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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.util.*;
public class Main {
    private static MyScanner scanner;
 
    public static void main (String[] args){
        Main instance = new Main();
        scanner = instance.new MyScanner();
        instance.solve();
    }
 
    private void solve() {
        try {
            long N = scanner.nextLong();
            long A = 1;
            long B = N;
            long min = Long.MAX_VALUE;
            while (A <= B) {
                if (A * B == N) {
                    int f = solveF(A, B);
                    if (f < min) {
                        min = f;
                    }
                }
                A++;
                while (N % A != 0) {
                    A++;
                }
                B = N / A;
            }
            System.out.println(min);
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
 
    private int solveF (long a, long b) {
        return a > b ? String.valueOf(a).length() : String.valueOf(b).length();
    }
 
    private class MyScanner {
        String[] s;
        int i;
        BufferedReader br;
        String reg = " ";
 
        MyScanner () {
            s = new String[0];
            i = 0;
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        public String next() throws IOException {
            if (i < s.length) return s[i++];
            String line = br.readLine();
            while (line.equals("")) {
                line = br.readLine();
            }
            s = line.split(reg, 0);
            i = 0;
            return s[i++];
        }
 
        public int nextInt() throws NumberFormatException, IOException {
            return Integer.parseInt(next());
        }
 
        public double nextDouble() throws NumberFormatException, IOException {
            return Double.parseDouble(next());
        }
 
        public long nextLong() throws NumberFormatException, IOException {
            return Long.parseLong(next());
        }
    }
}