Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Cube Problem

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYaroslav, Andrey and Roman love playing cubes. Sometimes they get together and play cubes for hours and hours!

Today they got together again and they are playing cubes. Yaroslav took unit cubes and composed them into an *a* × *a* × *a* cube, Andrey made a *b* × *b* × *b* cube and Roman made a *c* × *c* × *c* cube. After that the game was finished and the guys left. But later, Vitaly entered the room. He saw the cubes and wanted to make a cube as well. But what size should the cube be? Of course it should be a large cube with the side of length *a* + *b* + *c*. Besides, Vitaly decided to decompose the cubes built by Yaroslav, Andrey and Roman and compose his own large cube out of them. However, it turned out that the unit cubes he got from destroying the three cubes just weren't enough to make a large cube. We know that Vitaly was short of exactly *n* cubes. Vitaly got upset, demolished everything and left. As he was leaving, he met Petya and told him that there had been three cubes in the room and that he needed another *n* unit cubes to make his own large cube.

Petya entered the room and saw the messily scattered cubes. He wanted to make it neat and orderly again. But he only knows that there had been three cubes, made of small unit cubes and that Vitaly needed *n* more unit cubes to make a large one! Help Petya understand, how many ways of sizes *a*, *b*, *c* are there to restore Yaroslav's, Andrey's and Roman's cubes.

Input

The single line of the input contains integer *n* (1 ≤ *n* ≤ 10^{14}). We know that all numbers *a*, *b*, *c* are positive integers.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

In the single line print the required number of ways. If it turns out that there isn't a single way of suitable sizes of *a*, *b*, *c*, print 0.

Examples

Input

24

Output

1

Input

648

Output

7

Input

5

Output

0

Input

93163582512000

Output

39090

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/26/2017 20:00:59 (c2).

Desktop version, switch to mobile version.
User lists

Name |
---|