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;

const int N = 205;

char s[N];
long long A[N];

struct linarBase {
    long long c[64];
    bool insert(long long x) {
        for(int i = 60; ~i; --i) if(x >> i & 1) {
            if(!c[i]) {
                c[i] = x;
                return true;
            } else {
                x ^= c[i];
            }
        }
        return false;
    }
    void init() {
        for(int i = 0; i <= 60; ++i)
            c[i] = 0;
    }
} B;

int main() {
    int Case, n;
    scanf("%d", &Case);
    while(Case--) {
        B.init();
        scanf("%d", &n);
        for(int i = 1; i <= n; ++i)
            scanf("%lld", &A[i]);
        scanf("%s", s + 1);
        bool flag = true;
        for(int i = n; i >= 1; --i) {
            if(B.insert(A[i]) && s[i] == '1') {
                flag = false;
            }
        }
        puts(flag ? "0" : "1");
    }
    return 0;
}