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;
const int maxn = 200 + 10;
const int maxb = 62;
typedef long long ll;
ll a[maxn];
char s[maxn];
ll b[maxn];
void init()
{
	memset(b, 0, sizeof b);
}
ll insert(ll x)
{
	for(int i = maxb - 1; ~i; --i)
		if((x >> i) & 1)
		{
			if(!b[i])
			{
				b[i] = x;
				break;
			}
			else
				x ^= b[i];
		}
	return x;
}
int main()
{
	int T;
	scanf("%d", &T);
	while(T--)
	{
		int n;
		scanf("%d", &n);
		for(int i = 1; i <= n; ++i) scanf("%lld", &a[i]);
		scanf("%s", s + 1);
		init();
		int flag = 0;
		for(int i = n; i; --i)
			if(s[i] == '0')
				insert(a[i]);
			else if(insert(a[i]))
			{
				flag = 1;
				break;
			}
		cout << flag << endl;
	}
	return 0;
}