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 <cstdio>

typedef long long LL;
const int MN = 205;

int N;
LL A[MN];
char s[MN];
LL B[64];

int main() {
	int Tests;
	scanf("%d", &Tests);
	while (Tests--) {
		scanf("%d", &N);
		for (int i = 1; i <= N; ++i) scanf("%lld", &A[i]);
		scanf("%s", s + 1);
		int ok = 1;
		for (int j = 0; j < 60; ++j) B[j] = 0;
		for (int i = N; i >= 1; --i) {
			if (s[i] == '1') {
				LL x = A[i];
				for (int j = 59; j >= 0; --j) if (x >> j & 1) {
					if (B[j]) x ^= B[j];
					else break;
				}
				if (x) { ok = 0; break; }
			} else {
				LL x = A[i];
				for (int j = 59; j >= 0; --j) if (x >> j & 1) {
					if (!B[j]) B[j] = x;
					x ^= B[j];
				}
			}
		}
		puts(ok ? "0" : "1");
	}
	return 0;
}