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>
#define lsb(x) (x & (-x))
#define ll long long
#define ull unsigned long long
#define Test(tt) cout << "Case #" << tt << ": "

using namespace std;



int main() {
#ifdef HOME
    ifstream cin("B.in");
    ofstream cout("B.out");
#endif
   	int	t, i;
    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);

	cin >> t;
	while(t--) {
		int n;
		cin >> n;

		vector<ll> values(n);
		for(i = 0; i < n; i++) {
			cin >> values[i];
		}

		string str;
		cin >> str;

		vector<int> id(60, -1);
		bool ans = 1;

		for(i = n - 1; i >= 0; i--) {
			bool found = 1;

			for(int bit = 59; bit >= 0; bit--) {
				if(values[i] & (1LL << bit)) {
					if(id[bit] != -1) {
						values[i] ^= values[id[bit]];
					}
					else {
						id[bit] = i;
						found = 0;
						break;
					}
				}
			}

			if(str[i] == '1' && found == 0) {
				ans = 0;
				break;
			}
		}

		cout << (ans ^ 1) << "\n";
	}

    return 0;
}