
	cout << flag << "\n";	
  }
  return 0;
}