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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

namespace ABC057C
{
    class Program
    {
        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());
            long Amax = (long)Math.Ceiling(Math.Sqrt(N));
            long Fmin = N;
            for(long i=Amax; i > 0; i--){
                if(N % i == 0){
                    long B = N/i;
                    Fmin = F(i,B);
                    break;
                }
            }
            Console.WriteLine(Fmin);
        }
        public static long F(long a, long b){
            long c = 0; long d = 0;
            while(a > 0){
                c++; a /=10;
            }            
            while(b > 0){
                d++; b /=10;
            }
            if(c < d) return d; else return c;            
        }
    }
}