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 ll long long

typedef pair<int,int> P;
const int N=305;
const ll mod=1e9+7;
int n,m;
ll dp[N][N][N];
vector<P> r[N];

int main() {
	ios_base::sync_with_stdio(0);cin.tie(0);
	cin>>n>>m;
	for(int i=0;i<m;++i){
		int L,R,x;
		cin>>L>>R>>x;
		r[R].emplace_back(L,x);
	}
	dp[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){
				int t=max({i,j,k});
				for(P p:r[t]){
					int l=p.first;
					int x=p.second;
					if((l<=i)+(l<=j)+(l<=k)!=x) 
						dp[i][j][k]=0;
				}
				if(t==n||!dp[i][j][k]) continue;
				(dp[t+1][j][k]+=dp[i][j][k])%=mod;
				(dp[i][t+1][k]+=dp[i][j][k])%=mod;
				(dp[i][j][t+1]+=dp[i][j][k])%=mod;
			}
	ll res=0;
	for(int i=0;i<n;++i)
		for(int j=0;j<n;++j){
			(res+=dp[n][i][j])%=mod;
			(res+=dp[i][n][j])%=mod;
			(res+=dp[i][j][n])%=mod;
		}
	cout<<res<<'\n';
}