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;

fn main() {
    let n = read_int();
    let j = (1..(n as f64).sqrt().floor() as u64 + 1)
        .rev()
        .filter(|i| n % i == 0)
        .next()
        .expect("at least one divisor");
    println!("{}", digits(n / j));
}

fn digits(n: u64) -> usize {
    n.to_string().len()
}

fn get_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).expect("read");
    buf
}

fn read_int() -> u64 {
    get_line().trim().parse().expect("parse error")
}