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 P=1e9+7;
int n,m;
int f[307][307][307];
void inc(int&a,int b){
	if(~a&&(a+=b)>=P)a-=P;
}
void trans(int a,int b,int c,int d){
	int x=f[a][b][c];
	if(x<=0)return;
	inc(f[d][b][c],x);
	inc(f[a][d][c],x);
	inc(f[a][b][d],x);
}
int chk(int x){return x>0?x:0;}
int main(){
	scanf("%d%d",&n,&m);
	for(int i=0,l,r,x;i<m;++i){
		scanf("%d%d%d",&l,&r,&x);
		for(int a=0;a<=r;++a){
			for(int b=0;b<=r;++b){
				if((a>=l)+(b>=l)+1!=x)f[r][a][b]=f[a][r][b]=f[a][b][r]=-1;
			}
		}
	}
	inc(f[1][0][0],1);
	inc(f[0][1][0],1);
	inc(f[0][0][1],1);
	for(int t=1;t<n;++t){
		for(int a=0;a<t;++a){
			for(int b=0;b<t;++b){
				trans(t,a,b,t+1);
				trans(a,t,b,t+1);
				trans(a,b,t,t+1);
			} 
		}
	}
	long long s=0;
	for(int a=0;a<n;++a)
	for(int b=0;b<n;++b){
		s+=chk(f[n][a][b]);
		s+=chk(f[a][n][b]);
		s+=chk(f[a][b][n]);
	}
	printf("%lld\n",s%P);
	return 0;
}