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 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

A. Pythagorean Theorem II

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn mathematics, the Pythagorean theorem — is a relation in Euclidean geometry among the three sides of a right-angled triangle. In terms of areas, it states:

In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

The theorem can be written as an equation relating the lengths of the sides *a*, *b* and *c*, often called the Pythagorean equation:

where *c* represents the length of the hypotenuse, and *a* and *b* represent the lengths of the other two sides.

Given *n*, your task is to count how many right-angled triangles with side-lengths *a*, *b* and *c* that satisfied an inequality 1 ≤ *a* ≤ *b* ≤ *c* ≤ *n*.

Input

The only line contains one integer *n* (1 ≤ *n* ≤ 10^{4}) as we mentioned above.

Output

Print a single integer — the answer to the problem.

Examples

Input

5

Output

1

Input

74

Output

35

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/03/2020 23:18:32 (g1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|