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>
using namespace std;
#include<cstdio>
#define el "\n"
#define sp " "
typedef long long ll;

int main()
{
	ios_base::sync_with_stdio(false);
cin.tie(NULL);
ll n,m,x,y,i,j;
cin>>n>>m;
vector<ll> v[m];
for(i=0;i<m;i++)
{
	cin>>x;
	for(j=0;j<x;j++)
	{
		cin>>y;
		y--;
	
	v[i].push_back(y);
	}
}
ll p[m],ans=0;
for(i=0;i<m;i++)
cin>>p[i];
for(x=0;x<(1<<n);x++)
{
	ll f=1;
	for(i=0;i<m;i++)
	{
		ll cnt=0;
		for(auto j:v[i])
		{
			if(x&(1<<j))
			cnt++;
		}
		if(cnt%2!=p[i])
		f=0;
	}
	if(f)
	ans++;
}
cout<<ans;
}
