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>
#include<cstring>
#include<algorithm>
using namespace std;
struct edge
{
	int v,w,nxt;
}e[500005];
int n,m,h[100005],t;
int f[305][305][305],mod=1e9+7,ans;
void add(int u,int v,int w)
{
	e[++t].v=v;
	e[t].w=w;
	e[t].nxt=h[u];
	h[u]=t;
}
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		int l,r,x;
		scanf("%d%d%d",&l,&r,&x);
		add(r,l,x);
	}
	f[1][0][0]=3;
	for(int i=1;i<=n;i++)
	{
		for(int j=h[i];j;j=e[j].nxt)
		{
			int v=e[j].v,w=e[j].w;
			for(int k=0;k<i;k++)
				for(int l=0;l<=max(k-1,0);l++)
				{
					if(w==1&&k>=v) f[i][k][l]=0;
					if(w==2&&(k<v||l>=v)) f[i][k][l]=0;
					if(w==3&&l<v) f[i][k][l]=0; 
				}
		}
		for(int j=0;j<i;j++)
			for(int k=0;k<=max(j-1,0);k++)
			{
				f[i+1][j][k]=(f[i+1][j][k]+f[i][j][k])%mod;
				f[i+1][i][k]=(f[i+1][i][k]+f[i][j][k])%mod;
				f[i+1][i][j]=(f[i+1][i][j]+f[i][j][k])%mod;
			}
	}
	for(int i=0;i<n;i++)
		for(int j=0;j<=max(i-1,0);j++)
			ans=(ans+f[n][i][j])%mod;
	printf("%d",ans);
	return 0;
}