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 fore(i,a,b) for(int i=a,ggdem=b;i<ggdem;i++)
#define FIN ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pb push_back

const int MAXN=302,MOD=1e9+7;
int n,m,dp[MAXN][MAXN][MAXN],l[MAXN],r[MAXN],x[MAXN];
vector<int>g[MAXN];
int solve(int i,int j,int k) {
	int pos=max({i,j,k})+1;
	for(int p:g[pos]) {
		int expected=x[p];
		int have=(i>=l[p])+(j>=l[p])+(k>=l[p]);
		if(expected!=have) {
			return dp[i][j][k]=0;
		}
	}
	if(pos>n)return 1;
	if(dp[i][j][k]!=-1)return dp[i][j][k];
	int res=solve(pos,j,k);
	res=res+solve(i,pos,k);if(res>MOD)res-=MOD;
	res=res+solve(i,j,pos);if(res>MOD)res-=MOD;
	// cout<<i<<" "<<j<<" "<<k<<" : "<<res<<endl;
	return dp[i][j][k]=res;
}

int main() {FIN;
	memset(dp,-1,sizeof(dp));
	cin>>n>>m;
	fore(i,0,m) {
		cin>>l[i]>>r[i]>>x[i];r[i]++;
		g[r[i]].pb(i);
	}
	cout<<solve(0,0,0)<<"\n";
}