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 P=1e9+7;
const int N=305;

int n,m;
vector< pair<int,int> >a[N];

long long f[N][N][N];

int check(int i,int j,int k)
{
	int r=max(i,max(j,k));
	int len=a[r].size();
	for(int ii=0;ii<len;ii++)
	{
		int l=a[r][ii].first;
		int res=0;
		if(i>=l) res++;
		if(j>=l) res++;
		if(k>=l) res++;
		if(res!=a[r][ii].second) return 0;
	}
	return 1;
}

void Mod(long long &x)
{
	if(x>=P) x-=P;
}


int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		int l,r,x;
		scanf("%d%d%d",&l,&r,&x);
		if(l>r) swap(l,r);
		a[r].push_back(make_pair(l,x));
	}
	f[0][0][0]=1;
	long long Ans=0;
	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]) continue;
				if(!check(i,j,k)) continue;
				int r=max(i,max(j,k))+1;
				if(r==n+1)
				{
					Ans+=f[i][j][k];
					Mod(Ans);
					continue;
				}
				f[r][j][k]+=f[i][j][k],Mod(f[r][j][k]);
				f[i][r][k]+=f[i][j][k],Mod(f[i][r][k]);
				f[i][j][r]+=f[i][j][k],Mod(f[i][j][r]);
			}
	cout<<Ans<<endl;
	return 0;
}