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 int long long
inline void read (int &x) {
	char ch = getchar(); x = 0;
	while (!isdigit(ch)) ch = getchar();
	while (isdigit(ch)) x = x * 10 + ch - 48, ch = getchar();
} const int N = 238; int n, m = 62, a[N], k[N]; char ch[N]; 
signed main() {
	int T; read (T);
	while (T--) {
		read (n); int ok = 1;
		for (int i = 0; i <= 100; ++i) k[i] = 0;
		for (int i = 1; i <= n; ++i) read (a[i]);
		scanf ("%s", ch + 1);
		for (int i = n; i >= 1; --i) {
			for (int j = 0; j <= m; ++j) 
				if ((a[i] >> j) & 1) a[i] ^= k[j];
			if (ch[i] == '1') {
				if (a[i]) { ok = 0; break; }
			} else {
			  	for (int j = 0; j <= m; ++j)
					if ((a[i] >> j) & 1) { k[j] = a[i]; break; }
			}
		} ok ? puts ("0") : puts ("1");
	} return 0;
}