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 <iostream>
#include <cstdio>
#include <vector>

using namespace std;

typedef long long ll;

ll T;
ll n;
ll a[205];
string s;
vector<ll> ve;

int main()
{
    scanf("%lld", &T);
    while(T--)
    {
        bool v = false;
        ve.clear();
        scanf("%lld", &n);
        for(ll i = 0; i < n; i++)
        {
            scanf("%lld", &a[i]);
        }
        cin>>s;
        for(ll i = n - 1; i >= 0; i--)
        {
            for(ll j = 0; j < ve.size(); j++)
            {
                a[i] = min(a[i], a[i] ^ ve[j]);
            }
            if(s[i] == '0')
            {
                if(a[i] > 0) ve.push_back(a[i]);
            }
            else if(a[i] > 0)
            {
                printf("1\n");
                v = true;
                break;
            }
        }
        if(!v) printf("0\n");
    }
    return 0;
}