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

using namespace std;

const int mod = 1e9+7;

int dp[2][305][305]={};
vector<pair<int,int>> seg[305];

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	int n,m; cin >> n >> m;
	
	while(m--){
		int l,r,x; cin >> l >> r >> x;
		seg[r].emplace_back(l,x);
	}
	
	dp[0][0][0]=1;
	for(int i=0;i<=n;i++){
		int cur = i&1, nxt=(i+1)&1;
		for(int j=0;j<=i;j++){
			for(int k=0;k<=j;k++){
				
				for(auto s:seg[i]){
					
					int cx=1+(j>=s.fi)+(k>=s.fi);

					//cout << dp[cur][j][k] << " " << j << " " << k << " " << cx << endl;
					
					dp[cur][j][k]*=(cx==s.se);
				}
				
				
				dp[nxt][j][k]=(dp[nxt][j][k]+dp[cur][j][k])%mod;
				dp[nxt][i][k]=(dp[nxt][i][k]+dp[cur][j][k])%mod;
				dp[nxt][i][j]=(dp[nxt][i][j]+dp[cur][j][k])%mod;
			}
		}
		
		if(i<n)
			memset(dp[cur],0,sizeof(dp[cur]));
	}
	
	int ans=0;
	for(int i=0;i<=n;i++){
		for(int j=0;j<=n;j++){
			ans=(ans+dp[n&1][i][j])%mod;
		}
	}
	
	cout << ans << endl;
	return 0;
}