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 $x, y, z, w (0 \leq x < y < z < w \leq N)$ 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

• $3 \leq N \leq 40$
• $1 \leq X \leq 5$
• $1 \leq Y \leq 7$
• $1 \leq Z \leq 5$

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 $10^9+7$.

3 5 7 5

1

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

4 5 7 5

34

37 4 2 3

863912418

40 5 7 5

562805100