RGB Boxes

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.

Examples

Input

1 2 3 4

Output

4

Input

13 1 4 3000

Output

87058

inputFormat

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

outputFormat

Output

Print the answer.

Examples

Input

1 2 3 4

Output

4

Input

13 1 4 3000

Output

87058

样例

1 2 3 4

4