Problem:
Score : 700 points

Problem Statement

Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.

Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.

Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?

Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:

a_x + a_{x+1} + ... + a_{y-1} = X

a_y + a_{y+1} + ... + a_{z-1} = Y

a_z + a_{z+1} + ... + a_{w-1} = Z

Since the answer can be extremely large, print the number modulo 10^9+7.

Constraints

3 ≦ N ≦ 40

1 ≦ X ≦ 5

1 ≦ Y ≦ 7

1 ≦ Z ≦ 5

Input

The input is given from Standard Input in the following format:

N X Y Z

Output

Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.

Sample Input 1

3 5 7 5

Sample Output 1

1

Here, the only sequence that contains a 5,7,5-Haiku is [5, 7, 5].

Sample Input 2

4 5 7 5

Sample Output 2

34

Sample Input 3

37 4 2 3

Sample Output 3

863912418

Sample Input 4

40 5 7 5

Sample Output 4

562805100

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::io::*;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

pub trait InputValue {
    fn parse(s: &str) -> Self;
}

pub fn read<T: InputValue>() -> T {
    let mut buf = String::new();
    let _ = stdin().read_line(&mut buf);
    T::parse(&buf.trim())
}

pub fn readn<T: InputValue>(n: usize) -> Vec<T> {
    let mut vec = vec![];
    for _ in 0..n {
        vec.push(read());
    }
    vec
}

pub fn readnc<T: InputValue>() -> Vec<T> {
    let mut vec = vec![];
    let line: String = read();
    for token in line.split_whitespace() {
        vec.push(T::parse(token));
    }
    vec
}

macro_rules! parse_single_value {
    ($($t:ty),*) => {
        $(
            impl InputValue for $t {
                fn parse(s: &str) -> $t { s.parse().unwrap() }
            }
        )*
	}
}
parse_single_value!(i32, i64, f32, f64, usize, String);

macro_rules! parse_tuple {
	($($t:ident),*) => {
		impl<$($t),*> InputValue for ($($t),*) where $($t: InputValue),* {
			fn parse(s: &str) -> ($($t),*) {
				let mut tokens = s.split_whitespace();
				let t = ($($t::parse(tokens.next().unwrap())),*);
				t
			}
		}
	}
}
parse_tuple!(A, B);
parse_tuple!(A, B, C);
parse_tuple!(A, B, C, D);
parse_tuple!(A, B, C, D, E);

// ===

const MOD: u64 = 1000000007;


fn main() {
    let (n, x, y, z): (usize, usize, usize, usize) = read();
    let w = 1<<18;
    let mut table = vec![false; w];
    for p in 0..w {
        let a = decode(p);
        table[p] = check(&a, x, y, z);
    }

    let mask = (1<<18)-1;
    let mut dp = vec![vec![vec![0; w]; 2]; 2];
    dp[0][0][0] = 1;
    for i in 0..n {
        let fr = i & 1;
        let to = fr ^ 1;

        for f in 0..2 {
            for p in 0..w {
                dp[to][f][p] = 0;
            }
        }

        for f in 0..2 {
            for p in 0..w {
                let base = dp[fr][f][p];
                for x in 1..11 {
                    let tp = ((p << x) | (1 << (x-1))) & mask;
                    let tf = if f == 1 || table[tp] { 1 } else { 0 };

                    dp[to][tf][tp] += base;
                    if dp[to][tf][tp] >= MOD {
                        dp[to][tf][tp] -= MOD;
                    }
                }
            }
        }
    }

    let mut ans = 0;
    for i in 0..w {
        ans += dp[n%2][1][i];
    }
    println!("{}", ans % MOD);
}

fn check_dfs(a: &Vec<usize>, idx: usize, b: &Vec<usize>, midx: usize, psum: usize) -> bool {
    if midx == 3 {
        return true;
    }
    if psum == b[midx] {
        return check_dfs(a, idx, b, midx+1, 0);
    }
    if idx == a.len() {
        return false;
    }
    if psum > b[midx] {
        return false;
    }
    check_dfs(a, idx+1, b, midx, psum + a[idx])
}

fn check(a: &Vec<usize>, x: usize, y: usize, z: usize) -> bool {
    let n = a.len();
    let mut ok = false;
    for i in 0..n {
        ok |= check_dfs(a, i, &vec![x, y, z], 0, 0);
    }
    ok
}

fn encode(a: Vec<usize>) -> usize {
    let mut z = 0;
    let mut d = 0;
    let mask = (1<<18)-1;
    for ai in a {
        z <<= ai;
        z |= 1<<(ai-1);
        z &= mask;
    }
    z
}

fn decode(z: usize) -> Vec<usize> {
    let mut a = vec![];
    let mut z = z;
    while z >= 1 {
        let mut x = 1;
        while z & 1 == 0 {
            z >>= 1;
            x += 1;
        }
        z >>= 1;
        a.push(x);
    }
    a
}