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 <cstdio>
#include <vector>

using namespace std;

long long a[200];
char s[201];

long long check(vector<long long>& v, long long x) {
    int i;
    
    for (i = 0; i < v.size(); i++) {
        if ((x ^ v[i]) < x) x ^= v[i];
    }
    
    return x;
}

bool solve() {
    int n, i;
    vector<long long> v;
    
    scanf("%d", &n);
    
    for (i = 0; i < n; i++) scanf("%lld", &a[i]);
    
    scanf("%s", s);
    
    for (i = n - 1; i >= 0; i--) {
        long long x = check(v, a[i]);
        
        if (s[i] == '0') {
            if (x != 0) v.push_back(x);
        } else {
            if (x != 0) return false;
        }
    }
    
    return true;
}

int main() {
    int t, i;
    
    scanf("%d", &t);
    
    for (i = 0; i < t; i++) {
        if (solve()) {
            puts("0");
        } else {
            puts("1");
        }
    }
    
    return 0;
}