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>
#define fi first
#define se second
#define neko 310
#define pb push_back
#define f(i,a,b) for(register int i=(a);i<=(b);i=-(~(i)))
using namespace std;
typedef pair<int,int>pi;
vector<pi>vec[neko];
int n,m,dp[neko][neko][neko],ans,mod=1e9+7;
inline int cmax(int a,int b){return a>b?a:b;}
int ADD(int x,int y){return ((x+=y)>=mod)?x-mod:x;}
inline bool check(int r,int g,int b)
{
	int x=cmax(r,cmax(g,b)),len,l;len=vec[x].size()-1;
	f(i,0,len)
	{
		l=vec[x][i].fi;
		if(((r>=l)+(g>=l)+(b>=l))^vec[x][i].se)return 0;
	}return 1;
}
int main()
{
	int x,y,z;
	scanf("%d%d",&n,&m);
	f(i,1,m)scanf("%d%d%d",&x,&y,&z),vec[y].pb(pi(x,z));
	dp[0][0][0]=1;
	f(r,0,n)
	 f(g,0,n)
	  f(b,0,n)
	  {
		if(!dp[r][g][b])continue; 
		x=cmax(r,cmax(g,b))+1;
		if(!check(r,g,b))continue;
		if(x==n+1)ans=ADD(ans,dp[r][g][b]);
		dp[x][g][b]=ADD(dp[x][g][b],dp[r][g][b]);
		dp[r][x][b]=ADD(dp[r][x][b],dp[r][g][b]);
		dp[r][g][x]=ADD(dp[r][g][x],dp[r][g][b]);
	  }
	printf("%d\n",(ans+mod)%mod);
	return 0;
}