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<iostream>
#include<cstdio>
#include<cstdlib>
#include<vector>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define R max(i,max(j,k))
using namespace std;
const int N=310,mod=1e9+7;
int n,m,f[N][N][N],ans;
vector<pair<int,int> > E[N];
void add(int &a,int b) {a+=b;if(a>=mod) a-=mod;}
int main()
{
	cin>>n>>m;f[0][0][0]=1;
	for(int i=1,l,r,x;i<=m;i++) cin>>l>>r>>x,E[r].pb(mp(l,x));
	for(int i=0;i<=n;i++)
		for(int j=0;j<=n;j++)
			for(int k=0;k<=n;k++)
			{
				int &s=f[i][j][k];if(!s) continue;
				if((i&&i==k)||(j&&j==k)||(i&&i==j)) s=0;
				for(auto x:E[R]) if((i>=x.fi)+(j>=x.fi)+(k>=x.fi)!=x.se) s=0;
				if(!s) continue;add(f[R+1][j][k],s);
				add(f[i][R+1][k],s);add(f[i][j][R+1],s);
				if(R==n) (ans+=f[i][j][k])%=mod;
			}
	cout<<ans<<endl;return 0;
}