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 (1.42.0) (judge verdict: Accepted)

#![allow(
    non_snake_case,
    unused_variables,
    unused_assignments,
    unused_mut,
    dead_code
)]
use proconio::input;
//use proconio::marker::Usize1;
//use proconio::marker::Chars;
//use std::collections::HashSet;
use std::cmp::*;
//use std::num;

fn main() {
    input! {
        n:u64
    }
    // root n 以下の約数の列aを求める。
    // 各a[i]について、Fを計算する。
    // …しても良いけど、n以下で最大になるxを求めれば良いはず。
    // というか
    let mut ans = 10;
    let r: u64 = (n as f64).sqrt() as u64 + 1;
    for i in (1..(r + 1)).rev() {
        if n % i == 0 {
            ans = min(ans, max(getKeta(i), getKeta(n / i)));
        }
    }
    println!("{}", ans);
}
fn getKeta(i: u64) -> u64 {
    if i < 10 {
        1
    } else {
        getKeta(i / 10) + 1
    }
}