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<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int md=1000000007;
int n,m,i,j,k,l,x,g[305][305],h[305][305],cnt[305],f[305][305][305];
int main()
{
	scanf("%d%d",&n,&m);
	for(i=1;i<=m;++i)
	{
		scanf("%d%d%d",&j,&k,&x);
		++cnt[k];
		g[k][cnt[k]]=j,h[k][cnt[k]]=x;
		if(k==1&&x>1)
		{
			printf("0");
			return 0;
		}
	}
	f[1][0][0]=1;
	for(i=1;i<n;++i)
	{
		for(j=0;j<i;++j)
			for(k=0;k<i;++k)
				if(f[i][j][k])
				{
					f[i+1][j][i]=(f[i+1][j][i]+f[i][j][k])%md;
					f[i+1][k][i]=(f[i+1][k][i]+f[i][j][k])%md;
					f[i+1][j][k]=(f[i+1][j][k]+f[i][j][k])%md;
				}
		for(j=0;j<=i;++j)
			for(k=0;k<=i;++k)
			if(f[i+1][j][k])
			{
				for(x=1;x<=cnt[i+1];++x)
					if((j>=g[i+1][x])+(k>=g[i+1][x])+(i+1>=g[i+1][x])!=h[i+1][x])
					{
						f[i+1][j][k]=0;
						break;
					}
			}
		/*for(j=0;j<=i+1;++j)
			for(k=0;k<=i+1;++k)
				if(f[i+1][j][k])
					printf("%d %d %d %d\n",i+1,j,k,f[i+1][j][k]);*/
	}
	x=0;
	for(j=0;j<=n;++j)
		for(k=0;k<=n;++k)
			x=(x+f[n][j][k])%md;
	printf("%lld",x*3ll%md);
	return 0;
}