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 long long md=1e9+7;
int n,m;
vector<pair<int,int> >g[305];
long long ans,dp[305][305][305];
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=0;i<m;i++)
	{
		int l,r,x;
		scanf("%d%d%d",&l,&r,&x);
		g[r].push_back(make_pair(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 r=max(i,max(j,k));
		for(int l=0;l<g[r].size();l++)if((i>=g[r][l].first)+(j>=g[r][l].first)+(k>=g[r][l].first)!=g[r][l].second)dp[i][j][k]=0;
		if(r==n)ans=(ans+dp[i][j][k])%md;
		else
		{
			dp[r+1][j][k]=(dp[r+1][j][k]+dp[i][j][k])%md;
			dp[i][r+1][k]=(dp[i][r+1][k]+dp[i][j][k])%md;
			dp[i][j][r+1]=(dp[i][j][r+1]+dp[i][j][k])%md;
		}
	}
	printf("%lld\n",ans);
	return 0;
}