Counting Valid Vector Pairs

Given two 2D vectors \(\overrightarrow{A}=(X_A, Y_A)\) and \(\overrightarrow{B}=(X_B, Y_B)\) with positive integer components, count the number of distinct pairs \((X_A, Y_A), (X_B, Y_B)\) that satisfy:

\[ X_A \cdot X_B + Y_A \cdot Y_B \leq L \]

All components \(X_A, Y_A, X_B, Y_B\) are positive integers.

inputFormat

The input consists of a single integer \(L\) on a line.

outputFormat

Output a single integer representing the number of valid pairs of vectors.

sample

1

0