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 Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define Reg register
#define RI Reg int
#define Con const
#define CI Con int&
#define I inline
#define W while
#define N 200
#define LN 63
#define ull unsigned long long
using namespace std;
int n,ans;ull a[N+5],v[LN+5];char op[N+5];
I void Clear() {ans=0;for(RI i=LN;~i;--i) v[i]=0;}
I void Ins(ull x)
{
	for(RI i=LN;~i;--i) if((x>>i)&1) {if(!v[i]) return (void)(v[i]=x);x^=v[i];}
}
I bool Q(ull x)
{
	for(RI i=LN;~i;--i) if((x>>i)&1) {if(!v[i]) return 0;x^=v[i];}return 1;
}
int main()
{
	RI Tt,i;scanf("%d",&Tt);W(Tt--)
	{
		for(Clear(),scanf("%d",&n),i=1;i<=n;++i) scanf("%llu",a+i);scanf("%s",op+1);
		for(ans=1,i=n;i;--i) if(a[i])
			{if(op[i]=='1'&&!Q(a[i])) {ans=0;break;}op[i]=='0'&&(Ins(a[i]),0);}
		putchar(49-ans),putchar('\n');
	}return 0;
}