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 mod 1000000007
int n,m,dp[305][305][305];
vector<pair<int,int> > v[305];
int solve(int a,int b,int c)
{
	if (dp[a][b][c]!=-1)
	return dp[a][b][c];
	int idx=max(a,max(b,c));
	for (auto p:v[idx])
	{
		if ((a>=p.first)+(b>=p.first)+(c>=p.first)!=p.second)
		return dp[a][b][c]=0;
	}
	if (idx==n)
	return dp[a][b][c]=1;
	return dp[a][b][c]=((solve(idx+1,b,c)+solve(a,idx+1,c))%mod+solve(a,b,idx+1))%mod;
}
int main()
{
	scanf("%d%d",&n,&m);
	while (m--)
	{
		int l,r,x;
		scanf("%d%d%d",&l,&r,&x);
		v[r].push_back({l,x});
	}
	memset(dp,-1,sizeof(dp));
	printf("%d",solve(0,0,0));
}