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 (1.42.0) (judge verdict: Accepted)

use crate::mod_int::ModInt;

const MOD: u32 = 1_000_000_007;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let n: usize = sc.read();
    let m: usize = sc.read();
    let mut rules = vec![vec![]; n + 1];
    for _ in 0..m {
        let l: usize = sc.read();
        let r: usize = sc.read();
        let x: usize = sc.read();
        rules[r].push((l, x));
        if r == 1 && x != 1 {
            println!("0");
            return;
        }
    }

    let mut dp = vec![vec![vec![0; n + 1]; n + 1]; n + 1];
    dp[0][0][1] = 1;
    dp[0][1][0] = 1;
    dp[1][0][0] = 1;
    for max in 1..n {
        let next = max + 1;
        for a1 in 0..max {
            for a2 in a1..max {
                if a1 > 0 && a2 > 0 && a1 == a2 {
                    continue;
                }

                for &(r, g, b, f) in [
                    (a1, a2, max, true),
                    (a1, max, a2, true),
                    (a2, a1, max, false),
                    (a2, max, a1, false),
                    (max, a1, a2, true),
                    (max, a2, a1, false),
                ]
                .iter()
                {
                    if !f && a1 == a2 {
                        continue;
                    }
                    for &(nr, ng, nb) in [(r, g, next), (r, next, b), (next, g, b)].iter() {
                        let mut ok = true;
                        for &(l, x) in rules[next].iter() {
                            let mut count = 0;
                            if nr >= l {
                                count += 1;
                            }
                            if ng >= l {
                                count += 1;
                            }
                            if nb >= l {
                                count += 1;
                            }
                            if count != x {
                                ok = false;
                                break;
                            }
                        }
                        if ok {
                            let c = dp[r][g][b];
                            dp[nr][ng][nb] += c;
                            dp[nr][ng][nb] %= MOD;
                            // eprintln!("{:?}=>{:?} {}", (r, g, b), (nr, ng, nb), c.value());
                        }
                    }
                }
            }
        }
    }

    let mut ans = 0;
    for i in 0..n {
        for j in 0..n {
            ans += dp[i][j][n];
            ans += dp[i][n][j];
            ans += dp[n][i][j];
            ans %= MOD;

            // eprintln!("{:?} {}", (i, j, n), dp[i][j][n].value());
            // eprintln!("{:?} {}", (i, n, j), dp[i][n][j].value());
            // eprintln!("{:?} {}", (n, i, j), dp[n][i][j].value());
        }
    }

    println!("{}", ans);
}

pub mod mod_int {
    use std::ops::{
        Add, AddAssign, BitAnd, Div, DivAssign, Mul, MulAssign, RemAssign, ShrAssign, Sub,
        SubAssign,
    };

    pub struct ModInt<T> {
        v: T,
        m: T,
    }

    impl<T> ModInt<T>
    where
        T: Copy,
    {
        pub fn value(&self) -> T {
            self.v
        }
        pub fn modulo(&self) -> T {
            self.m
        }
    }

    impl<T> ModInt<T> {
        fn new_unchecked(v: T, modulo: T) -> Self {
            Self { v, m: modulo }
        }
    }

    impl<T> ModInt<T>
    where
        T: Copy + RemAssign + PartialOrd,
    {
        pub fn new(mut v: T, modulo: T) -> Self {
            if v >= modulo {
                v %= modulo;
            }
            Self::new_unchecked(v, modulo)
        }
    }

    impl<T> ModInt<T>
    where
        T: Copy
            + Sub<Output = T>
            + ShrAssign
            + BitAnd<Output = T>
            + PartialEq
            + PartialOrd
            + Div<Output = T>
            + RemAssign,
        ModInt<T>: MulAssign,
    {
        pub fn pow(self, e: T) -> Self {
            let zero = self.modulo() - self.modulo();
            let one = self.modulo() / self.modulo();
            let mut e = e;
            let mut result = Self::new_unchecked(one, self.modulo());
            let mut cur = self;
            while e > zero {
                if e & one == one {
                    result *= cur;
                }
                e >>= one;
                cur *= cur;
            }
            result
        }
    }

    impl<T> Copy for ModInt<T> where T: Copy {}
    impl<T> Clone for ModInt<T>
    where
        T: Copy,
    {
        fn clone(&self) -> Self {
            Self::new_unchecked(self.value(), self.modulo())
        }
    }

