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>
#define fi first
#define se second
#define mk(x,y) make_pair(x,y)
#define pii pair<int,int> 
using namespace std;
const int maxn=305;
const int mod=1e9+7;
int n,m;
int dp[maxn][maxn][maxn];
int ans;
vector<pii> vec[maxn];
int main(){
	cin>>n>>m;
	for(int i=1;i<=m;i++){
		int l,r,x;
		cin>>l>>r>>x;
		vec[r].push_back(make_pair(l,x));
	}
	dp[1][0][0]=3;
	for(int i=0;i<=n;i++){
		for(int j=0;j<=n;j++){
			for(int k=0;k<=n;k++){
				for(int l=0;l<vec[i].size();l++){
					if(1+(j>=vec[i][l].fi)+(k>=vec[i][l].fi)!=vec[i][l].se){
						dp[i][j][k]=0;
					}
				}
				if(i==n) ans=(ans+dp[i][j][k])%mod;
				else{
					dp[i+1][j][k]=(dp[i+1][j][k]+dp[i][j][k])%mod;
					dp[i+1][i][k]=(dp[i+1][i][k]+dp[i][j][k])%mod;
					dp[i+1][i][j]=(dp[i+1][i][j]+dp[i][j][k])%mod;
				}
			}
		}
	}
	cout<<ans;
	return 0;
}