using System;

using System.Diagnostics;

​

public class Program

{

    public static void Main()

    {

        var digits = int.MaxValue / 32 - 4;

        void test(string name, Func<int, int> f) {

            var sw = new Stopwatch();

            sw.Start();

            var res = f(digits);

            sw.Stop();

            Console.WriteLine($"{name.PadRight(15)} result: {res} ticks: {sw.ElapsedTicks}");

        }

        test(nameof(CountPagesSlow), CountPagesSlow);

        test(nameof(CountPages), CountPages);

        test(nameof(CountPagesOpt), CountPagesOpt);

    }

    public static int CountPagesSlow(int digits) {

        var pages = 0;

        while (digits > 0) {

            pages++;

            digits -= pages.ToString().Length;

        }

        return pages;

    }

    public static int CountPages(int digits) {

        var pages = 0;

        var digitsPerPage = 1;

        var currentRange = 0;

        var nextRange = 9;

        while (digits > nextRange * digitsPerPage) {

            digits -= nextRange * digitsPerPage;

            pages += nextRange;

            currentRange = nextRange;

            nextRange = nextRange * 10;

            digitsPerPage++;

        }

        while (digits > 0) {

            pages++;

            digits -= digitsPerPage;

        }

        return pages;

    }

    public static int CountPagesOpt(int digits) {

        var pages = 0;

        var digitsPerPage = 1;

        var currentRange = 0;

        var nextRange = 9;

        while (digits > nextRange * digitsPerPage) {

            digits -= nextRange * digitsPerPage;

            pages += nextRange;

            currentRange = nextRange;

            nextRange = nextRange * 10;

            digitsPerPage++;

        }

        while (digits > 0) {

            var mul = 1;

            while (digits >= digitsPerPage * mul) {

                pages += mul;

                digits -= digitsPerPage * mul;

                mul *= 2;

            }

            if (digits > 0 && digits < digitsPerPage) {

                throw new Exception("Incorrect digit count");

            }

        }

        return pages;

    }

}