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.

1 2 3 4

4

Four triples achieve the objective, as follows:

• $(4,0,0)$
• $(2,1,0)$
• $(1,0,1)$
• $(0,2,0)$

13 1 4 3000

87058