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>
#define N 17
#define MASK 70000
#define mod 1000000007
using namespace std;

int n,m,tp,sum;
int g[MASK][N], F[MASK],e[N*N];
inline int lowbit(int x) {return x&(-x);}
inline int rd() {int r;scanf("%d",&r);return r;}
inline void inc(int &x,int y) {x=(x+y)%mod;}

int main() {
	n = rd(), m = rd(), tp = (1<<n) - 1;

	e[0] = 1;
	for (int _=1;_<=m;_++) e[_] = 1LL * e[_-1] * 2 % mod;
	sum = e[m];

	for (int _=1;_<=m;_++) {
		int a = rd(), b = rd();
		g[1<<(b-1)][a] = 1;
	}
	
	for (int _=1;_<=tp;_++)
		for (int i=1;i<=n;i++) {
			int x = lowbit(_);
			g[_][i] = g[_^x][i] + g[x][i];
		}
		
	F[0] = 1;
	for (int i=1;i<=tp;i++) if ((i&1) == ((i>>1)&1)){
		for (int k=i;k;k=(k-1)&i) if ((k&1) == ((k>>1)&1)){
			int j = i^k, cur = F[j], tmp = 1;
			for (int x=1;x<=n;x++) if ((1<<(x-1))&i) {
				if ((1<<(x-1)) & j)
					tmp = 1LL * tmp * (e[g[k][x]]-1) % mod;
				else
					tmp = 1LL * tmp * e[g[j][x]] % mod;
			}
			inc(F[i], 1LL * cur * tmp % mod);
		}
	}
	
	int ans = (sum - F[tp]) % mod;
	ans < 0 ? ans += mod : 0;
	cout << ans << endl;
	return 0;
}