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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define int long long
#define inf 1000000007
#define LINF 1000000000000000007mope
#define ll long long
using namespace std;
int dp[301][301][301],used[301][301][301];
vector< pair<int,int> > cons[301];
bool isvalid(int i,int j, int k){
	if( i!=0 && i==j )return false;
	if( j!=0 && j==k )return false;
	if( k!=0 && k==i )return false;
	return true;
}
void checker(int i,int j, int k ){
	int rig = max( i, max( j, k ) );
	int lef = min( i, min( j, k ) );
	int mid = i + j + k - rig - lef;
	for(int p = 0; p < cons[rig].size(); p++){
		int cl = cons[rig][p].first;
		int cr = rig;
		int cx = cons[rig][p].second;
		if( cx == 1 ){
			if( mid >= cl )dp[i][j][k] = 0;
		}
		if( cx == 2 ){
			if( !( mid >= cl && lef < cl ) )dp[i][j][k] = 0;
		}
		if( cx == 3 ){
			if( !( lef >= cl ) )dp[i][j][k] = 0;
		}
	}
}
void addtonext(int i,int j,int k){
	if(used[i][j][k] == 0){
		int ma = max(i,max(j,k));
		dp[ma+1][j][k] += dp[i][j][k];
		dp[ma+1][j][k] %= inf;
		dp[i][ma+1][k] += dp[i][j][k];
		dp[i][ma+1][k] %= inf;
		dp[i][j][ma+1] += dp[i][j][k];
		dp[i][j][ma+1] %= inf;
		used[i][j][k] = 1;
	}
}
signed main(){
	int n,m;
	cin>>n>>m;
	for(int i=0;i<m;i++){
		int mope,rr,xx;
		cin>>mope>>rr>>xx;
		cons[rr].pb( mp(mope,xx) );
	}
	dp[0][0][0] = 1;
	for(int i=0;i<=n;i++){
		for(int j=0;j<=n;j++){
			for(int k=0;k<=n;k++){
				if( isvalid(i,j,k) ){
					checker(i,j,k);addtonext(i,j,k);
					checker(i,k,j);addtonext(i,k,j);
					checker(j,i,k);addtonext(j,i,k);
					checker(j,k,i);addtonext(j,k,i);
					checker(k,i,j);addtonext(k,i,j);
					checker(k,j,i);addtonext(k,j,i);
				}
			}
		}
	}
	int ans = 0;
	for(int i=0;i<=n;i++){
		for(int j=0;j<=i;j++){
			if(isvalid(n,i,j)){
				ans += dp[n][i][j];
				ans += dp[n][j][i];
				ans += dp[i][n][j];
				ans += dp[i][j][n];
				ans += dp[j][n][i];
				ans += dp[j][i][n];
			}
		}
	}
	ans += dp[0][n][0];
	ans += dp[n][0][0];
	ans += dp[0][0][n];
	cout<<ans<<endl;
	return 0;
}