Problem: There are N squares arranged in a row. The squares are numbered 1, 2, ..., N, from left to right.

Snuke is painting each square in red, green or blue. According to his aesthetic sense, the following M conditions must all be satisfied. The i-th condition is:

* There are exactly x_i different colors among squares l_i, l_i + 1, ..., r_i.



In how many ways can the squares be painted to satisfy all the conditions? Find the count modulo 10^9+7.

Constraints

* 1 ≤ N ≤ 300
* 1 ≤ M ≤ 300
* 1 ≤ l_i ≤ r_i ≤ N
* 1 ≤ x_i ≤ 3

Input

Input is given from Standard Input in the following format:


N M
l_1 r_1 x_1
l_2 r_2 x_2
:
l_M r_M x_M


Output

Print the number of ways to paint the squares to satisfy all the conditions, modulo 10^9+7.

Examples

Input

3 1
1 3 3


Output

6


Input

4 2
1 3 1
2 4 2


Output

6


Input

1 3
1 1 1
1 1 2
1 1 3


Output

0


Input

8 10
2 6 2
5 5 1
3 5 2
4 7 3
4 4 1
2 3 1
7 7 1
1 5 2
1 7 3
3 4 2


Output

108

Solution (in CPP):

Solution:
#include<cstdio>
const int mod=1000000007;
int N,M,f[310][310][310];
struct item{int l,x;item*next;}a[310],*fir[310];
bool chk(int i,int j,int k){
	for(item*it=fir[i];it;it=it->next)
		if((i>=it->l)+(j>=it->l)+(k>=it->l)!=it->x)return 0;
	return 1;
}
int main(){
	scanf("%d%d",&N,&M);
	for(int i=0;i<M;i++){
		int l,r,x;scanf("%d%d%d",&l,&r,&x);
		a[i]=(item){l,x,fir[r]};fir[r]=a+i;
	}
	f[0][0][0]=1;
	for(int i=0;i<N;i++)for(int j=0;j<=i;j++)for(int k=0,g;k<=j;k++){
		if(g=(chk(i,j,k)?f[i][j][k]:0)){
			(f[i+1][j][k]+=g)%=mod;
			(f[i+1][i][k]+=g)%=mod;
			(f[i+1][i][j]+=g)%=mod;
		}
	}
	int s=0;
	for(int j=0;j<=N;j++)for(int k=0;k<=j;k++)
		if(chk(N,j,k))(s+=f[N][j][k])%=mod;
	printf("%d\n",s);
}