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;

int solve () {
	int n;
	cin >> n;
	vector<long long> a(n);
	for (auto &e : a) cin >> e;
	string s;
	cin >> s;
	
	vector<long long> b;
	for (int i = n; i--> 0;) {
		long long e = a[i];
		for (const auto &c : b) e = min(e, e^c);
		if (e > 0) {
			if (s[i] == '1') return 1;
			b.push_back(e);
		}
	}
	return 0;
}

int main() {
	int t;
	cin >> t;
	while (t--) cout << solve() << '\n';
	return 0;
}