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>
#include<vector>
#define N 305
#define oo (1<<30)
using namespace std;
const int mo=1e9+7;
int n,m,f[N][N][N],ans,L[4][N],R[4][N];
void inc(int &x,int y){ x=x+y>=mo ? x+y-mo : x+y;}
bool in(int s,int t,int l,int r){ return s>=l&&t<=r;}
int main()
{
	int i,j,k,l,r,x,y;
	scanf("%d %d",&n,&m);
	for(i=1;i<=n;i++)
		for(j=1;j<=3;j++)
			L[j][i]=oo,R[j][i]=-oo;
	for(i=1;i<=m;i++){
		scanf("%d %d %d",&l,&r,&x);
		R[x][r]=max(R[x][r],l);
		L[x][r]=min(L[x][r],l);
	  }
	f[1][0][0]=3;
	for(i=1;i<n;i++)
		for(j=0;j<i;j++)
			for(k=0;k<i;k++){
				x=max(j,k),y=j+k-x;
				if(!in(L[1][i],R[1][i],x+1,i)) continue;
				if(!in(L[2][i],R[2][i],y+1,x)) continue;
				if(!in(L[3][i],R[3][i],1,y)) continue;
				inc(f[i+1][j][k],f[i][j][k]);
				inc(f[i+1][i][k],f[i][j][k]);
				inc(f[i+1][i][j],f[i][j][k]);
			  }
	for(i=0;i<n;i++)
		for(j=0;j<n;j++){
			x=max(i,j),y=i+j-x;
			if(!in(L[1][n],R[1][n],x+1,n)) continue;
			if(!in(L[2][n],R[2][n],y+1,x)) continue;
			if(!in(L[3][n],R[3][n],1,y)) continue;
			inc(ans,f[n][i][j]);
		  }
	cout<<ans;
	return 0;
}