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::cmp;

fn n_digits(n: u64) -> u64 {
  let mut ans = 1;
  let mut tmp = n;
  while tmp >= 10 {
    ans += 1;
    tmp /= 10;
  }
  return ans;
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf);
    let mut s = buf.split_whitespace();
    let n: u64 = s.next().unwrap().parse().unwrap();

    let mut i = 0;
    let mut ans = 20;
    while i*i <= n {
      i += 1;
      
      if n % i != 0 { continue; }

      let j = n / i;
      let cur = cmp::max(n_digits(i), n_digits(j));
      ans = cmp::min(ans, cur);
    }
    println!("{}", ans);
}