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 N=305,mod=1e9+7;
int n,m,f[N][N][N];
bool vis[N][N][N];
vector<pair<int,int> >lim[N];
bool Judge(int i,int j,int k){
	int len=max(i,max(j,k));
	for(int p=0;p<lim[len].size();p++){
		int cnt=(i>=lim[len][p].first)+(j>=lim[len][p].first)+(k>=lim[len][p].first);
		if(cnt!=lim[len][p].second)return 0;
	}
	return 1;
}
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++){
		int l,r,x;
		scanf("%d%d%d",&l,&r,&x);
		lim[r].push_back(make_pair(l,x));
	}
	int ans=0;
	f[0][0][0]=1;
	for(int i=0;i<=n;i++)
		for(int j=0;j<=n;j++)
			for(int k=0;k<=n;k++){
				if(vis[i][j][k]||!Judge(i,j,k))continue;
				vis[i][j][k]=1;
				if(i==n||j==n||k==n)ans=(ans+f[i][j][k])%mod;
				int len=max(i,max(j,k));
				f[len+1][j][k]=(f[len+1][j][k]+f[i][j][k])%mod;
				f[i][len+1][k]=(f[i][len+1][k]+f[i][j][k])%mod;
				f[i][j][len+1]=(f[i][j][len+1]+f[i][j][k])%mod;
			}
	cout<<ans<<"\n";
}