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 MAXN = 205;

int T,n;

ll base[64];
ll a[MAXN];

char s[MAXN];

void insert(ll v)
{
	for (int i = 62;i >= 0;i--)
		if (v >> i & 1)
		{
			if (!base[i])
			{
				base[i] = v;
				return;
			}
			v ^= base[i];
		}
}

bool ok(ll v)
{
	for (int i = 62;i >= 0;i--)
		if (v >> i & 1)
		{
			if (!base[i])
				return 0;
			v ^= base[i];
		}
	return 1;
}

int main()
{
	scanf("%d",&T);
	while (T--)
	{
		scanf("%d",&n);
		for (int i = 1;i <= n;i++)
			scanf("%lld",&a[i]);
		scanf("%s",s + 1);
		memset(base,0,sizeof(base));
		int flag = 0;
		for (int i = n;i >= 1;i--)
			if (s[i] == '0')
				insert(a[i]);
			else if (!ok(a[i]))
			{
				flag = 1;
				break;
			}
		printf("%d\n",flag);
	}
	return 0;
}