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>
#define Maxn 307
#define modp 1000000007
using namespace std;
int read()
{
	int x=0,f=1;char ch=getchar();
	while (ch<'0'||ch>'9'){if (ch=='-') f=-1;ch=getchar();}
	while (ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
int n,m;
bool vis[Maxn][Maxn][Maxn];
int f[Maxn][Maxn][Maxn];
multiset<pair<int,int> >s[Maxn];
int dfs(int a,int b,int c)
{
	if (vis[a][b][c]) return f[a][b][c];
	vis[a][b][c]=true;
	int now=max(a,max(b,c));
	for (multiset<pair<int,int> >::iterator it=s[now].begin();it!=s[now].end();it++)
	{
		int r=0;
		r=(a>=(*it).first)+(b>=(*it).first)+(c>=(*it).first);
		if (r!=(*it).second)
		{
			f[a][b][c]=0;
			return 0;
		}
	}
	if (now>=n)
	{
		f[a][b][c]=1;
		return 1;
	}
	f[a][b][c]=(f[a][b][c]+dfs(now+1,b,c))%modp;
	f[a][b][c]=(f[a][b][c]+dfs(a,now+1,c))%modp;
	f[a][b][c]=(f[a][b][c]+dfs(a,b,now+1))%modp;
	return f[a][b][c];
}
int main()
{
	n=read(),m=read();
	for (int i=1;i<=m;i++)
	{
		int l=read(),r=read(),x=read();
		s[r].insert(make_pair(l,x));
	}
	printf("%d\n",dfs(0,0,0));
	return 0;
}