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 PA pair<int,int>
const int N=310,mod=1000000007;
int n,m,ans;
struct node
{
	int l,r,num;
	friend bool operator < (const node &r1,const node &r2)
	{return r1.r<r2.r;}
}a[N];
int f[N][N][N];
int main()
{
	//freopen("tt.in","r",stdin);
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
		scanf("%d%d%d",&a[i].l,&a[i].r,&a[i].num);
	sort(a+1,a+1+m);
	f[1][0][0]=3;
	for(int i=1,now=1;i<=n;i++)
	{
		while(now<=m&&a[now].r==i)
		{
			int l=a[now].l,num=a[now].num;
			for(int j=0;j<i;j++)
				for(int k=0;k<=j;k++)
				{
					int t=1;
					if(j>=l)t++;
					if(k>=l)t++;
					if(t!=num)f[i][j][k]=0;
				}
			now++;
		}
		if(i==n)break;
		for(int j=0;j<i;j++)
			for(int k=0;k<=j;k++)
			{
				(f[i+1][j][k]+=f[i][j][k])%=mod;
				(f[i+1][i][k]+=f[i][j][k])%=mod;
				(f[i+1][i][j]+=f[i][j][k])%=mod;
			}
	}
	for(int j=0;j<n;j++)
		for(int k=0;k<=j;k++)
			(ans+=f[n][j][k])%=mod;
	printf("%d\n",ans);
	return 0;
}