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>
using namespace std;
#define re register
#define ll long long
const int N=310;
struct node{
	int l,x;
};
vector<node>G[N];
const int Mod=1e9+7;
int f[N][N][N],n,m;
bool check(int a,int b,int c){
	int r=max(a,max(b,c));
	for(int i=0,t=G[r].size();i<t;i++){
		int l=G[r][i].l,x=G[r][i].x,s=0;
		s=(a>=l)+(b>=l)+(c>=l);
		if(s!=x)return false;
	}
	return true;	
}
int main(){
	scanf("%d%d",&n,&m);
	for(re int i=1;i<=m;i++){
		int x,l,r;scanf("%d%d%d",&l,&r,&x);
		G[r].push_back((node){l,x});
	}
	f[0][0][0]=1;ll ans=0;
	for(re int i=0;i<=n;i++)
		for(re int j=0;j<=n;j++)
			for(re int k=0;k<=n;k++)
				if(f[i][j][k]){
					if((i && j && i==j) || (j && k && j==k) || (i && k && i==k))continue;
					if(!check(i,j,k)){f[i][j][k]=0;continue;}
					int r=max(i,max(j,k));
					f[r+1][j][k]+=f[i][j][k];if(f[r+1][j][k]>=Mod)f[r+1][j][k]-=Mod;
					f[i][r+1][k]+=f[i][j][k];if(f[i][r+1][k]>=Mod)f[i][r+1][k]-=Mod;
					f[i][j][r+1]+=f[i][j][k];if(f[i][j][r+1]>=Mod)f[i][j][r+1]-=Mod;
					if(r==n){
						ans+=f[i][j][k];if(ans>=Mod)ans-=Mod;
					}
				}
	printf("%lld\n",ans);
	return 0;
}