Сумма цифр

## (1).Step.PrintLines(d-> (1 - (BigInteger.Pow(-10, d)-1) div 11 * 9) div 2 );

## function F1Digit(d: integer) := d and 1 * d - d shr 1;
 
//Reset(input, 'input.txt');
//Rewrite(output, 'output.txt');
 
var N := ReadInt64;
//var N := int64(BigInteger.Pow(10,15));
if N<10 then
begin
  F1Digit(N).Println;
  exit;
end;
 
var digits := new List<integer>(19); // Масимум 19 цифр в N
var max_ten_pow := int64(1);
begin
  var x := N;
  while true do
  begin
    var d: int64;
    x := System.Math.DivRem(x,10,d);
    digits += integer(d);
    if x=0 then break;
    max_ten_pow *= 10;
  end;
end;
 
var sign := digits.Count and 1*2-1; // digits.Count.IsEven ? -1 : +1;
var F9s := (1 - (max_ten_pow*sign-1) div 11 * 9) div 2; // Геом. прогрессия: b0=4.5, q=-10, f=0.5+b0*(q^n-1)/(q-1)
 
if digits.Count.IsEven then
begin
  var tail_N: int64;
  var first_d := System.Math.DivRem(N, max_ten_pow, tail_N);
  var body := max_ten_pow shr 1 * ( (first_d-1)*(9-first_d) ); // max_ten_pow div 10 * ( -first_d*(first_d-1)*5 + (first_d-1)*45 )
  var tail := digits[0]*(digits[0]+1) div 2 - first_d * (tail_N+1);
  for var i := 1 to digits.Count-2 do
  begin
    max_ten_pow := max_ten_pow div 10;
    first_d := System.Math.DivRem(tail_N, max_ten_pow, tail_N);
    var d_tail := max_ten_pow shr 1*(first_d-1) + tail_N+1;
    if i.IsEven then
      d_tail := 45 - d_tail;
    tail += first_d*d_tail;
  end;
  (F9s+body+tail).Println;
end else
begin
  var body := (N-max_ten_pow) div 10 * 5;
  var tail := F1Digit(digits[0]);
  if N and 1 = 0 then for var i := 1 to digits.Count-1 do
    tail += (i and 1*2-1) * digits[i];
  (F9s+body+tail).Println;
end;