We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.

Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.

How many combinations of "on" and "off" states of the switches light all the bulbs?

Constraints

* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M


Output

Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.

Examples

Input

2 2
2 1 2
1 2
0 1


Output

1


Input

2 3
2 1 2
1 1
1 2
0 0 1


Output

0


Input

5 2
3 1 2 5
2 2 3
1 0


Output

8
#include<bits/stdc++.h>
#define For(a,b,c) for(int a=b;a<=c;++a)
#define Dor(a,b,c) for(int a=b;a>=c;--a)
using namespace std;
const int N=12;
int n,m,P[N],K[N],A[N][N];
bool ok(int i) {
	For(j,1,m) {
		int c=0;
		For(k,1,K[j]) if(i&(1<<A[j][k]>>1)) ++c;
		if(c%2!=P[j]) return 0;
	}
	return 1;
}
int main() {
	scanf("%d%d",&n,&m);
	For(i,1,m) {
		scanf("%d",&K[i]);
		For(j,1,K[i]) scanf("%d",&A[i][j]);
	}
	For(i,1,m) scanf("%d",&P[i]);
	int ans=0;
	For(i,0,(1<<n)-1)
		if(ok(i)) ++ans;
	printf("%d",ans);
	return 0;
}