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 (1.15.1) (judge verdict: Accepted)

use std::io::stdin;

#[allow(unused_variables)]
fn main() {
    let n = input_ints()[0] as u64;
    let mut ans = 0;

    for i in (2..(n as f64).sqrt() as u64 + 1).rev() {
        if n % i == 0 {
            ans = (n / i).to_string().len();
            break;
        }
    }

    if ans == 0 {
        ans = n.to_string().len();
    }

    println!("{}",ans);
}

#[allow(dead_code)]
fn input_ints() -> Vec<i64> {
    let mut s = String::new();
    match stdin().read_line(&mut s) {
        Ok(_) => s.split_whitespace().map(|s| s.parse().unwrap()).collect(),
        Err(_) => panic!("Error occured while input."),
    }
}