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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;
using System.Text;
using System.Net;

    
public class Program
{
    public void Proc() {
        Reader.IsDebug = false;
        int[] inpt = Reader.ReadLine().Split(' ').Select(a=>int.Parse(a)).ToArray();
        this.MaxLength = inpt[0];
        int seiyakuCount = inpt[1];

        for(int i=0; i<seiyakuCount; i++) {
            Seiyaku s = new Seiyaku(i, Reader.ReadLine());
            this.SeiyakuList.Add(s);
            if(!FromDic.ContainsKey(s.FromIdx)) {
                FromDic.Add(s.FromIdx, new List<Seiyaku>());
            }
            FromDic[s.FromIdx].Add(s);
            if(!ToDic.ContainsKey(s.ToIdx)) {
                ToDic.Add(s.ToIdx, new List<Seiyaku>());
            }
            ToDic[s.ToIdx].Add(s);
        }
        long ans = GetAns(-1,-1,-1,0);
        Console.WriteLine(ans);
    }

    private Dictionary<int, Dictionary<int, Dictionary<int, long>>> dic = new Dictionary<int, Dictionary<int, Dictionary<int, long>>>();

    private long GetAns(int lastR, int lastG, int lastB, int idx) {
        if(!dic.ContainsKey(lastR)) {
            dic.Add(lastR, new Dictionary<int, Dictionary<int, long>>());
        }
        if(!dic[lastR].ContainsKey(lastG)) {
            dic[lastR].Add(lastG, new Dictionary<int, long>());
        }
        if(dic[lastR][lastG].ContainsKey(lastB)) {
            return dic[lastR][lastG][lastB];
        }

        bool isValid = true;

        if(ToDic.ContainsKey(idx-1)) {
            foreach(Seiyaku s in ToDic[idx-1]) {
                int cnt = 0;
                if(lastR >= s.FromIdx) {
                    cnt++;
                }
                if(lastG >= s.FromIdx) {
                    cnt++;
                }
                if(lastB >= s.FromIdx) {
                    cnt++;
                }
                if(s.Count != cnt) {
                    isValid = false;
                    break;
                }
            }
        }
        if(!isValid) {
            this.dic[lastR][lastG][lastB] = 0;
            return 0;
        }
        if(idx >= this.MaxLength) {
            this.dic[lastR][lastG][lastB] = 1;
            return 1;
        }

        long ans = 0;
        ans += this.GetAns(idx, lastG, lastB, idx+1);
        ans += this.GetAns(lastR, idx, lastB, idx+1);
        ans += this.GetAns(lastR, lastG, idx, idx+1);
        ans = ans % (1000000000 + 7);
        dic[lastR][lastG][lastB] = ans;
        return ans;
    }
    private int MaxLength = 0;

    private List<Seiyaku> SeiyakuList = new List<Seiyaku>();

    private Dictionary<int, List<Seiyaku>> FromDic = new Dictionary<int, List<Seiyaku>>();
    private Dictionary<int, List<Seiyaku>> ToDic = new Dictionary<int, List<Seiyaku>>();
    private class Seiyaku {
        public int ID = 0;
        public int FromIdx = 0;
        public int ToIdx = 0;

        public int Count = 0;

        public Seiyaku(int id, string init) {
            int[] tmp = init.Split(' ').Select(a=>int.Parse(a)).ToArray();
            this.ID = id;
            this.FromIdx = tmp[0]-1;
            this.ToIdx = tmp[1]-1;
            this.Count = tmp[2];
        }
    }





    public class Reader {
        public static bool IsDebug = true;
        private static System.IO.StringReader SReader;
        private static string InitText = @"






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





";
        public static string ReadLine() {
            if(IsDebug) {
                if(SReader == null) {
                    SReader = new System.IO.StringReader(InitText.Trim());
                }
                return SReader.ReadLine();
            } else {
                return Console.ReadLine();
            }
        }
    }
    public static void Main(string[] args)
    {
        Program prg = new Program();
        prg.Proc();
    }
}