Perfect Square Checker

You are given a single integer N. Your task is to determine whether N is a perfect square.

If N is a perfect square, output its integer square root and the boolean value True. Otherwise, output the smallest integer greater than the square root (i.e. the ceiling value) and the boolean value False.

Mathematically, if N is a perfect square, then there exists an integer x such that:

$x^2 = N$

Otherwise, if:

$x^2 < N < (x+1)^2$, then output x+1 and False.

inputFormat

The input consists of a single integer N (1 ≤ N ≤ 10⁹) given via standard input (stdin).

outputFormat

Output two values separated by a space: the computed integer (the square root if N is a perfect square, or the ceiling of the square root otherwise) and a boolean value (True/False) indicating whether N is a perfect square.

16

4 True