Quadroquadratures

An ordered quadruple of natural numbers (a, b, c, d) is defined as a quad-square of a natural number N if it satisfies the following equation:

[ a^2 + b^2 + c^2 + d^2 = N ]

Quad-squares are considered distinct if they differ in the sequence of numbers.

Write a program to determine the number of quad-squares for a given natural number N.

Input

The input consists of a single natural number N (1 ≤ N ≤ 1000000).

Output

Output a single number, which is the count of quad-squares for the number N.

Examples