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.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Set;
import java.util.HashSet;

public class Main {

    public static void main(String[] args) throws IOException {
        try (InputReader reader = new InputReader(System.in)) {
            solve(reader);
        }
    }

    private static void solve(InputReader reader) throws IOException {
        long n = reader.readLong();
        long min = Long.MAX_VALUE;
        for (long i = 1; i <= n; i++) {
            long b = n / i;
            if (i > b) {
                break;
            }

            if (i * b == n) {
                long f = Math.max(String.valueOf(i).length(), String.valueOf(b).length());
                min = Math.min(min, f);
            }
        }
        System.out.println(min);
    }
}

class Util {
    static int gcd(int m, int n) {
        int min = Math.min(m, n);
        int max = Math.max(m, n);
        while (min != 0) {
            int tmp = min;
            min = max % tmp;
            max = tmp;
        }

        return max;
    }
}

class InputReader implements Closeable, AutoCloseable {
    private final BufferedReader br;

    InputReader(InputStream inputStream) {
        this.br = new BufferedReader(new InputStreamReader(inputStream));
    }

    String readLine() throws IOException {
        return this.br.readLine();
    }

    int readInt() throws IOException {
        return Integer.parseInt(this.readLine());
    }

    long readLong() throws IOException {
        return Long.parseLong(this.readLine());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(this.readLine());
    }

    String[] readStringsSplitByDelimiter(String delimiter) throws IOException {
        return this.readLine().split(delimiter);
    }

    int[] readIntsSplitByDelimiter(String delimiter) throws IOException {
        String[] strings = this.readStringsSplitByDelimiter(delimiter);

        int stringsLength = strings.length;
        int[] ints = new int[stringsLength];
        for (int i = 0; i < stringsLength; i++) {
            ints[i] = Integer.parseInt(strings[i]);
        }

        return ints;
    }

    long[] readLongsSplitByDelimiter(String delimiter) throws IOException {
        String[] strings = this.readStringsSplitByDelimiter(delimiter);

        int stringsLength = strings.length;
        long[] longs = new long[stringsLength];
        for (int i = 0; i < stringsLength; i++) {
            longs[i] = Long.parseLong(strings[i]);
        }

        return longs;
    }

    double[] readDoublesSplitByDelimiter(String delimiter) throws IOException {
        String[] strings = this.readStringsSplitByDelimiter(delimiter);

        int stringsLength = strings.length;
        double[] doubles = new double[stringsLength];
        for (int i = 0; i < stringsLength; i++) {
            doubles[i] = Double.parseDouble(strings[i]);
        }

        return doubles;
    }

    @Override
    public void close() throws IOException {
        this.br.close();
    }
}