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>
#define int long long
#define pb push_back
#define fi first
#define se second
#define FOR(i,a,b) for (int i = a; i < b; ++i)
#define ROF(i,a,b) for (int i = (b-1); i >= a; --i)
#define REP(i,a,b) for (int i = a; i <= b; ++i)
#define PER(i,a,b) for (int i = b; i >= a; --i)
#define F0R(i,b) FOR(i,0,b)
#define R0F(i,b) ROF(i,0,b)
#define R1P(i,b) REP(i,1,b)
#define P1R(i,b) PER(i,1,b)
using namespace std;

int n, a[200];
char s[201];
int x[63];

void solve() {
	int n;
	cin >> n;
	F0R(i,n) cin >> a[i];
	cin >> s;
	memset(x, 0, sizeof(x));
	R0F(i,n) {
		if (s[i] == '0') {
			R0F(j, 63) if (a[i] & (1ll<<j)) {
				if (!x[j]) { x[j] = a[i]; break; }
				a[i] ^= x[j];
			}
		} else {
			R0F(j, 63) if (a[i] & (1ll<<j)) a[i] ^= x[j];
			if (a[i]) { puts("1"); return; }
		}
	}
	puts("0");
}

signed main() {
	int t;
	cin >> t;
	while (t--) solve();
}