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 <algorithm>
#include <cstdio>

const int mo=1000000007;
int f[305][305];

struct info{
	int l,r,x;
}p[305];

bool cmp(info a,info b){
	return a.r<b.r;
}

int main(){
	int n,m;
	scanf("%d%d\n",&n,&m);
	for (int i=1;i<=m;i++)
		scanf("%d%d%d\n",&p[i].l,&p[i].r,&p[i].x);
	std::sort(p+1,p+m+1,cmp);
	f[0][0]=3;
	for (int i=0,t=1;i<n;i++){
		if (i)
		for (int j=i-1;j>=0;j--)
			for (int k=j?j-1:0;k>=0;k--){
				(f[i][k]+=f[j][k])%=mo;
				(f[i][j]+=f[j][k])%=mo;
			}
		for (;t<=m && p[t].r==i+1;t++)
		if (p[t].x==1){
			for (int j=p[t].l;j<=i;j++)
				for (int k=0;k<=j;k++) f[j][k]=0;
		}
		else if (p[t].x==2){
			for (int j=0;j<=i;j++)
				for (int k=0;k<=j;k++)
				if (!(k<p[t].l && p[t].l<=j)) f[j][k]=0;
		}
		else{
			for (int j=0;j<=i;j++)
				for (int k=0;k<p[t].l;k++) f[j][k]=0;
		}
	}
	int ans=0;
	for (int i=0;i<n;i++)
		for (int j=0;j<=i;j++) (ans+=f[i][j])%=mo;
	printf("%d\n",ans);
}