Problem:
Score : 300 points

Problem Statement

You are given an integer N.

For two positive integers A and B, we will define F(A,B) as the larger of the following: the number of digits in the decimal notation of A, and the number of digits in the decimal notation of B.

For example, F(3,11) = 2 since 3 has one digit and 11 has two digits.

Find the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Constraints

1 \leq N \leq 10^{10}

N is an integer.

Input

The input is given from Standard Input in the following format:

N

Output

Print the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Sample Input 1

10000

Sample Output 1

3

F(A,B) has a minimum value of 3 at (A,B)=(100,100).

Sample Input 2

1000003

Sample Output 2

7

There are two pairs (A,B) that satisfy the condition: (1,1000003) and (1000003,1). For these pairs, F(1,1000003)=F(1000003,1)=7.

Sample Input 3

9876543210

Sample Output 3

6

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::{input, fastout};

#[fastout]
fn main() {
    input!{
        n: usize
    }

    let mut min_digits = 100;
    for i in 1..=(n as f64).sqrt() as usize {
        if n % i == 0 {
            let a_digits = ((i as f64).log10() as usize) + 1;
            let b_digits = (((n / i) as f64).log10() as usize) + 1;
            min_digits = min_digits.min(a_digits.max(b_digits));
        }
    }
    println!("{}", min_digits);
}