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 PyPy3 (2.4.0) (judge verdict: Accepted)

n, x, y, z = map(int,input().split())
mod = 10 ** 9 + 7
forbit = (1<<(x + y + z -1)) + (1<<(y + z -1 )) + (1<<(z -1))
mask = ((1<<(x+y+z)) -1)
l1 = set()
for i in range(mask + 1):
    if i & forbit:
        l1.add(i)
d = [[0] * (mask + 1) for i in range(n + 1)]
d[0][0] = 1
for j in range(n):
    for i in range(mask + 1):
        for k in range(10):
            t = ((i <<(k + 1)) | 1<<k) & mask
            if (t & forbit) == forbit:
                continue
            d[j + 1][t] += d[j][i]
            d[j + 1][t] %= mod
answer = (10 ** n) % mod
for i in range(mask + 1):
    answer -= d[n][i]
    answer %= mod
print(answer)