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: Time Limit Exceeded)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

const MOD: i64 = 1e+9 as i64 + 7;
fn calc(
    memo: &mut Vec<Vec<Vec<i64>>>,
    cs: &Vec<usize>,
    in_constraint: &Vec<Vec<usize>>,
    out_constraint: &Vec<Vec<usize>>,
) -> i64 {
    assert!(cs[0] >= cs[1]);
    assert!(cs[1] >= cs[2]);
    let n = memo.len() - 1;
    if cs[0] == n {
        return 1;
    }
    if memo[cs[0]][cs[1]][cs[2]] != -1 {
        return memo[cs[0]][cs[1]][cs[2]];
    }
    let index = cs[0];
    let mut ret = 0;
    'outer_loop: for t in 0..3 {
        let mut ncs = vec![index + 1];
        for i in 0..3 {
            if t == i {
                continue;
            }
            ncs.push(cs[i]);
        }
        ncs.sort();
        ncs.reverse();
        for c in 0..3 {
            if c != 2 && ncs[c + 1] >= in_constraint[c][index + 1] {
                continue 'outer_loop;
            }
            if ncs[c] < out_constraint[c][index + 1] {
                continue 'outer_loop;
            }
        }
        ret = (ret + calc(memo, &ncs, in_constraint, out_constraint)) % MOD;
    }
    memo[cs[0]][cs[1]][cs[2]] = ret;
    ret
}

fn main() {
    let n = read::<usize>();
    let m = read::<usize>();
    let mut seq = vec![(0, 0, 0); m];
    for i in 0..m {
        seq[i].0 = read::<usize>();
        seq[i].1 = read::<usize>();
        seq[i].2 = read::<usize>();
    }
    seq.sort();
    let mut in_constraint = vec![vec![n + 2; n + 1]; 3];
    let mut out_constraint = vec![vec![0; n + 1]; 3];
    for i in 0..m {
        let (l, r, c) = seq[i];
        for j in l..r + 1 {
            in_constraint[c - 1][j] = std::cmp::min(in_constraint[c - 1][j], l);
        }
        out_constraint[c - 1][r] = std::cmp::max(out_constraint[c - 1][r], l);
    }
    let mut memo = vec![vec![vec![-1; n + 1]; n + 1]; n + 1];
    let ans = calc(&mut memo, &vec![0, 0, 0], &in_constraint, &out_constraint);
    println!("{}", ans);
}