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 X first
#define Y second

const int mo=1e9+7;

int n,m,dp[305][305][305],lim[305][2];
bool vis[305][305][305];

int main()
{
#ifdef h10
	freopen("E.in","r",stdin);
	freopen("E.out","w",stdout);
#endif
	int i,j,k,l,r,x;
	scanf("%d%d",&n,&m);
	memset(vis,1,sizeof(vis));
	for (i=1;i<=m;i++)
	{
		scanf("%d%d%d",&l,&r,&x);
		if (x==1)
		{
			for (j=0;j<=n;j++)
			for (k=0;k<=n;k++)
				vis[r][j][k]&=j<l;
		}
		if (x==2)
		{
			for (j=0;j<=n;j++)
			for (k=0;k<=n;k++)
				vis[r][j][k]&=j>=l&&k<l;
		}
		if (x==3)
		{
			for (j=0;j<=n;j++)
			for (k=0;k<=n;k++)
				vis[r][j][k]&=k>=l;
		}
	}
	dp[0][0][0]=1;
	for (i=0;i<n;i++)
	for (j=0;j<=i;j++)
	for (k=0;k<=j;k++)
	{
		if (dp[i][j][k]&&vis[i][j][k])
		{
			(dp[i+1][j][k]+=dp[i][j][k])%=mo;
			(dp[i+1][i][j]+=dp[i][j][k])%=mo;
			(dp[i+1][i][k]+=dp[i][j][k])%=mo;
		}
	}
	int Ans=0;
	for (j=0;j<=n;j++)
	for (k=0;k<=j;k++)
		if (vis[n][j][k]) (Ans+=dp[n][j][k])%=mo;
	printf("%d\n",Ans);
}