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.Collections.Generic;
using System.Linq;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
            // 入力
            long lN = long.Parse(Console.ReadLine().Trim());

            System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
            sw.Start();

            // 解析
            long lSq = (long)Math.Sqrt(lN);
            List<int> lstSmp = new List<int>();
            for (long i = 1; i <= lSq; i++)
            {
                if (lN % i == 0)
                {
                    int iA = i.ToString().Length;                       // Aの桁数
                    int iB = ((long)(lN / i)).ToString().Length;        // Bの桁数
                    if (iA >= iB) { lstSmp.Add(iA); }                   // 大きい方を保持
                    else { lstSmp.Add(iB); }
                }
            }
            if (lstSmp.Count > 1) { lstSmp.Sort(); }                    // 昇順にソート

            //出力
            Console.WriteLine("{0}", lstSmp[0].ToString().Trim());

            sw.Stop();
#if DEBUG
            Console.WriteLine();
            Console.WriteLine("{0}", sw.Elapsed.ToString());
            Console.WriteLine("続行するには何かキーを押してください．．．");
            Console.ReadKey();
#endif
    }
}