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 mod=1e9+7;

#define add(a,b) (a+=b)>=mod&&(a-=mod)

int dp[302][301][301],first[301];

struct query{ int l,x,nx; }q[301];

int main()
{
	int i,j,k,l,m,n,ans=0;
	scanf("%d%d",&n,&m);
	for(i=1;i<=m;i++)
		scanf("%d%d%d",&q[i].l,&j,&q[i].x),
			q[i].nx=first[j],first[j]=i;
	dp[0][0][0]=1;
	for(i=0;i<=n;i++)
		for(j=0;j<i||!j;j++)
			for(k=0;k<j||!k;k++)
				if(dp[i][j][k])
				{
					for(l=first[i];l;l=q[l].nx)
						switch(q[l].x){
						case 1:if(j>=q[l].l)goto loop;break;
						case 2:if(k>=q[l].l||j<q[l].l)goto loop;break;
						case 3:if(k<q[l].l)goto loop;break;
						}
					if(i==n)add(ans,dp[i][j][k]);
					else
					{
						add(dp[i+1][j][k],dp[i][j][k]);
						add(dp[i+1][i][k],dp[i][j][k]);
						add(dp[i+1][i][j],dp[i][j][k]);
					}
				loop:;
				}
	printf("%d\n",ans);
}