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;
using UL = unsigned int;
using ULL = unsigned long long;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)

struct Problem {
public:
	UL N;
	ULL A[200];
	string S;

	void Solve() {
		UL T; scanf("%u", &T);
		while (T--) {
			scanf("%u", &N);
			rep(i, N) scanf("%llu", &A[i]);
			cin >> S;
			reverse(S.begin(), S.end());
			reverse(A, A + N);
			UL ans = 0;
			rep(i, N) {
				if (S[i] == '0') {
					ULL d = ~(A[i] - 1) & A[i];
					for (UL j = i + 1; j < N; j++)
						if (A[j] & d) A[j] ^= A[i];
				}
				else {
					if (A[i]) {
						ans = 1;
					}
				}
			}
			printf("%u\n", ans);
		}
	}
};

int main() {
	unique_ptr<Problem> p(new Problem());
	p->Solve();
	return 0;
}