fun is_older( (yr1 : int, mth1 : int, day1 : int), (yr2 : int, mth2 : int, day2 : int)) =
    let
        val year = yr1 - yr2;
        val month = mth1 - mth2;
        val days = day1 - day2;
    in
        if year = 0
        then
            if month = 0
            then
                if days = 0
                then false
                else days < 0
            else month < 0
        else year < 0
    end

fun number_in_month(dates : (int * int * int) list, month: int) =
    if null dates
    then 0
    else
        let
            val date = hd dates
            val date_month = #2 date
        in
            if date_month = month
            then 1 + number_in_month(tl dates, month)
            else 0 + number_in_month(tl dates, month)
        end

fun number_in_months(dates: (int * int * int) list, months: int list) =
    if null months
    then 0
    else
        if null dates
        then 0
        else number_in_month(dates, (hd months)) + number_in_months(dates, (tl months))


fun dates_in_month(dates : (int * int * int) list, month : int) =
    if null dates
    then []
    else
        let
            val date = hd dates
            val date_month = #2 date
        in
            if date_month = month
            then date :: dates_in_month(tl dates, month)
            else dates_in_month(tl dates, month)
        end

fun dates_in_months(dates: (int * int * int) list, months: int list) =
    if null months
    then []
    else
        if null dates
        then []
        else
            let
                val new_dates = dates_in_month(dates, (hd months))
            in
                if null new_dates
                then dates_in_months(dates, (tl months))
                else (hd new_dates) :: dates_in_months(dates, (tl months))
            end

fun get_nth (strings : string list, nth: int) =
    if nth = 1
    then hd strings
    else get_nth(tl strings, nth -1)

fun date_to_string(date: (int * int * int)) =
    let
        val months = [ "January", "February", "March", "April", "May",
            "June", "July", "August", "September", "October",
            "November", "December"
        ];
        val month = get_nth(months, #2 date)
    in
        month ^ " " ^ Int.toString(#3 date) ^ ", " ^ Int.toString(#1 date)
    end


fun number_before_reaching_sum(sum: int, positives: int list) =
    let
        val first = hd positives;
        val new_sum = sum - first;
    in
        if new_sum <= 0
        then 0
        else 1 + number_before_reaching_sum(new_sum, (tl positives))
    end

fun what_month(days: int) =
    let
        val days_in_month = [31, 28, 31, 30, 31,
            30, 31, 31, 30, 31,
            30, 31
        ];
    in
        number_before_reaching_sum(days, days_in_month) + 1
    end

fun month_range(day1: int, day2: int) =
    if day2 < day1
    then []
    else what_month(day1) :: month_range(day1 + 1, day2)


fun oldest(dates: (int * int * int) list) =
    if null dates
    then NONE
    else
        if null (tl dates)
        then SOME (hd dates)
        else
            let
                fun oldest_with_at_least_two() =
                    let
                        val first_date = hd dates
                        val second_date = hd (tl dates)
                        val first_is_older = is_older(first_date, second_date);
                    in
                        if first_is_older
                        then first_date
                        else second_date
                    end
            in
                 oldest(oldest_with_at_least_two() :: (tl (tl dates)))
            end

fun remove_duplicated(numbers: int list) =
    if null numbers
    then []
    else
        if null (tl numbers)
        then numbers
        else
            let
                val first = hd numbers;

                fun is_in(numbers: int list) =
                    if null numbers
                    then false
                    else
                        if first = hd numbers
                        then true
                        else is_in(tl numbers);

            in
                if is_in (tl numbers)
                then remove_duplicated(tl numbers)
                else first :: remove_duplicated(tl numbers)
            end;

fun number_in_months_challenge(dates: (int * int * int) list, months: int list) =
    let
        val months = remove_duplicated(months)
    in
        number_in_months(dates, months)
    end

fun dates_in_months_challenge(dates: (int * int * int) list, months: int list) =
    let
        val months = remove_duplicated(months)
    in
        dates_in_months(dates, months)
    end