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=305,mod=1e9+7;
inline void add(int &a,int b){a+=b;if(a>=mod)a-=mod;}
int dp[N][N][N],n,m,ans;
vector<int>l[N],x[N];
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		int a,b,c;
		scanf("%d%d%d",&a,&b,&c);
		l[b].push_back(a);
		x[b].push_back(c);
	}
	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(max(i,j),k);
				int &f=dp[i][j][k];
				for(int z=0;z<l[r].size();z++)
				{
					int s=(i>=l[r][z])+(j>=l[r][z])+(k>=l[r][z]);
					if(s!=x[r][z])
						f=0;
				}
				add(dp[r+1][j][k],f);
				add(dp[i][r+1][k],f);
				add(dp[i][j][r+1],f);
				if(r==n)
					add(ans,f);
			}
		}
	}
	printf("%d\n",ans);
	return 0;
}