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: Accepted)

import java.io.*;
import java.util.*;
import java.lang.Math.*;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve(args);
    }

    public void solve(String[] args) {
        MyScanner scanner = new MyScanner();
        long N = scanner.nextLong();
        List<Long> list = new ArrayList<>();
        long ans = ("" + N).length();
        for (long i = 1; i * i <= N; i++) {
            if (N % i == 0) {
                long b = N / i;
                long c = Math.max(("" + i).length(), ("" + b).length());
                ans = Math.min(c, ans);
            }
        }

        System.out.println(ans);
    }

    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() {
            try {
                return Integer.parseInt(next());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return -1;
        }

        public double nextDouble() {
            try {
                return Double.parseDouble(next());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return -1;
        }

        public long nextLong()  {
            try {
                return Long.parseLong(next());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return -1;
        }
    }
}