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)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn cnt(mut u: u64) -> i32 {
    let mut a = 0;
    loop {
        a += 1;
        u /= 10;
        if u == 0 {
            break;
        }
    }
    a
}

fn solve(n: u64) -> u64 {
    let s = (n as f64).sqrt() as u64;
    let mut ret: u64 = s;

    for i in 0..s {
        let tmp = s - i;
        if tmp * (n / tmp) == n {
            ret = n / tmp;
            break;
        }
    }
    ret
}

fn main() {
    let n: u64 = read();

    println!("{}", cnt(solve(n)));
}