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 main() {
    let mut sc = cin();
    while sc.read() {
        let n: i64 = sc.next();
        let mut ans = 20;
        for i in 1..n+1 {
            if n < i*i {
                break;
            }
            if n % i != 0 {
                continue;
            }
            let a = format!("{}", i).len().into();
            let b = format!("{}", n / i).len();
            use std::cmp::*;
            ans = min(ans, max(a, b));
        }
        println!("{}", ans);
    }
}

#[allow(dead_code)]
fn cin() -> Scanner<std::io::Stdin> {
    Scanner::new(std::io::stdin())
}

#[allow(dead_code)]
pub struct Scanner<T> {
    buf: Vec<u8>,
    len: usize,
    idx: usize,
    next: Option<String>,
    reader: T,
}

#[allow(dead_code)]
impl<Reader: std::io::Read> Scanner<Reader> {
    fn new(r: Reader) -> Scanner<Reader> {
        Scanner {
            buf: vec![0; 8192],
            len: 0,
            idx: 0,
            next: None,
            reader: r,
        }
    }

    fn next<T: std::str::FromStr>(&mut self) -> T {
        self.wrapped::<T>().unwrap()
    }

    fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.next()).collect()
    }

    fn mat<T: std::str::FromStr>(&mut self, r: usize, c: usize) -> Vec<Vec<T>> {
        (0..r).map(|_| self.vec(c)).collect()
    }

    fn vec_char(&mut self) -> Vec<char> {
        self.read();
        self.next.take().unwrap().chars().collect()
    }

    fn mat_char(&mut self, r: usize) -> Vec<Vec<char>> {
        (0..r).map(|_| self.vec_char()).collect()
    }

    fn wrapped<T: std::str::FromStr>(&mut self) -> Option<T> {
        self.read();
        self.next.take().and_then(|s| s.parse::<T>().ok())
    }

    fn read(&mut self) -> bool {
        if self.next.is_some() {
            return true;
        }
        let mut s = String::with_capacity(16);
        while let Some(c) = self.get_char() {
            if !c.is_whitespace() {
                s.push(c);
            } else if !s.is_empty() {
                break;
            }
        }
        self.next = if !s.is_empty() { Some(s) } else { None };
        self.next.is_some()
    }

    fn get_char(&mut self) -> Option<char> {
        if self.idx == self.len {
            match self.reader.read(&mut self.buf[..]) {
                Ok(l) if l > 0 => {
                    self.idx = 0;
                    self.len = l;
                }
                _ => return None,
            }
        }
        self.idx += 1;
        Some(self.buf[self.idx - 1] as char)
    }
}