hewmatt10's Card

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Points: 7 (partial)
Time limit: 2.0s
Memory limit: 64M

Problem type

hewmatt10 is making a birthday card for the love of his life, [REDACTED]! However, because hewmatt10 can't draw a heart, he has resorted to drawing a circle. hewmatt10 wants to draw R different concentric circles centred on (0, 0), with the i^{th} circle having a radius of \sqrt{i}. To do this, he needs to know all the integer-valued coordinates points that lie on any of the circles. However, because hewmatt10 doesn't have the capacity to visualize all the points, he only asks for the number. Please help him!

Input Specification

The first line contains R\ (1 \le R \le 10^9).

Output Specification

The number of integer-valued points that lie on any of the circles.


Subtask 1 [30%]

R \le 10^5

Subtask 2 [70%]

No further constraints.

Sample Input


Sample Output



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