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;
const int nm=301,mod=1e9+7;
int f[nm][nm][nm];
vector<int>lb[nm],kind[nm];
void update(int &a,int b){a=(a+b)%mod;}
int main(){
	int n,m,ans=0;
	scanf("%d%d",&n,&m);
	for(int l,r,x;m--;){
		scanf("%d%d%d",&l,&r,&x);
		lb[r].push_back(l),kind[r].push_back(x);
	}f[1][0][0]=1;
	for(int r=1;;r++){
		for(int i=0,Lb,Kind;i<lb[r].size();i++){
			Lb=lb[r][i],Kind=kind[r][i];
			for(int g=0;g<r;g++)
				for(int b=0;b<g||!b;b++){
					if(Kind==1){
						if(Lb<=g)f[r][g][b]=0;
					}else
						if(Kind==2){
							if(Lb<=b||g<Lb)f[r][g][b]=0;
						}else if(b<Lb)f[r][g][b]=0;
				}
		}if(r==n)break;
		for(int g=0;g<r;g++)
			for(int b=0,x;b<g||!b;b++){
				x=f[r][g][b];
				update(f[r+1][g][b],x);
				update(f[r+1][r][b],x);
				update(f[r+1][r][g],x);
			}
	}for(int g=0;g<n;g++)
		for(int b=0;b<g||!b;b++)update(ans,f[n][g][b]);
	return printf("%lld\n",(long long)ans*3%mod),0;
}