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 REP(i, n) for (int i = 0; i < (n); i++)
using namespace std;
using ll = long long;

int main() {
    cin.tie(0)->sync_with_stdio(false);

    int t;
    cin >> t;

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

        vector<ll> a(n);
        REP(i, n) cin >> a[i];

        string s;
        cin >> s;

        int ans = 0;
        vector<ll> dp;
        for (int i = n - 1; i >= 0; i--) {
            for (auto j : dp) a[i] = min(a[i], a[i]^j);
            if (s[i] == '0') {
                if (a[i]) dp.push_back(a[i]);
            } else if (a[i]) {
                ans = 1;
                break ;
            }
        }
        cout << ans << '\n';
    }
    return 0;
}