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;
typedef long long ll;
struct base
{
    ll c[65];
    bool insert(ll x)
    {
        for(int i=62;i>=0;i--)
            if(x&(1ll<<i))
                if(!c[i]){c[i]=x;return 1;}
                else x^=c[i];
        return 0;
    }
}b;
string str;
ll a[205];
int main()
{
    int _;
    scanf("%d",&_);
    while(_--)
    {
        memset(b.c,0,sizeof(b.c));
        int n;
        scanf("%d",&n);
        for(int i=1;i<=n;i++)scanf("%lld",&a[i]);
        cin>>str;
        for(int i=n;i>=1;i--)
        {
            if(str[i-1]=='0')b.insert(a[i]);
            else if(b.insert(a[i])){puts("1");goto nxt;}
        }
        puts("0");
        nxt:;
    }
    return 0;
}