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 Rust (1.15.1) (judge verdict: Accepted)

use std::fmt::Debug;
use std::io;
use std::io::{Read, Stdin};
use std::str;
use std::str::FromStr;
use std::usize;
use std::cmp;

struct Rule {
    left: usize,
    x: usize,
}

fn main() {
    let mut sc = Scanner::new();
    let n = sc.parse::<usize>();
    let m = sc.parse::<usize>();

    let mut rules: Vec<Vec<Rule>> = Vec::new();
    for _ in 0..(n + 1) {
        rules.push(Vec::new());
    }
    for _ in 0..m {
        let l = sc.parse::<usize>();
        let r = sc.parse::<usize>();
        let x = sc.parse::<usize>();
        rules[r].push(Rule { left: l, x: x });
    }

    let mut dp = vec![vec![vec![0;(n+1)];(n+1)];(n+1)];
    dp[0][0][0] = 1;
    let modulo = 1000000007;
    for r in 0..n {
        for g in 0..n {
            for b in 0..n {
                let k = cmp::max(cmp::max(r, g), b);
                if check(&rules, k + 1, g, b) {
                    dp[k + 1][g][b] += dp[r][g][b];
                    dp[k + 1][g][b] %= modulo;
                }
                if check(&rules, r, k + 1, b) {
                    dp[r][k + 1][b] += dp[r][g][b];
                    dp[r][k + 1][b] %= modulo;
                }
                if check(&rules, r, g, k + 1) {
                    dp[r][g][k + 1] += dp[r][g][b];
                    dp[r][g][k + 1] %= modulo;
                }
            }
        }
    }

    let mut ans = 0;
    for i in 0..n {
        for j in 0..n {
            ans += dp[i][j][n];
            ans %= modulo;
            ans += dp[i][n][j];
            ans %= modulo;
            ans += dp[n][i][j];
            ans %= modulo;
        }
    }
    println!("{}", ans);
}

fn check(rules: &Vec<Vec<Rule>>, r: usize, g: usize, b: usize) -> bool {
    let k = cmp::max(cmp::max(r, g), b);
    for rule in &rules[k] {
        let left = rule.left;
        let mut count = 0;
        if r >= left {
            count += 1;
        }
        if g >= left {
            count += 1;
        }
        if b >= left {
            count += 1;
        }
        if count != rule.x {
            return false;
        }
    }
    return true;
}

struct Scanner {
    stdin: Stdin,
    buf: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner {
            stdin: io::stdin(),
            buf: Vec::with_capacity(256),
        }
    }

    fn parse<T: FromStr>(&mut self) -> T
        where <T as FromStr>::Err: Debug
    {
        self.buf.clear();
        let mut it = self.stdin.lock().bytes();
        let mut c = it.next().unwrap().unwrap();
        while c == ' ' as u8 || c == '\n' as u8 {
            c = it.next().unwrap().unwrap();
        }
        while !(c == ' ' as u8 || c == '\n' as u8) {
            self.buf.push(c);
            c = it.next().unwrap().unwrap();
        }
        str::from_utf8(&self.buf).unwrap().parse::<T>().unwrap()
    }
}