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 modulo 1000000007
#define mod(mod_x) ((((long long)mod_x+modulo))%modulo)
#define Inf 1000000000000

int main(){

	int N,M;
	cin>>N>>M;
	
	vector<vector<pair<int,int>>> Q(N+1,vector<pair<int,int>>());
	
	for(int i=0;i<M;i++){
		int l,r,x;
		cin>>l>>r>>x;
		Q[r].emplace_back(l,x);
	}
	
	vector<vector<vector<int>>> dp(N+1,vector<vector<int>>(N+1,vector<int>(N+1,0)));
	dp[0][0][0] = 1;
	
	for(int i=0;i<=N;i++){
		for(int j=0;j<Q[i].size();j++){
			for(int x=0;x<=N;x++){
				for(int y=0;y<=N;y++){
					int t = 1;
					if(x>=Q[i][j].first)t++;
					if(y>=Q[i][j].first)t++;
					if(t!=Q[i][j].second){
						dp[i][x][y]=0;
					}
				}
			}
		}
		if(i==N)break;
		for(int j=0;j<=N;j++){
			for(int k=0;k<=N;k++){
				if(dp[i][j][k]==0)continue;
				int t = dp[i][j][k];
				dp[i+1][j][k] = mod(dp[i+1][j][k]+t);
				dp[i+1][k][i] = mod(dp[i+1][k][i]+t);
				dp[i+1][i][j] = mod(dp[i+1][i][j]+t);
			}
		}
	}
	
	int ans =  0;
	for(int j=0;j<=N;j++){
		for(int k=0;k<=N;k++){
			ans = mod(ans + dp.back()[j][k]);
		}
	}
	cout<<ans<<endl;
	return 0;
}