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
#define mp make_pair
#define pb push_back

#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#define rep(i, n) for (int i = 0; i < (int)(n); ++ i)

#define ull unsigned ll

struct LB {
	ull a[64];
	void clr() { memset(a, 0, sizeof(a)); }
	bool ins(ull x) {
		for (int i = 63; ~i; -- i)
			if (x & 1ull << i) {
				if (not a[i]) {
					a[i] = x;
					return 1;
				} else {
					x ^= a[i];
				}
			}
		return 0;
	}
} lb;

int n;
ull a[205];
char s[205];

void Main() {
	scanf("%d", &n);
	rep(i, n) scanf("%llu", &a[i]);
	scanf("%s", s);
	lb.clr();
	for (int i = n - 1; ~i; -- i) {
		bool ok = lb.ins(a[i]);
		if (s[i] == '1' and ok) { puts("1"); return ; }
	}
	puts("0");
}

int main() {
	int T; scanf("%d", &T);
	while (T --) Main();
	return 0;
}