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
#define ld long double
#define fs first
#define sc second
#define task "tst"
using namespace std;
const ll N = 300 + 9;
const ll inf = 1e6 + 7;
typedef pair<ll,ll> LL;

ll t,n,a[N],i,j;
string s;
bool chk(){
    vector<ll> v;
    v.push_back(0);
    for (i = n;i >= 1;i--){
        ll p = a[i];
        for (auto j : v) p = min(p,p^j);
        if (p){
            if (s[i] == '1') return true;
            v.push_back(p);
        }
    }
    return false;
}
int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    if (fopen(task".inp", "r")){
        freopen(task".inp", "r", stdin);
        //freopen(task".out", "w", stdout);
    }
    cin>>t;
    while(t--){
        cin>>n;
        for (i = 1;i <= n;i++) cin>>a[i];
        cin>>s; s = " " + s;
        cout<<chk()<<"\n";
    }
}