Source: Facebook Hacker Cup Qualification Round 2011

A double-square number is an integer X which can be expressed as the sum of two perfect squares. For example, 10 is a double-square because 10 = 32 + 12. Given X, how can we determine the number of ways in which it can be written as the sum of two squares? For example, 10 can only be written as 32 + 12 (we don't count 12 + 32 as being different). On the other hand, 25 can be written as 52 + 02 or as 42 + 32.

You need to solve this problem for 0 ≤ X ≤ 2,147,483,647.

Examples:

  • 10 => 1
  • 25 => 2
  • 3 => 0
  • 0 => 1
  • 1 => 1
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