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<iostream>
#include<cstdio>
#include<algorithm>
#define mod 1000000007
using namespace std;
int dp[310][310][310];
struct xxx{int l,r,x;}q[310];
bool cmp(xxx a,xxx b){return a.r<b.r;}
int main()
{
	int n,m;scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)scanf("%d%d%d",&q[i].l,&q[i].r,&q[i].x);
	sort(q+1,q+m+1,cmp);
	int j=1;
	dp[0][0][1]=3;
	for(int i=1;i<=n;i++)
	{
		int kkk;
		for(int b=0;b<i;b++)
		{
			for(int a=0;a<max(b,1);a++)
			{
				int k=j;
				while(j<=m&&q[j].r==i)
				{
					int ok=0;
					if(q[j].l<=a)ok++;
					if(q[j].l<=b)ok++;
					if(q[j].l<=i)ok++;
					if(ok!=q[j].x)dp[a][b][i]=0;
					j++;
				}
				kkk=j;j=k;
				dp[a][b][i+1]=(dp[a][b][i+1]+dp[a][b][i])%mod;
				dp[a][i][i+1]=(dp[a][i][i+1]+dp[a][b][i])%mod;
				dp[b][i][i+1]=(dp[b][i][i+1]+dp[a][b][i])%mod;	
			}
		}
		j=kkk;
	}
	int ans=0;
	for(int b=0;b<n;b++)for(int a=0;a<max(b,1);a++)ans=(ans+dp[a][b][n])%mod;
	printf("%d",ans);return 0;
}