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::{Read, stdin};
use std::str::FromStr;
use std::cmp::max;

fn main() {
    let n: i64 = read();
    let rn: i64 = (n as f64).sqrt().floor() as i64;
    let mut v: Vec<i64> = Vec::new();
    for i in 1..rn+1 {
        if n % i == 0 {
            v.push(i);
            v.push(n / i);
        }
    }
    v.sort();
    let mut ans = 1000;
    for i in 0.. v.len()/2 +1 {
        let u = max(((n / v[i] as i64) as f64).log10().floor() as i64 ,
                    (v[i] as f64).log10().floor() as i64) + 1;
        if ans > u {ans = u;}
    }

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

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}