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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace SandboxCSharp
{
    class Solver
    {
        private long Func(long a)
        {
            if (a == 0) return 0;
            return 1 + Func(a / 10);
        }

        public void Solve()
        {
            long n = io.ScanLong();
            long m = (long)(Math.Sqrt(n));

            long best = 99999999;

            for (long a = 1; a <= m; ++a)
            {
                if (n % a > 0) continue;
                long b = n / a;
                best = Math.Min(best, Math.Max(Func(a), Func(b)));
            }

            io.WriteLine(best);
        }

        // =================================================
        // =================================================

        Stdio io;
        bool isjdg;
        static void Main()
        {
            var s = new Solver();
            s.Solve();
            s.io.Flush();
        }
        public Solver(Stdio _io = null)
        {
            isjdg = _io == null;
            io = _io == null ? new Stdio() : _io;
        }

        void Exit()
        {
            if (isjdg)
            {
                io.Flush();
                Environment.Exit(0);
            }
            else
                throw new HaltException();
        }
    }
    class Stdio
    {
        protected string[] stack = new string[0];
        protected int stackptr = 0;
        protected StringBuilder outbuff = new StringBuilder();

        public virtual int ScanInt()
        {
            return Check() ? int.Parse(stack[stackptr++]) : 0;
        }
        public virtual long ScanLong()
        {
            return Check() ? long.Parse(stack[stackptr++]) : 0;
        }
        public virtual string ScanString()
        {
            return Check() ? stack[stackptr++] : string.Empty;
        }
        public virtual double ScanDouble()
        {
            return Check() ? double.Parse(stack[stackptr++]) : 0;
        }
        protected virtual bool Check()
        {
            if (stackptr < stack.Length) return true;
            var l = Console.ReadLine();
            if (l == null) return false;
            stack = l.Split(' ').ToArray(); stackptr = 0;
            return Check();
        }
        public Stdio Write(long v) { return Write($"{v}"); }
        public Stdio WriteLine(long v) { return WriteLine($"{v}"); }
        public Stdio Write(string str)
        {
            outbuff.Append(str);
            return this;
        }
        public Stdio WriteLine(string str = "")
        {
            outbuff.AppendLine(str);
            return this;
        }
        public virtual Stdio Flush()
        {
            Console.Write(outbuff.ToString());
            outbuff.Clear();
            return this;
        }
    }
    class HaltException : Exception { }

}