Perfect Squares

Given an integer n, return the least number of perfect square numbers that sum to n.

A perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 1,4, 9, and 16 are perfect squares while 3 and 11 are not.

Input Format

First Parameter - An integer n

Output Format

Return a single integer

Example 1

Input: n = 12
Output: 3
Explanation: 12 = 4 + 4 + 4.

Example 2

Input: n = 13
Output: 2
Explanation: 13 = 4 + 9.

Constraints

• 1 <= n <= 10^4
• Expected Time Complexity - O(n)
• Expected Space Complexity - O(n)