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;
using System.Linq;

namespace ABC057C
{
    class Program
    {
        static void Main(string[] args)
        {
            new Solver().Solve();
#if DEBUG
            Console.ReadLine();
#endif
        }
    }

    class Solver
    {
        long N;

        public void Solve()
        {

            int ans = 0;

            for (long a = (int)Math.Sqrt(N); a > 0; a--)
            {
                long r;
                long b = Math.DivRem(N, a, out r);
                if (r == 0)
                {
                    ans = F(a, b);
                    break;
                }
            }

            Console.WriteLine(ans);
        }

        public Solver()
        {
            N = ReadLong();
        }

        /// <summary>
        /// 正整数の桁数を返す.
        /// </summary>
        /// <param name="x"></param>
        /// <returns>桁数</returns>
        int GetDigit(long x)
        {
            int dgt = 0;
            while (x > 0)
            {
                x /= 10;
                dgt++;
            }
            return dgt;
        }

        int F(long a, long b)
        {
            return GetDigit(Math.Max(a, b));
        }

        static String ReadString() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Console.ReadLine()); }
        static long ReadLong() { return long.Parse(Console.ReadLine()); }
        static double ReadDouble() { return double.Parse(Console.ReadLine()); }
        static String[] ReadStringArray() { return Console.ReadLine().Split(' '); }
        static int[] ReadIntArray() { return Console.ReadLine().Split(' ').Select(e => int.Parse(e)).ToArray(); }
        static long[] ReadLongArray() { return Console.ReadLine().Split(' ').Select(e => long.Parse(e)).ToArray(); }
        static double[] ReadDoubleArray() { return Console.ReadLine().Split(' ').Select(e => double.Parse(e)).ToArray(); }
    }

}