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;

#define LL long long

const int maxN = 505, lim = 61;

int n, T;
LL a[maxN + 1], p[maxN + 1];
char s[maxN + 1];

inline void insert(LL x)
{
	for(int i = lim; i >= 0; i--)
		if(x & (1ll << i))
		{
			if(p[i]) x ^= p[i];
			else
			{ 
				p[i] = x; 
				break; 
			}
		}
}

inline bool check(LL x)
{
	for(int i = lim; i >= 0; i--)
		if(x & (1ll << i)) x ^= p[i];
	return x == 0;
}

int main()
{
	scanf("%d", &T);
	while(T --)
	{
		scanf("%d", &n);
		for(int i = 1; i <= n; i++) scanf("%lld", &a[i]);
		
		for(int i = 0; i <= lim; i++) p[i] = 0;
		scanf("%s", s + 1);

		bool flag = true;
		for(int i = n; i >= 1; i--)
			if(s[i] == '0') insert(a[i]);
			else if(!check(a[i])) { flag = false; break; }
		
		puts(flag ? "0" : "1");
	}
	return 0;
}