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!{
        mut n:i64,
    }
    let v:Vec<i64>=func(n);
    let mut ans:i64=digit(n);
    for i in v{
        ans=std::cmp::min(ans,digit(i));
    }
    println!("{}",ans);
}

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

fn func(n:i64)->Vec<i64>{
    let mut v:Vec<i64>=Vec::new();
    for i in 2..((n as f64).sqrt() as i64 +1){
        if n%i==0{
            v.push(n/i);
        }
    }
    v
}