    impl<T> Add<T> for ModInt<T>
    where
        T: AddAssign + SubAssign + RemAssign + Copy + PartialOrd,
    {
        type Output = Self;
        fn add(self, mut rhs: T) -> Self::Output {
            if rhs >= self.modulo() {
                rhs %= self.modulo();
            }
            rhs += self.value();
            if rhs >= self.modulo() {
                rhs -= self.modulo();
            }
            Self::new_unchecked(rhs, self.modulo())
        }
    }

    impl<T> Sub<T> for ModInt<T>
    where
        T: AddAssign + SubAssign + RemAssign + Copy + PartialOrd,
    {
        type Output = Self;
        fn sub(self, mut rhs: T) -> Self::Output {
            if rhs >= self.modulo() {
                rhs %= self.modulo();
            }

            let mut result = self.value();
            result += self.modulo();
            result -= rhs;

            if result >= self.modulo() {
                result -= self.modulo();
            }
            Self::new_unchecked(result, self.modulo())
        }
    }

    impl<T> Mul<T> for ModInt<T>
    where
        T: MulAssign + RemAssign + Copy + PartialOrd,
    {
        type Output = Self;
        fn mul(self, mut rhs: T) -> Self::Output {
            if rhs >= self.modulo() {
                rhs %= self.modulo();
            }
            rhs *= self.value();
            rhs %= self.modulo();
            Self::new_unchecked(rhs, self.modulo())
        }
    }

    impl<T> Add<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Add<T, Output = ModInt<T>>,
    {
        type Output = Self;
        fn add(self, rhs: ModInt<T>) -> Self::Output {
            self + rhs.value()
        }
    }
    impl<T> Sub<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Sub<T, Output = ModInt<T>>,
    {
        type Output = Self;
        fn sub(self, rhs: ModInt<T>) -> Self::Output {
            self - rhs.value()
        }
    }
    impl<T> Mul<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Mul<T, Output = ModInt<T>>,
    {
        type Output = Self;
        fn mul(self, rhs: ModInt<T>) -> Self::Output {
            self * rhs.value()
        }
    }
    impl<T> Div<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Div<T, Output = ModInt<T>>,
    {
        type Output = Self;
        fn div(self, rhs: ModInt<T>) -> Self::Output {
            self / rhs.value()
        }
    }

    impl<T> AddAssign<T> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Add<T, Output = ModInt<T>>,
    {
        fn add_assign(&mut self, other: T) {
            *self = *self + other;
        }
    }
    impl<T> AddAssign<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Add<ModInt<T>, Output = ModInt<T>>,
    {
        fn add_assign(&mut self, other: ModInt<T>) {
            *self = *self + other;
        }
    }

    impl<T> SubAssign<T> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Sub<T, Output = ModInt<T>>,
    {
        fn sub_assign(&mut self, other: T) {
            *self = *self - other;
        }
    }

    impl<T> SubAssign<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Sub<ModInt<T>, Output = ModInt<T>>,
    {
        fn sub_assign(&mut self, other: ModInt<T>) {
            *self = *self - other;
        }
    }

    impl<T> DivAssign<T> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Div<T, Output = ModInt<T>>,
    {
        fn div_assign(&mut self, rhs: T) {
            *self = *self / rhs
        }
    }
    impl<T> DivAssign<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Div<ModInt<T>, Output = ModInt<T>>,
    {
        fn div_assign(&mut self, rhs: ModInt<T>) {
            *self = *self / rhs
        }
    }

    impl<T> MulAssign<T> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Mul<T, Output = ModInt<T>>,
    {
        fn mul_assign(&mut self, rhs: T) {
            *self = *self * rhs;
        }
    }

    impl<T> MulAssign<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Mul<ModInt<T>, Output = ModInt<T>>,
    {
        fn mul_assign(&mut self, rhs: ModInt<T>) {
            *self = *self * rhs;
        }
    }

    impl<T> Div<T> for ModInt<T>
    where
        T: Copy
            + Add<Output = T>
            + Sub<Output = T>
            + Div<Output = T>
            + BitAnd<Output = T>
            + PartialEq
            + PartialOrd
            + ShrAssign
            + RemAssign
            + MulAssign,
    {
        type Output = Self;
        fn div(self, mut rhs: T) -> Self::Output {
            if rhs >= self.modulo() {
                rhs %= self.modulo();
            }
            let one = self.modulo() / self.modulo();
            let two = one + one;
            self * Self::new_unchecked(rhs, self.modulo()).pow(self.modulo() - two)
        }
    }
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        Self(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}