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)

#[allow(unused_imports)]
use std::io;
use std::io::stdin;
use std::cmp;

fn read_line_as_vec() -> Vec<String> {
    let mut s = String::new();
    stdin().read_line(&mut s).expect("");
    s.split(' ').map(|x| x.to_string()).collect::<Vec<String>>()
}

fn digit(x: u64) -> u32 {
    let mut d: u32 = 1;
    while 10u64.pow(d) <= x {
        d += 1;
    }
    d
}

fn main() {
    let n: u64 = read_line_as_vec()[0].trim().parse().expect("");
    let mut a: u64 = 1;
    let mut min_d: u32 = u32::max_value();
    while a * a <= n {
        if n % a != 0 {
            a += 1;
            continue;
        }
        min_d = cmp::min(min_d, digit(n / a));
        a += 1;
    }
    println!("{}", min_d);
}