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.PrintStream;
import java.util.Scanner;

public class Main {
    static final Scanner     sc = new Scanner(System.in);
    static final PrintStream so = System.out;
    public static void main(String[] args) {
        long N = nlong();
        long maxA = 0;
        
        for (long a = 1; a <= Math.sqrt(N); a++) {
            if (N % a == 0) {
                maxA = a; 
            }
        }
        long b = N/maxA;
        so.println(keta(b));
    }

    private static int keta(long n) {
        int count = 0;
        while (n > 0) {
            count++;
            n /= 10;
        }
        return count;
    }

    private static long nlong() {
        return sc.nextLong();
    }

    private static int nint() {
        return sc.nextInt();
    }

    private static String nstr() {
        return sc.next();
    }

    private static char[] nchars() {
        return sc.next().toCharArray();
    }

    private static long[] nlongs(int n) {
        return nlongs(n, 0, 0);
    }
    
    private static int[] nints(int n) {
        return nints(n, 0, 0);
    }

    private static int[] nints(int n, int padL, int padR) {
        int[] a = new int[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nint();
        return a;
    }

    private static long[] nlongs(int n, int padL, int padR) {
        long[] a = new long[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nlong();
        return a;
    }
    
    private static String[] nstrs(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = nstr();
        return a;
    }
    
    private static char[][] nchars2D(int h, int w) {
        return nchars2D(h, w, 0);
    }
    
    private static char[][] nchars2D(int h, int w, int pad) {
        char[][] a2 = new char[h+pad*2][w+pad*2];
        for(int i = 0; i < h; i++)
            System.arraycopy(nchars(), 0, a2[pad+i], pad, w);
        return a2;
    }
}