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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		label:
		for (int x = 0; x < t; x++) {
			int n = Integer.parseInt(br.readLine());
			String[] sa = br.readLine().split(" ");
			long[] a = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = Long.parseLong(sa[i]);
			}
			char[] s = br.readLine().toCharArray();

			for (int i = n - 1; i >= 0; i--) {
				if (s[i] == '0') {
					for (int k = 0; k < 61; k++) {
						if ((a[i] >> k & 1) == 1) {
							for (int j = 0; j < n; j++) {
								if (i != j && (a[j] >> k & 1) == 1) {
									a[j] ^= a[i];
								}
							}
						}
					}
				} else {
					if (a[i] != 0) {
						System.out.println(1);
						continue label;
					}
				}
			}
			System.out.println(0);
		}
	}
}