Problem:
Score : 800 points

Problem Statement

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.

Sample Input 1

3 1
1 3 3

Sample Output 1

6

The six ways are:

RGB

RBG

GRB

GBR

BRG

BGR

where R, G and B correspond to red, green and blue squares, respectively.

Sample Input 2

4 2
1 3 1
2 4 2

Sample Output 2

6

The six ways are:

RRRG

RRRB

GGGR

GGGB

BBBR

BBBG

Sample Input 3

1 3
1 1 1
1 1 2
1 1 3

Sample Output 3

0

There are zero ways.

Sample Input 4

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

Sample Output 4

108

Solution in C++ (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define LL long long
#define db double
#define il inline
#define re register
#define mkpr make_pair

using namespace std;
const int N=300+10,mod=1e9+7;
il LL rd()
{
    LL x=0,w=1;char ch=0;
    while(ch<'0'||ch>'9') {if(ch=='-') w=-1;ch=getchar();}
    while(ch>='0'&&ch<='9') {x=(x<<3)+(x<<1)+(ch^48);ch=getchar();}
    return x*w;
}
int f[N][N][N],n,m,s[3];
struct qu
{
	int l,r,z;
	bool operator < (const qu &bb) const {return r<bb.r;}
}qq[N];
bool ck(int l,int r)
{
	for(int i=l;i<=r;++i)
	{
		int cn=0;
		for(int j=0;j<3;++j) cn+=s[j]>=qq[i].l;
		if(cn!=qq[i].z) return 0;
	}
	return 1;
}

int main()
{
	n=rd(),m=rd();
	for(int i=1;i<=m;++i) qq[i].l=rd(),qq[i].r=rd(),qq[i].z=rd();
	sort(qq+1,qq+m+1);
	f[0][0][0]=1;
	for(int i=0,h=1;i<n;++i)
	{
		int l=h,r=h-1;
		while(r<=m&&qq[r+1].r==i+1) ++r;
		for(int j=0;j<=i;++j)
			for(int k=0;k<=j;++k)
			{
				if(!f[i][j][k]) continue;
				s[0]=i+1,s[1]=j,s[2]=k;
				if(ck(l,r)) f[s[0]][s[1]][s[2]]=(f[s[0]][s[1]][s[2]]+f[i][j][k])%mod;
				s[0]=i+1,s[1]=i,s[2]=k;
				if(ck(l,r)) f[s[0]][s[1]][s[2]]=(f[s[0]][s[1]][s[2]]+f[i][j][k])%mod;
				s[0]=i+1,s[1]=i,s[2]=j;
				if(ck(l,r)) f[s[0]][s[1]][s[2]]=(f[s[0]][s[1]][s[2]]+f[i][j][k])%mod;
			}
		h=r+1;
	}
	int ans=0;
	for(int j=0;j<=n;++j)
		for(int k=0;k<=j;++k)
			ans=(ans+f[n][j][k])%mod;
	printf("%d\n",ans);
    return 0;
}