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
// C - Switches
#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;

int main(){
	int N,M; cin>>N>>M;

	vi S(M);
	for(int m=0; m<M; ++m){
		int k; cin>>k;
		while(k--){ int s; cin>>s; S[m] |= 1<<(s-1); }
	}

	vi P(M); for(int p=0; p<M; ++p) cin>>P[p];

	int all = 1<<N, unmatch_count = 0;
	for(int s=0; s<all; ++s){//s: sw all pattern
		int b,m;
		for(m=0; m<M; ++m){//S[m]: sw data matching
			int sw = s & S[m];
			b = 0; while(sw){ if(sw&1) b=++b%2; sw/=2; }//count bit '1'
			if(b!=P[m]) break;
		}
		if(m<M && b!=P[m]) ++unmatch_count;
	}
	cout<< all - unmatch_count <<endl;
}