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 <algorithm>
#include <vector>
using namespace std;
typedef long long ll;
const int N = 205;
ll a[N];
char s[N];
int main()
{
    int T; scanf("%d", &T);
    while(T--) {
        int n; scanf("%d", &n);
        for(int i = 1; i <= n; i++) scanf("%lld", &a[i]);
        scanf("%s", s + 1);
        vector<ll> v;
        bool flag = 1;
        for(int i = n; i >= 1; i--) {
            ll b = a[i];
            for(int k = 0; k < v.size(); k++) b = min(b, b ^ v[k]);
            if (b) {
                if(s[i] == '1') {flag = 0; break;}
                v.push_back(b);
            }
        }
        if(flag) puts("0");
        else puts("1");
    }
    return 0;
}