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=310,mod=1000000007;
int f[N][N][N],n,m,ans;
vector<pair<int,int> >g[N];
inline void reduce(int&x){x+=x>>31&mod;}
int chk(int i,int j,int k){
	int L=max(max(i,j),k);
	for(auto x:g[L])
		if((i>=x.first)+(j>=x.first)+(k>=x.first)!=x.second)return 0;
	return 1;
}

int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n>>m;
	for(;m --> 0;){
		int x,y,z;cin>>x>>y>>z;
		g[y].emplace_back(x,z);
	}
	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(f[i][j][k]&&chk(i,j,k)){
				int L=max(max(i,j),k);
				if(L==n)reduce(ans+=f[i][j][k]-mod);
				else{
					reduce(f[L+1][j][k]+=f[i][j][k]-mod);
					reduce(f[i][L+1][k]+=f[i][j][k]-mod);
					reduce(f[i][j][L+1]+=f[i][j][k]-mod);
				}
			}
	cout<<ans<<'\n';
	return 0;
}