GeloBer

Задача решена. Код:

with open('27-B.txt') as f:
    count_row = int(f.readline())
    count_even, count_odd, total_sum = 0, 0, 0
    diff_parity_more_less_array = []  # [разница; 10 – разной чётности при большем чётном, 01 – разной чётности при большем нечётном, 00 – одинаковой чётности]
    for row in range(count_row):
        numbers_array = sorted(list(map(int, f.readline().split())))
        max_number = numbers_array[1]
        if max_number % 2 == 0:
            count_even += 1
        else:
            count_odd += 1
        total_sum += max_number
        if (numbers_array[0] + numbers_array[1]) % 2 == 0:
            diff_parity_more_less_array.append([abs(numbers_array[0] - numbers_array[1]), '00'])
        else:
            if numbers_array[1] % 2 == 0:
                diff_parity_more_less_array.append([abs(numbers_array[0] - numbers_array[1]), '10'])
            else:
                diff_parity_more_less_array.append([abs(numbers_array[0] - numbers_array[1]), '01'])

diff_parity_more_less_array = sorted(diff_parity_more_less_array)
i = 0
while True:
    if count_even > count_odd and total_sum % 2 != 0 or count_odd > count_even and total_sum % 2 == 0:
        total_sum -= diff_parity_more_less_array[i][0]
        if diff_parity_more_less_array[i][1] == '01':
            count_even += 1
            count_odd -= 1
        elif diff_parity_more_less_array[i][1] == '10':
            count_even -= 1
            count_odd += 1
    else:
        print(total_sum)
        break
    i += 1

Если есть советы, как оптимизировать, то, пожалуйста, очень буду рад)