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;
const int sz = 205;

ll a[sz], b[69];
char s[sz];

bool gauss(ll x)
{
   for(int i=0; i<61; i++) {
      if(x & 1LL << i) {
         if(b[i]) x ^= b[i];
         else {
            b[i] = x;
            return 0;
         }
      }
   }
   return 1;
}

void solve()
{
   int n;
   scanf("%d", &n);
   for(int i=0; i<n; i++) scanf("%lld", &a[i]);
   scanf("%s", s);

   int ans = 0;
   memset(b, 0, sizeof b);
   for(int i=n-1; i>=0 && !ans; i--) {
      if(!gauss(a[i]) && s[i] == '1') ans = 1;
   }
   printf("%d\n", ans);
}

int main()
{
   int t;
   cin >> t;
   while(t--) solve();
}