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:
//https://atcoder.jp/contests/arc074/tasks/arc074_c
#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int N=310;
int n,m;
ll f[N][N][N];
struct node
{
	int l,w;
};
vector<node>G[N];
const int p=1e9+7;
void add(ll &x,ll y){x=(x+y)%p;}
bool check(int x,int y,int z)
{
	int r=max(x,max(y,z));
	for(int i=0;i<G[r].size();i++)
	{
		int l=G[r][i].l,w=G[r][i].w,s=0;
		s=(x>=l)+(y>=l)+(z>=l);
		if(s!=w) return 0;
	}
	return 1;
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0),cout.tie(0);
	cin>>n>>m;
	for(int i=1,x,y,w;i<=m;i++) 
	{
		cin>>x>>y>>w;
		G[y].push_back({x,w});
	}
	f[0][0][0]=1;
	ll ans=0;
	for(int i=0;i<=n;i++) 
	 for(int j=0;j<=n;j++)
	  for(int k=0;k<=n;k++)
	  {
	  	 if(!f[i][j][k]) continue;
	  	 if((i&&j&&i==j)||(j&&k&&j==k)||(i==k&&i&&k)) continue;
	  	 if(check(i,j,k)==0) 
	  	 {
	  	 	f[i][j][k]=0;
	  	 	continue;
	  	 }
	  	 int r=max(i,max(j,k));
	  	 add(f[r+1][j][k],f[i][j][k]);
	  	 add(f[i][r+1][k],f[i][j][k]);
		 add(f[i][j][r+1],f[i][j][k]);
		 if(r==n) add(ans,f[i][j][k]); 
	  }
    cout<<ans<<endl;
    return 0;
	 
}