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;
use std::cmp;

fn main() {
    let mut n = String::new();
    io::stdin().read_line(&mut n);
    let n = n.trim().parse::<u64>().unwrap();

    let mut min = std::u64::MAX;
    for i in 1u64..((n as f64).sqrt() as u64 + 1u64) {
        let a = n / i;
        if a * i != n {
            continue;
        }
        // log10(10) == 1 , log10(100) == 2
        min = cmp::min(min, 
            cmp::max(
                (a as f64).log10().floor() as u64 + 1u64,
                (i as f64).log10().floor() as u64 + 1u64
            )
        );
    }

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