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<bits/stdc++.h>
#define L long long
#define vi vector<int>
#define pb push_back
#define pi pair<int,int>
#define pii pair<pi,int>
#define aa first
#define bb second
#define xx aa.aa
#define yy aa.bb
#define zz bb
#define mp make_pair
#define mpp(a,b,c) mp(mp(a,b),c)
using namespace std;
const int q=1000000007;
int n,m,f[310][310][310],p;
vi l[310],x[310];
inline void add(int &a,int b)
{
	a=(a+b)%q;
}
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i,j,k,u,v;
	scanf("%d%d",&n,&m);
	for(i=1;i<=m;i++)
	  {
	   scanf("%d%d%d",&j,&k,&u);
	   l[k].pb(j);
	   x[k].pb(u);
	  }
	f[0][0][0]=1;
	for(i=0;i<=n;i++)
	  for(j=0;j<=n;j++)
	    for(k=0;k<=n;k++)
	      if(f[i][j][k])
	        {
			 u=max(i,max(j,k));
			 for(v=0;v<l[u].size();v++)
			   if((i>=l[u][v])+(j>=l[u][v])+(k>=l[u][v])!=x[u][v])
			     break;
			 if(v<l[u].size())
			   continue;
			 if(u==n)
			   add(p,f[i][j][k]);
			 else
			   {
				add(f[u+1][j][k],f[i][j][k]);
				add(f[i][u+1][k],f[i][j][k]);
				add(f[i][j][u+1],f[i][j][k]);
			   }
			}
	printf("%d\n",p);
	return 0;
}