Problem Description

Given a positive integer, determine if it is a factorial of some integer. If yes, return that integer; if no, return -1. A factorial n! = n × (n-1) × (n-2) × ... × 2 × 1.

Input Format

A single positive integer.

Output Format

The integer n such that n! equals the input, or -1 if no such integer exists.

Constraints

• 1 ≤ input ≤ 10^18

• Handle large numbers efficiently

• 0! = 1, 1! = 1

• Factorial grows very quickly

• Use iterative division approach

Sample Input/Output

Explanation

120 = 5! = 5 × 4 × 3 × 2 × 1 = 120. So the answer is 5.