Tiles Into a Full Square

Easy

A tiler has tiles identical square tiles and wants to lay them out as one solid square, using every single tile. Return True if that is possible (that is, tiles equals k · k for some integer k), and False otherwise. Do not use built-in square-root helpers such as sqrt, isqrt or ** 0.5.

Example 1

tiles=36 → True

36 tiles make a 6 × 6 square.

Example 2

tiles=20 → False

4 × 4 = 16 is too few and 5 × 5 = 25 too many, so no square works.

Example 3

tiles=1 → True

Constraints

1 ≤ tiles ≤ 2³¹ − 1

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Math Binary Search

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Input

tiles=36

Expected

True

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