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<cstdlib>
#define mod 1000000007
#define ll long long
#define N 310
using namespace std;
ll f[N][N][N];
int head[N],nxt[N<<1],x[N<<1],to[N<<1],cnt;
void add(int r,int l,int lim)
{
	nxt[++cnt]=head[r];
	to[cnt]=l;
	x[cnt]=lim;
	head[r]=cnt;
}
int main()
{
	int n,m;
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		int l,r,x;
		scanf("%d%d%d",&l,&r,&x);
		add(r,l,x);
	}
	f[1][0][0]=1;
	for(int r=1;r<=n;r++)
	{
		for(int o=head[r];o;o=nxt[o])
		{
			int l=to[o];
			for(int i=0;i<r;i++)
				for(int j=0;j<=max(0,i-1);j++)
				{
 					if(x[o]==1 && l<=i) f[r][i][j]=0;
 					if(x[o]==2 && (i<l || l<=j)) f[r][i][j]=0;
					if(x[o]==3 && j<l) f[r][i][j]=0;
                }
		}
		for(int l=0;l<r;l++)
			for(int i=0;i<=max(0,l-1);i++)
			if(f[r][l][i])
			{
				f[r+1][l][i]=(f[r+1][l][i]+f[r][l][i])%mod;
				f[r+1][r][i]=(f[r+1][r][i]+f[r][l][i])%mod;
				f[r+1][r][l]=(f[r+1][r][l]+f[r][l][i])%mod;
			}
	}
	ll ans=0;
	for(int i=0;i<n;i++)
		for(int j=0;j<=max(0,i-1);j++)
		ans=(ans+f[n][i][j])%mod;
    printf("%lld\n",ans*3%mod);
	return 0;
}