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 <iostream>
#include <cstdio>
#include <vector>
using namespace std;
typedef long long ll;

ll T, n, a[205], res;
string s;
vector<ll> vt;
int main() {
	ll i, t;
	cin >> T;
	while(T--) {
		cin >> n;
		for(i=0; i<n; i++) cin >> a[i];
		cin >> s;
		res = 0;
		vt.clear();
		for(i=n-1; i>=0; i--) {
			if(s[i]=='0') {
				t = a[i];
				for(auto x:vt) t = min(t, t^x);
				if(t) vt.push_back(t);
			} else {
				t = a[i];
				for(auto x:vt) t = min(t, t^x);
				if(t) {res=1; break;}
			}
		}
		cout << res << endl;
	}
	return 0;
}