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 (3.4.3) (judge verdict: Time Limit Exceeded)

def input_from_console():
    r, g, b, n = map(int, input().split())

    return r, g, b, n


def main():
    r, g, b, n = input_from_console()
    counter = 0
    r, g, b = sorted([r, g, b], reverse=True)
    # print(r,g,b)
    for i1 in reversed(range(int(n / r) + 1)):
        n1 = n - r * i1
        for i2 in reversed(range(int(n1 / g) + 1)):
            n2 = n1 - g * i2
            # print(n2, i1, i2)
            if r * i1 + g * i2 + b * (n - i1 - i2) < n2:
                continue
            for i3 in reversed(range(int(n2 / b) + 1)):
                # print(i1, i2, i3, r * i1 + g * i2 + b * i3)
                n_new = r * i1 + g * i2 + b * i3
                if r * i1 + g * i2 + b * i3 == n:
                    counter += 1
                    break
                elif n_new < n:
                    break

    print(counter)


if __name__ == "__main__":
    main()