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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;
namespace AtCoder {
    class MainClass {
        //C#7.0

        long N;
        void Solve() {
            io.i(out N);

            Mathf mat = new Mathf();
            long div = 2;
            long A = div;
            long B = N;
            long ideal = (int)Math.Sqrt(N);

            while (true) {
                if (B % div == 0) {
                    B /= div;
                    A *= div;
                    div = 2;
                } else {
                    div++;
                }
                if (mat.Digit(A) == mat.Digit(B) || A > B ||A>ideal|| div > B / 2||div>N/2)
                    break;
            }

            io.o(mat.Digit(B));

        }

        public static void Main(string[] args) { new MainClass().Stream(); }
        IO io = new IO();
        void Stream() { Solve(); io.writeFlush(); }

        class IO {
            string[] nextBuffer; int BufferCnt; char[] cs = new char[] { ' ' };
            StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            public IO() { nextBuffer = new string[0]; BufferCnt = 0; Console.SetOut(sw); }
            public string next() {
                if (BufferCnt < nextBuffer.Length) return nextBuffer[BufferCnt++];
                string st = Console.ReadLine();
                while (st == "") st = Console.ReadLine();
                nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
                BufferCnt = 0;
                return nextBuffer[BufferCnt++];
            }
            public char nextChar() { return char.Parse(next()); }
            public int nextInt() { return int.Parse(next()); }
            public long nextLong() { return long.Parse(next()); }
            public double nextDouble() { return double.Parse(next()); }
            public string[] array() { return Console.ReadLine().Split(' '); }
            public char[] arrayChar() { return Array.ConvertAll(array(), char.Parse); }
            public int[] arrayInt() { return Array.ConvertAll(array(), int.Parse); }
            public long[] arrayLong() { return Array.ConvertAll(array(), long.Parse); }
            public double[] arrayDouble() { return Array.ConvertAll(array(), double.Parse); }
            private bool typeEQ<T, U>() { return typeof(T).Equals(typeof(U)); }
            private T convertType<T, U>(U v) { return (T)Convert.ChangeType(v, typeof(T)); }
            private T suitType<T>(string s) {
                if (typeEQ<T, int>()) return convertType<T, int>(int.Parse(s));
                if (typeEQ<T, long>()) return convertType<T, long>(long.Parse(s));
                if (typeEQ<T, double>()) return convertType<T, double>(double.Parse(s));
                if (typeEQ<T, char>()) return convertType<T, char>(char.Parse(s));
                return convertType<T, string>(s);
            }
            public void i<T>(out T v) { v = suitType<T>(next()); }
            public void i<T, U>(out T v1, out U v2) {
                var a = array(); v1 = suitType<T>(a[0]); v2 = suitType<U>(a[1]);
            }
            public void i<T, U, V>(out T v1, out U v2, out V v3) {
                var a = array(); v1 = suitType<T>(a[0]); v2 = suitType<U>(a[1]);
                v3 = suitType<V>(a[2]);
            }
            public void i<T, U, V, W>(out T v1, out U v2, out V v3, out W v4) {
                var a = array(); v1 = suitType<T>(a[0]); v2 = suitType<U>(a[1]);
                v3 = suitType<V>(a[2]); v4 = suitType<W>(a[3]);
            }
            public void ini(out int[] a, int size) {
                a = new int[size]; for (int i = 0; i < size; i++) a[i] = nextInt();
            }
            public void ini(out int[] a1, out int[] a2, int size) {
                a1 = new int[size]; a2 = new int[size];
                for (int i = 0; i < size; i++) { a1[i] = nextInt(); a2[i] = nextInt(); }
            }
            public void ini(out string[] a, int size) {
                a = new string[size]; for (int i = 0; i < size; i++) a[i] = next();
            }
            public void inii(out int[] a, int size) {
                a = new int[size]; for (int i = 0; i < size; i++) a[i] = nextInt() - 1;
            }
            public void inii(out int[] a1, out int[] a2, int size) {
                a1 = new int[size]; a2 = new int[size];
                for (int i = 0; i < size; i++) { a1[i] = nextInt() - 1; a2[i] = nextInt() - 1; }
            }
            public void o<T>(T v) { Console.WriteLine(v); }
            public void o<T>(params T[] a) { foreach (T v in a) Console.WriteLine(v); }
            public void o<T>(List<T> l) { foreach (T v in l) sw.WriteLine(v); }
            public void ol<T>(T v) { Console.Write(v + " "); }
            public void ol<T>(params T[] a) { foreach (T v in a) Console.Write(v + " "); Console.WriteLine(""); }
            public void YN(bool f) { Console.WriteLine(f ? "YES" : "NO"); }
            public void Yn(bool f) { Console.WriteLine(f ? "Yes" : "No"); }
            public void yn(bool f) { Console.WriteLine(f ? "yes" : "no"); }
            public void writeFlush() { Console.Out.Flush(); }
        }

        class Mathf {
            public int mod = 1000000007;//10^9+7
            public long Pow(long a, long b) {
                if (b == 0) return 1;
                if (b % 2 == 1) return (a % mod * Pow(a % mod, b - 1) % mod) % mod;
                else return Pow(a * a % mod, b / 2) % mod;
            }
            public long Fact(long n) { return n != 0 ? (n % mod * (Fact(n - 1) % mod) % mod) : 1; }
            public long C(long n, long r) {
                if (r == 0 || n == r) return 1;
                else return (Fact(n) % mod * Pow((Fact(n - r) % mod * Fact(r) % mod) % mod, mod - 2) % mod) % mod;
            }
            public long Sum(params long[] a) { return a.Aggregate((v, next) => (v % mod + next) % mod); }
            public int GCD(int a, int b) { if (a < b) Swap(ref a, ref b); return b == 0 ? a : GCD(b, a % b); }
            public int GCD(int[] array) { return array.Aggregate((v, next) => GCD(v, next)); }
            public void Swap<T>(ref T a, ref T b) { T tmp = a; a = b; b = tmp; }
            public T Max<T>(params T[] v) { return v.Max(); }
            public T Min<T>(params T[] v) { return v.Min(); }
            public double Dis(int x1, int y1, int x2, int y2) {
                return Math.Sqrt(Math.Pow((x2 - x1), 2) + Math.Pow((y2 - y1), 2));
            }
            public int Digit(long n) { return (n == 0) ? 1 : (int)Math.Log10(n) + 1; }
        }
    }
    class BucketSort {
        public int[] bucket;
        public void Init(int[] a) {
            bucket = new int[a.Max() + 1];
            for (int i = 0; i < a.Length; ++i) ++bucket[a[i]];
            for (int i = 0, j = 0; j < bucket.Length; ++j)
                for (int k = bucket[j]; k != 0; --k, ++i) a[i] = j;
        }

    }
    static class StringEX {
        public static string Reversed(this string s) { return string.Join("", s.Reverse()); }
        public static string Repeat(this string s, int n) { return string.Concat(Enumerable.Repeat(s, n).ToArray()); }
    }
}