Quadroquadratures#672

Quadroquadratures

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An ordered quadruple of natural numbers $(a, b, c, d)$ (a, b, c, d) is called a quadroquadrature of a natural number $N$ if the following equation holds:

a^{2} + b^{2} + c^{2} + d^{2} = N

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

Quadroquadratures that differ in the order of the numbers are considered distinct.

Write a program that determines the number of quadroquadratures for a given natural number $N$ .

Input

The input file contains a single natural number $N$ ( $1 \leq N \leq 1000000$ 1 \leq N \leq 1000000).

Output

Print a single number—the number of quadroquadratures of $N$ .

Examples

Example 1

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(a, b, c, d)

a^{2} + b^{2} + c^{2} + d^{2} = N

1 \leq N \leq 1000000