Integer Square Verification

Easy

Given a positive integer num, determine whether it represents a complete square — that is, whether there exists another integer whose product with itself equals num . A complete square (also known as a square number) is formed when an integer is multiplied by itself. For instance, 1, 4, 9, 16, 25, and 36 are complete squares because they equal 1\times1, 2\times2, 3\times3, 4\times4, 5\times5, and 6\times6 respectively. Return true if num is a complete square, and false otherwise. Important Constraint : You are prohibited from using any built-in library functions that compute square roots (such as sqrt, Math.sqrt, pow, or equivalent). Your solution must rely solely on fundamental arithmetic operations and logical constructs.

Example 1

Input

num = 16

Output

true

Explanation

The number 16 is a complete square because 4 × 4 = 16, where 4 is an integer.

Example 2

Input

num = 14

Output

false

Explanation

The number 14 is not a complete square. The square root of 14 is approximately 3.742, which is not an integer. No integer multiplied by itself produces 14.

Example 3

Input

num = 9

Output

true

Explanation

The number 9 is a complete square because 3 × 3 = 9, where 3 is an integer.

Constraints

1 ≤ num ≤ 2³¹ - 1