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:
// M
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 303;
int q, n;
ll A[N];
char S[N];
int main()
{
	scanf("%d", &q);
	for (; q; q --)
	{
		scanf("%d", &n);
		for (int i = 0; i < n; i ++)
			scanf("%lld", &A[i]);
		memset(S, 0, sizeof(S));
		scanf("%s", &S);
		bool Sec = 0;
		vector < ll > B;
		for (int i = n - 1; ~ i; i --)
			if (A[i])
			{
				if (S[i] == '0')
				{
					ll a = A[i];
					for (ll b : B)
						a = min(a, a ^ b);
					for (ll &b : B)
						b = min(b, a ^ b);
					if (a) B.push_back(a);
				}
				else
				{
					ll a = A[i];
					for (ll b : B)
						a = min(a, a ^ b);
					if (a) {Sec = 1; break;}
				}
			}
		printf("%d\n", (int)Sec);
	}
	return 0;
}