//16

int years = 2003;
int weeks = CalculateWeekends(years);
Console.WriteLine($"Количество выходных дней в {years} году: {weeks}");

static int CalculateWeekends(int year)
{
    DateTime date1 = new DateTime(year, 1, 1);
    DateTime date2 = new DateTime(year, 12, 31);
    int c = 0;
    for (var date = date1; date <= date2; date = date.AddDays(1))
    {
        if (date.DayOfWeek == DayOfWeek.Saturday || date.DayOfWeek == DayOfWeek.Sunday)
        {
            c++;
        }
    }
    return c;
}