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
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<n;i++)
#define rev(i,n) for(int i=n-1;i>=0;i--)
#define all(v) v.begin(),v.end()
#define P pair<int,int>
#define len(s) (int)s.size()
#define pb push_back

template<class T> inline bool chmin(T &a, T b){
	if(a>b){a=b;return true;}
	return false;
}
template<class T> inline bool chmax(T &a, T b){
	if(a<b){a=b;return true;}
	return false;
}
constexpr int mod = 1e9+7;
constexpr int inf = 3e18;


int N,A[205];
string S;
void solve(){
	cin>>N;
	rep(i,N)cin>>A[i];
	cin>>S;
	vector<int>v;
	rev(i,N){
		int j=A[i];
		for(int k:v)chmin(j,j^k);
		if(j){
			if(S[i]=='0')v.pb(j);
			else {
				puts("1");return;
			}
		}
	}
	puts("0");
}
signed main(){
	int t;cin>>t;
	while(t--)solve();
}