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 N 305
#define P 1000000007
using namespace std;
int n,m,dp[N][N][N],ans;
struct T
{
	int x,y;
};
vector<T>v[N];
void upd(int &x,int y)
{
	x=x+y;
	if (x>P) x-=P;
}
bool pd(int s[3],int t)
{
	int a[4];
	a[0]=0;a[1]=s[0];a[2]=s[1];a[3]=s[2];
	sort(a,a+4);
	for (int i=0;i<v[t].size();i++)
		if (!(v[t][i].x>a[3-v[t][i].y]&&v[t][i].x<=a[4-v[t][i].y]))
			return 0;
//	cout<<s[0]<<' '<<s[1]<<' '<<s[2]<<'-'<<t<<endl;
	return 1;
}
int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i<=m;i++)
	{
		int x,y,z;
		scanf("%d%d%d",&x,&y,&z);
		v[y].push_back((T){x,z});
	}
	dp[0][0][0]=1;
	for (int a=0;a<=n;a++)
	for (int b=0;b<=n;b++)
	for (int c=0;c<=n;c++)
	{
		int t=max(a,max(b,c))+1,s[3];
		if (t>n)
		{
			upd(ans,dp[a][b][c]);
			continue;
		}
		s[0]=a;s[1]=b;s[2]=c;
		for (int k=0;k<=2;k++)
		{
			int tmp=s[k];s[k]=t;
			if (pd(s,t))
				upd(dp[s[0]][s[1]][s[2]],dp[a][b][c]);
			s[k]=tmp;
		}
	}
	//cout<<dp[0][0][1]<<endl;
	printf("%d\n",ans);
}