Problem: There is a directed graph G with N vertices and M edges. The vertices are numbered 1 through N, and the edges are numbered 1 through M. Edge i is directed from x_i to y_i. Here, x_i < y_i holds. Also, there are no multiple edges in G.

Consider selecting a subset of the set of the M edges in G, and removing these edges from G to obtain another graph G'. There are 2^M different possible graphs as G'.

Alice and Bob play against each other in the following game played on G'. First, place two pieces on vertices 1 and 2, one on each. Then, starting from Alice, Alice and Bob alternately perform the following operation:

* Select an edge i such that there is a piece placed on vertex x_i, and move the piece to vertex y_i (if there are two pieces on vertex x_i, only move one). The two pieces are allowed to be placed on the same vertex.



The player loses when he/she becomes unable to perform the operation. We assume that both players play optimally.

Among the 2^M different possible graphs as G', how many lead to Alice's victory? Find the count modulo 10^9+7.

Constraints

* 2 ≤ N ≤ 15
* 1 ≤ M ≤ N(N-1)/2
* 1 ≤ x_i < y_i ≤ N
* All (x_i,\ y_i) are distinct.

Input

Input is given from Standard Input in the following format:


N M
x_1 y_1
x_2 y_2
:
x_M y_M


Output

Print the number of G' that lead to Alice's victory, modulo 10^9+7.

Examples

Input

2 1
1 2


Output

1


Input

3 3
1 2
1 3
2 3


Output

6


Input

4 2
1 3
2 4


Output

2


Input

5 10
2 4
3 4
2 5
2 3
1 2
3 5
1 3
1 5
4 5
1 4


Output

816

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int read(){
	int x=0;
	char ch=getchar();
	while (!isdigit(ch))
		ch=getchar();
	while (isdigit(ch))
		x=(x<<1)+(x<<3)+(ch^48),ch=getchar();
	return x;
}
const int N=15,S=1<<N,mod=1e9+7;
void Add(int &x,int y){
	if ((x+=y)>=mod)
		x-=mod;
}
int n,m;
int g[N][N],pw[N*N],cnte[N][S],dp[S];
int DP(int S){
	int &v=dp[S];
	if (~v)
		return v;
	if (!S)
		return v=1;
	int d[N],t=0;
	for (int i=0;i<n;i++)
		if (S>>i&1)
			d[t++]=i;
	v=0;
	for (int k=1;k<(1<<t);k++){
		int i=0;
		for (int j=0;j<t;j++)
			if (k>>j&1)
				i|=1<<d[j];
		if ((i&3)==1||(i&3)==2)
			continue;
		int j=S^i,now=1;
		// i -> i  no Edges
		// j -> i  at least one per node
		for (int x=0;now&&x<n;x++)
			if (j>>x&1)
				now=1LL*now*(pw[cnte[x][i]]-1)%mod;
		if (!now)
			continue;
		// i -> j  all
		for (int x=0;x<n;x++)
			if (i>>x&1)
				now=1LL*now*pw[cnte[x][j]]%mod;
		// j -> j  DP(j)
		now=1LL*now*DP(j)%mod;
		Add(v,now);
	}
	return v;
}
int main(){
	for (int i=pw[0]=1;i<N*N;i++)
		pw[i]=2*pw[i-1]%mod;
	n=read(),m=read();
	memset(g,0,sizeof g);
	for (int i=1;i<=m;i++){
		int a=read()-1,b=read()-1;
		g[a][b]=1;
	}
	for (int x=0;x<n;x++)
		for (int i=0;i<(1<<n);i++)
			for (int y=0;y<n;y++)
				if (g[x][y]&&(i>>y&1))
					cnte[x][i]++;
	memset(dp,-1,sizeof dp);
	cout << (pw[m]-DP((1<<n)-1)+mod)%mod << endl;
	return 0;
}