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;

#define N 2020
typedef long long ll;

int n;
ll a[N];
char s[N];
ll pos[66];

int main() {
    int T;
    scanf("%d", &T);
    while (T --) {
        scanf("%d", &n); memset(pos, -1, sizeof pos);
        for (int i = 1; i <= n; i ++) scanf("%lld", &a[i]); scanf("%s", s + 1);
        int ans = 0;
        for (int i = n; i >= 1; i --) {
            ll x = a[i];
            int k;
            for (k = 60; k >= 0; k --) if (x >> k & 1) {
                if (pos[k] < 0) break;
                else x ^= pos[k];
            }
            if (k < 0) continue;
            if (s[i] == '1') ans = 1;
            else pos[k] = x;
        }
        printf("%d\n", ans);
    }
}