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>

int main() {
	using namespace std;
	ios_base::sync_with_stdio(false), cin.tie(nullptr);
	int T; cin >> T;
	while (T--) {
		int N; cin >> N;
		vector<uint64_t> A(N); for (auto& a : A) cin >> a;
		string S; cin >> S;

		vector<uint64_t> basis; basis.reserve(64);
		bool ans = 0;
		for (int i = N-1; i >= 0; i--) {
			uint64_t v = A[i];
			for (uint64_t b : basis) {
				v = min(v, b ^ v);
			}
			if (v) {
				if (S[i] == '0') {
					basis.push_back(v);
				} else if (S[i] == '1') {
					ans = 1;
					break;
				} else assert(false);
			}
		}
		cout << ans << '\n';
	}

	return 0;
}