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>

const int p=1000000007;

int f[320][320][320];
int ord1[320],ord2[320],next[320],first[320];
int i,j,k,m,n,s,x,y,z,sum_edge;

inline void addedge(int x,int y,int z)
{
	sum_edge++,ord1[sum_edge]=y,ord2[sum_edge]=z,next[sum_edge]=first[x],first[x]=sum_edge;
	return;
}

inline bool check(int x,int y,int z)
{
	for (int i=first[z];i!=0;i=next[i])
	{
		if ((ord2[i]==1) && (ord1[i]<=y)) return false;
		if ((ord2[i]==2) && ((ord1[i]>y) || (ord1[i]<=x))) return false;
		if ((ord2[i]==3) && (ord1[i]>x)) return false;
	}
	return true;
}

int main()
{
	scanf("%d%d",&n,&m);
	for (i=1;i<=m;i++)
		scanf("%d%d%d",&x,&y,&z),addedge(y,x,z);
	f[0][0][0]=1;
	for (i=0;i<=n;i++)
		for (j=0;j<=i;j++)
			for (k=j;k<=i;k++)
				if (f[i][j][k])
				{
					if (! check(j,k,i)) f[i][j][k]=0;
					f[i+1][j][i]=(f[i+1][j][i]+f[i][j][k])%p;
					f[i+1][k][i]=(f[i+1][k][i]+f[i][j][k])%p;
					f[i+1][j][k]=(f[i+1][j][k]+f[i][j][k])%p;
				}
	for (j=0;j<=n;j++)
		for (k=j;k<=n;k++)
			s=(s+f[n][j][k])%p;
	printf("%d",s);
	return 0;
}