Program WarmUp4;
{
 The program should calculate the sum of n numbers in the entered number system
}

{$APPTYPE CONSOLE}

Uses
  System.SysUtils;

Const
  MaxSize=256;
  MaxAmount=50;
  NSAlphabet = '0123456789ABCDEFGHIJ';
  MaxNS = length(NSAlphabet);
  //MaxSize - maximum amount of digits for entered numbers
  //MaxAmount - maximum amount of numbers
  //NSAlphabet - transfer between symbols and numbers
  //MaxNS - maximum number system

Var
  Num1 :array[1..(MaxSize + (MaxAmount div 10) + 1)] of ShortInt;
  Num2 :array[1..MaxSize] of ShortInt;
  str :string;
  NS, Amount : Integer;
  j, Sum, Carry : ShortInt;
  Len1, Len2, Size, i: Word;
  flag: boolean;
  //Num1 - array of digits of the first number (further the sum of the two previous numbers)
  //Num2 - array of digits of the second numbers (with which need to add the first number)
  //str - string variable for writing numbers
  //NS - number system
  //Amount - amount of numbers
  //Sum - sum of digits
  //Carry - сarry 1 (if there is) to the next element
  //Len1 - the length of the first entered number
  //Len2 - the length of the second entered number
  //Size - the size of the sum
  //i,j - cycle counter
  //flag - flag to confirm the correctness of entering numbers

Begin

  Writeln('Enter number system (maximum number system is ',MaxNS,', minimal is 2). The program will calculate their sum.');

  //Cycle with postcondition for entering correct data.
  Repeat

    //Initialize the flag
    flag:= False;

    //Validating the correct input data type
    Try
      Readln(NS);
    Except
      Writeln('Wrong input of number system! It must be an integer');
      flag:= True;
    End;

    //Validate Range
    if ((NS > MaxNS) or (NS < 2)) and (flag = False) then
    begin
      Writeln('Wrong input of number system! It must be >=2 and <=',MaxNS);
      flag:= True;
    end;

  Until flag = False;

  Writeln;
  Writeln('Enter amount of numbers (no more than ',MaxAmount,' and more than 1)');

  //Cycle with postcondition for entering correct data.
  Repeat

    //Initialize the flag
    flag:= False;

    //Validating the correct input data type
    Try
      Readln(Amount);
    Except
      Writeln('Wrong input of amount of numbers! It must be an integer');
      flag:= True;
    End;

    //Validate Range
    if ((Amount > MaxAmount) or (Amount <= 1)) and (flag = False) then
    begin
      Writeln('Wrong input of amount of numbers! It must be >1 and <=',MaxAmount);
      flag:= True;
    end;

  Until flag = False;

  //Declaring available symbols and their value
  Writeln;
  Writeln('Available symbols on the ',NS,'th number system and their number system:');
  for i := 0 to (NS - 1) do
    Writeln('Symbol ', NSAlphabet[i+1],' Value = ',i);
  Writeln;

  Writeln('Enter numbers (no more than ',MaxSize,' digits).');

  //Cycle with postcondition for entering correct data.
  Repeat

    //Initialize the flag
    flag:= False;

    //Read the first entered number and check for correctness.
    Readln(str);

    //Find length of the first number
    Len1:= length(str);

    //Checking the correct length
    if Len1 > MaxSize then
    begin
      Writeln('Wrong input of number! The length of the number must be no more than ',MaxSize,' digits.');
      flag:= True;
    end

    //Else if length >1, the first digit cannot be 0 (in the mirrored view it is last)
    else if (Len1 > 1) and (str[1] = '0') then
    begin
      Writeln('Wrong input of number! The first digit of a number cannot be 0');
      flag:= True;
    end

    //Else writing a number to an array and checking for valid symbols
    else
    begin

      //Reset the first number for the input
      for i := 1 to length(Num1) do
        Num1[i]:= 0;

      //Write the first entered number in mirrored view to an array
      i:= 1;
      while (i <= Len1) and (flag = False) do
      begin

        //Transfer to numerical value (-1 because numbering in delphi starts from 1)
        Num1[i]:= Pos(str[Len1-i+1], NSAlphabet) - 1;

        //Checking for correct input in the number system
        //Num1[i] will be <0 if the symbol is not in NSAlphabet
        if (Num1[i] < 0) or (Num1[i] >= NS) then
        begin
          Writeln('Wrong input of number! Namely, wrong input of symbols! See available symbols above!');
          flag:= True;
        end;

        //Modernize i
        i:= i + 1;
      end;

    end;

  Until flag = False;

  //The cycle go (Amount - 1) times to add all the numbers
  for j := 1 to (Amount - 1) do
  begin

    Writeln('+');

    //Cycle with postcondition for entering correct data.
    Repeat

      //Initialize the flag
      flag:= False;

      //Read the second entered number and check for correctness.
      Readln(str);

      //Find length of the second number
      Len2:= length(str);

      //Checking the correct length
      if Len2 > MaxSize then
      begin
        Writeln('Wrong input of number! The length of the number must be no more than ',MaxSize,' digits.');
        flag:= True;
      end

      //Else if length >1, the first digit cannot be 0 (in the mirrored view it is last)
      else if (Len2 > 1) and (str[1] = '0') then
      begin
        Writeln('Wrong input of number! The first digit of a number cannot be 0');
        flag:= True;
      end

      //Else writing a number to an array and checking for valid symbols
      else
      begin

        //Reset the second number for the input
        for i := 1 to length(Num2) do
          Num2[i]:= 0;

        //Write the second number in mirrored view to an array
        i:= 1;
        while (i <= Len2) and (flag = False) do
        begin

          //Transfer to numerical value (-1 because numbering in delphi starts from 1)
          Num2[i]:= Pos(str[Len2-i+1], NSAlphabet) - 1;

          //Checking for correct input in the number system
          //Num2[i] will be <0 if the symbol is not in NSAlphabet
          if (Num2[i] < 0) or (Num2[i] >= NS) then
          begin
            Writeln('Wrong input of number! Namely, wrong input of symbols! See available symbols above!');
            flag:= True;
          end;

          //Modernize i
          i:= i + 1;
        end;

      end;

    Until flag = False;

    //Compare the sizes of the first and second numbers.
    //The larger size assign in a Size (this is the size of the sum of the numbers)
    if Len1 > Len2 then
      Size:= Len1
    else
      Size:= Len2;

    //Start adding digits separately in the cycle
    for i := 1 to Size do
    begin

      //Starting to add the last digits of the numbers (in the mirrored view it is first)
      //and add the carry (if there is).
      Sum:= Carry + Num1[i] + Num2[i];

      //The modulo of the Sum by number system is the last (in the mirrored it is first) digit of sums (array Num1).
      Num1[i]:= Sum mod NS;

      //The integer part of dividing by number system is the carry that will go to the next element
      Carry:= Sum div NS;

      //If there is a carry on the last digit, then increase the size of sum by 1 and add a carry to the next element
      if (i = Size) and (Carry = 1) then
      begin
        Size:= Size + 1;
        Num1[i+1]:= Carry;
      end;

    end;

    //Update the length of the first number
    Len1:= Size;

    //Reset the carry for the following operations
    Carry:= 0;

  end;

  //Write the answer, mirroring the back
  //Transfer to symbolic value (+1 because numbering in delphi starts from 1)
  Writeln('The sum of the numbers is:');
  for i := Size downto 1 do
    Write(NSAlphabet[Num1[i]+1]);

  Readln;
End.