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_mut)]
#![allow(non_snake_case)]
#![allow(unused_imports)]
#![allow(dead_code)]
use std::collections::HashSet; use std::collections::HashMap;
use std::collections::BTreeSet;
use std::collections::VecDeque;
use std::cmp::{max, min};
use std::io::prelude::*;

use std::io::prelude::*;

fn input<T>() -> T
    where T: std::str::FromStr {
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn cnt_digits(mut n: i64) -> i64 {
    let mut digits = 0;
    while n > 0 {
        n /= 10;
        digits += 1;
    }
    digits
}

fn main() {
    let n: i64 = input();
    let mut ans = cnt_digits(n);
    let mut a = 1;
    while a * a <= n {
        if n % a == 0 {
            let b = n / a;
            let cur = max(cnt_digits(a), cnt_digits(b));
            if ans > cur {
                ans = cur;
            }
        }
        a+=1;
    }
    println!("{}", ans);
}