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 Maxn 207
using namespace std;
int T,n;
long long a[Maxn];
int op[Maxn];
long long r[62];
bool add(long long x)
{
    for (int i=60;i>=0;i--)
        if (x&(1LL<<i))
        {
            if (r[i]) x^=r[i];
            else
            {
                r[i]=x;
                return true;
            }
        }
    return false;
}
void solve()
{
    scanf("%d",&n);
    for (int i=1;i<=n;i++)
        scanf("%lld",&a[i]);
    for (int i=1;i<=n;i++)
    {
        char ch=getchar();
        while (ch!='0'&&ch!='1') ch=getchar();
        if (ch=='0') op[i]=0; else op[i]=1;
    }
    memset(r,0,sizeof(r));
    for (int i=n;i;i--)
    {
        if (op[i]==0) add(a[i]);
        else if (op[i]==1&&add(a[i]))
        {
            printf("%d\n",1);
            return;
        }
    }
    printf("%d\n",0);
}
int main()
{
    scanf("%d",&T);
    while (T--) solve();
    return 0;
}