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)

use proconio::input;

fn main() {
	input!(n: usize);

	let nmax: usize = (n as f64).sqrt() as usize + 1;

	let mut ans = 99999999;
	for i in 1..nmax {
		if n % i != 0 {
			continue;
		}
		let j = n / i;
		let si: String = i.to_string();
		let sj: String = j.to_string();
		let dmax = std::cmp::max(si.len(), sj.len());
		if dmax < ans {
			ans = dmax;
		}
	}
	println!("{}", ans);
}