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 mod 1000000007
#define int long long int
#define pii pair<int,int>
#define vpii vector<pii>
#define vi vector<int>
#define fi first
#define se second
#define psb push_back
#define ppb pop_back
#define fio ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL)
#define all(x) x.begin(),x.end()
#define endl "\n"

int ar[300];

int32_t main()
{
	int t;
	cin>>t;
	while(t--)
	{
		int n;
		cin>>n;
		for(int i=0;i<n;i++)
			cin>>ar[i];
		string s;
		cin>>s;
		int ans=0;
		set<int,greater<int>> st;
		for(int i=n-1;i>=0;i--)
		{
			for(int e:st)
				ar[i]=min(ar[i],ar[i]^e);
			if(ar[i]==0)
				continue;
			if(s[i]=='0')
				st.insert(ar[i]);
			else
			{
				ans=1;
				break;
			}
		}
		cout<<ans<<endl;
	}
}