Problem:
Score : 200 points

Problem Statement

Snuke has come to a store that sells boxes containing balls. The store sells the following three kinds of boxes:

Red boxes, each containing R red balls

Green boxes, each containing G green balls

Blue boxes, each containing B blue balls

Snuke wants to get a total of exactly N balls by buying r red boxes, g green boxes and b blue boxes.
How many triples of non-negative integers (r,g,b) achieve this?

Constraints

All values in input are integers.

1 \leq R,G,B,N \leq 3000

Input

Input is given from Standard Input in the following format:

R G B N

Output

Print the answer.

Sample Input 1

1 2 3 4

Sample Output 1

4

Four triples achieve the objective, as follows:

(4,0,0)

(2,1,0)

(1,0,1)

(0,2,0)

Sample Input 2

13 1 4 3000

Sample Output 2

87058

Solution in Python (3.8.2) (judge verdict: Time Limit Exceeded)

colorn = list(map(int, input().split()))
color = colorn[0:3]
n = colorn[-1]
color.sort()

a, b, c = color[2], color[1], color[0]

a_max = n // a
b_max = n // b
c_max = n // c
cnt = 0

for i in range(a_max + 1)[::-1]:
    b_max = (n - a * i) // b
    for j in range(b_max + 1)[::-1]:
        c_max = (n - a * i - b * j) // c
        for k in range(c_max + 1)[::-1]:
            if a * i + b * j + c * k == n:
                cnt += 1
            elif a * i + b * j + c * k < n:
                break     
print(cnt)