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:
#define fi first
#define se second
#define mp make_pair
#define pb push_back

#define LOCAL 1

#include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#define dbg(...) cout<<#__VA_ARGS__ ": ["; for(auto e: __VA_ARGS__){cout<<e<<", ";} cout<<"]\n"
#define dbg1(...) cout<<#__VA_ARGS__ " "<< __VA_ARGS__ 
#else
#define dbg(...) 1;
#define dbg1(...) 1;
#endif

typedef long long ll;
typedef unsigned long long ull;
constexpr int R=5e5+69, INF=2e9+6969;

int qq;

int main()
{
	scanf("%d", &qq);
	while(qq--)
	{
		ll n,t[R];
		string s;
		scanf("%lld", &n);
		for(int i=0;i<n;++i) scanf("%lld", &t[i]);
		cin >> s;
		vector <ll> base;
		base.clear();
		bool ok=1;
		for(int i=n-1;i>=0;--i)
		{
			ll x = t[i];
			for(ll e: base) x = min(x,e^x);
			if(x==0) continue;
			if(s[i]=='0') base.pb(x);
			else
			{
				ok=0;
				break;
			}
		}
		puts(ok ? "0" : "1");
	}
	return 0;
}