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 rep(i,n) for(int i=0;i<(n);++i)
#define Rep(i,n) for(int i=1;i<=(n);++i)
using LL = long long;
using ULL = unsigned long long;

const LL INF = 1e18;

LL b[60];

bool f(LL x) {
    rep(i, 60) if((1ll << i) & x) {
        if(!b[i]) {
            b[i] = x;
            return true;
        }
        x ^= b[i];
    }
    return false;
}

int main()
{
    int T;
    cin >> T;
    while(T--) {
        memset(b, 0, sizeof b);
        int n;
        cin >> n;
        vector<LL> a(n);
        for(LL &x: a) cin >> x;
        string s;
        cin >> s;
        for(int i = n-1; i >= 0; --i) {
            if(f(a[i]) && s[i] == '1') {
                puts("1");
                goto _;
            }
        }
        puts("0");
        _: ;
    }
	return 0;
}