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>
#define ll long long
using namespace std;
ll t[100];
ll a[209];
int n;
string S;
void add(ll x){
    for(int i=59; i>=0; --i){
        if(x&(1ll<<i))x^=t[i];
        if(x&(1ll<<i)){
            t[i]=x;
            break;
        }
    }
}

bool check(ll x){
    for(int i=59; i>=0 && x; --i)
    if(x&(1ll<<i))x^=t[i];
    return x;
}

void xuli(){
    for(int i=0; i<60; ++i)t[i]=0;
    cin >> n;
    for(int i=1; i<=n; ++i) cin >> a[i];
    cin >> S;
    S=" "+S;
    for(int i=n; i>=1; --i){
        if(S[i]=='0')add(a[i]);
        else
        if(check(a[i])){
            cout << 1<<endl;
            return;
        }
    }
    cout << 0 <<endl;
}

int main()
{
    #ifdef abcxyz
    freopen("a.inp","r", stdin);
    #endif // abcxyz
    int t;
    cin >> t;
    while(t--)xuli();
    return 0;
}