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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int N=sc.nextInt();
		int M=sc.nextInt();
		int[][] state=new int[M][3];
		for(int i=0;i<M;i++){
			state[i][0]=sc.nextInt();
			state[i][1]=sc.nextInt();
			state[i][2]=sc.nextInt();
		}
		String list="#";
		
		int result=depend(list,state,N);
		System.out.println(result);
	}
	
	public static int depend(String list,int[][] state,int N){
		//depend if ok
		if(list.length()>N) return 1;
		//depend
		boolean depend=true;
		for(int i=0;i<state.length;i++){
			if(list.length()>state[i][1]+1)continue;
			if(list.length()<state[i][0])continue;
			
			if(list.length()==state[i][1]+1){
			String temp=list.substring(state[i][0], Math.min(list.length(), state[i][1]+1));
			int count=0;
			if(temp.indexOf("r")!=-1)count++;
			if(temp.indexOf("g")!=-1)count++;
			if(temp.indexOf("b")!=-1)count++;
			if(count!=state[i][2]){
				depend=false;
				break;
			}
			}
		}
		if(!depend) return 0;
		return depend(list+"r",state,N)+depend(list+"g",state,N)+depend(list+"b",state,N);
	}
	
}