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Спробуйте наш новий інтерфейс для відправки розв'язків
Задачі

Явна формула

Явна формула

Розглянемо \textbf{10} бульових змінних \textbf{x_1},\textbf{ x_2},\textbf{ x_3},\textbf{ x_4},\textbf{ x_5},\textbf{ x_6},\textbf{ x_7},\textbf{ x_8},\textbf{ x_9} та \textbf{x_10}. Розглянемо усі можливі пари та трійки різних змінних із цих десяти (усього існує \textbf{45} пари та \textbf{120} трійки). Обчисліть кількість пар та трійок, у яких хоча б одна змінна встановлена в \textbf{1}. Покладемо \textbf{f(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)} = \textbf{1} якщо ця кількість непарна і \textbf{f(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)} = \textbf{0} якщо кількість парна. Розглянемо явну формулу, яка реалізує функцію \textbf{f(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)}: \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} 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\includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} \textbf{f(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)} = (\textbf{x_1} V \textbf{x_2}) (\textbf{x_1} V \textbf{x_3}) (\textbf{x_1} V \textbf{x_4}) (\textbf{x_1} V \textbf{x_5}) (\textbf{x_1} V \textbf{x_6}) (\textbf{x_1} V \textbf{x_7}) (\textbf{x_1} V \textbf{x_8}) (\textbf{x_1} V \textbf{x_9}) (\textbf{x_1} V \textbf{x_10}) (\textbf{x_2} V \textbf{x_3}) (\textbf{x_2} V \textbf{x_4}) (\textbf{x_2} V \textbf{x_5}) (\textbf{x_2} V \textbf{x_6}) (\textbf{x_2} V \textbf{x_7}) (\textbf{x_2} V \textbf{x_8}) (\textbf{x_2} V \textbf{x_9}) (\textbf{x_2} V \textbf{x_10}) (\textbf{x_3} V \textbf{x_4}) (\textbf{x_3} V \textbf{x_5}) (\textbf{x_3} V \textbf{x_6}) (\textbf{x_3} V \textbf{x_7}) (\textbf{x_3} V \textbf{x_8}) (\textbf{x_3} V \textbf{x_9}) (\textbf{x_3} V \textbf{x_10}) (\textbf{x_4} V \textbf{x_5}) (\textbf{x_4} V \textbf{x_6}) (\textbf{x_4} V \textbf{x_7}) (\textbf{x_4} V \textbf{x_8}) (\textbf{x_4} V \textbf{x_9}) (\textbf{x_4} V \textbf{x_10}) (\textbf{x_5} V \textbf{x_6}) (\textbf{x_5} V \textbf{x_7}) (\textbf{x_5} V \textbf{x_8}) (\textbf{x_5} V \textbf{x_9}) (\textbf{x_5} V \textbf{x_10}) (\textbf{x_6} V \textbf{x_7}) (\textbf{x_6} V \textbf{x_8}) (\textbf{x_6} V \textbf{x_9}) (\textbf{x_6} V \textbf{x_10}) (\textbf{x_7} V \textbf{x_8}) (\textbf{x_7} V \textbf{x_9}) (\textbf{x_7} V \textbf{x_10}) (\textbf{x_8} V \textbf{x_9}) (\textbf{x_8} V \textbf{x_10}) (\textbf{x_9} V \textbf{x_10}) (\textbf{x_1} V \textbf{x_2} V \textbf{x_3}) (\textbf{x_1} V \textbf{x_2} V \textbf{x_4}) (\textbf{x_1} V \textbf{x_2} V \textbf{x_5}) (\textbf{x_1} V \textbf{x_2} V \textbf{x_6}) (\textbf{x_1} V \textbf{x_2} V \textbf{x_7}) (\textbf{x_1} V \textbf{x_2} V \textbf{x_8}) (\textbf{x_1} V \textbf{x_2} V \textbf{x_9}) (\textbf{x_1} V \textbf{x_2} V \textbf{x_10}) (\textbf{x_1} V \textbf{x_3} V \textbf{x_4}) (\textbf{x_1} V \textbf{x_3} V \textbf{x_5}) (\textbf{x_1} V \textbf{x_3} V \textbf{x_6}) (\textbf{x_1} V \textbf{x_3} V \textbf{x_7}) (\textbf{x_1} V \textbf{x_3} V \textbf{x_8}) (\textbf{x_1} V \textbf{x_3} V \textbf{x_9}) (\textbf{x_1} V \textbf{x_3} V \textbf{x_10}) (\textbf{x_1} V \textbf{x_4} V \textbf{x_5}) (\textbf{x_1} V \textbf{x_4} V \textbf{x_6}) (\textbf{x_1} V \textbf{x_4} V \textbf{x_7}) (\textbf{x_1} V \textbf{x_4} V \textbf{x_8}) (\textbf{x_1} V \textbf{x_4} V \textbf{x_9}) (\textbf{x_1} V \textbf{x_4} V \textbf{x_10}) (\textbf{x_1} V \textbf{x_5} V \textbf{x_6}) (\textbf{x_1} V \textbf{x_5} V \textbf{x_7}) (\textbf{x_1} V \textbf{x_5} V \textbf{x_8}) (\textbf{x_1} V \textbf{x_5} V \textbf{x_9}) (\textbf{x_1} V \textbf{x_5} V \textbf{x_10}) (\textbf{x_1} V \textbf{x_6} V \textbf{x_7}) (\textbf{x_1} V \textbf{x_6} V \textbf{x_8}) (\textbf{x_1} V \textbf{x_6} V \textbf{x_9}) (\textbf{x_1} V \textbf{x_6} V \textbf{x_10}) (\textbf{x_1} V \textbf{x_7} V \textbf{x_8}) (\textbf{x_1} V \textbf{x_7} V \textbf{x_9}) (\textbf{x_1} V \textbf{x_7} V \textbf{x_10}) (\textbf{x_1} V \textbf{x_8} V \textbf{x_9}) (\textbf{x_1} V \textbf{x_8} V \textbf{x_10}) (\textbf{x_1} V \textbf{x_9} V \textbf{x_10}) (\textbf{x_2} V \textbf{x_3} V \textbf{x_4}) (\textbf{x_2} V \textbf{x_3} V \textbf{x_5}) (\textbf{x_2} V \textbf{x_3} V \textbf{x_6}) (\textbf{x_2} V \textbf{x_3} V \textbf{x_7}) (\textbf{x_2} V \textbf{x_3} V \textbf{x_8}) (\textbf{x_2} V \textbf{x_3} V \textbf{x_9}) (\textbf{x_2} V \textbf{x_3} V \textbf{x_10}) (\textbf{x_2} V \textbf{x_4} V \textbf{x_5}) (\textbf{x_2} V \textbf{x_4} V \textbf{x_6}) (\textbf{x_2} V \textbf{x_4} V \textbf{x_7}) (\textbf{x_2} V \textbf{x_4} V \textbf{x_8}) (\textbf{x_2} V \textbf{x_4} V \textbf{x_9}) (\textbf{x_2} V \textbf{x_4} V \textbf{x_10}) (\textbf{x_2} V \textbf{x_5} V \textbf{x_6}) (\textbf{x_2} V \textbf{x_5} V \textbf{x_7}) (\textbf{x_2} V \textbf{x_5} V \textbf{x_8}) (\textbf{x_2} V \textbf{x_5} V \textbf{x_9}) (\textbf{x_2} V \textbf{x_5} V \textbf{x_10}) (\textbf{x_2} V \textbf{x_6} V \textbf{x_7}) (\textbf{x_2} V \textbf{x_6} V \textbf{x_8}) (\textbf{x_2} V \textbf{x_6} V \textbf{x_9}) (\textbf{x_2} V \textbf{x_6} V \textbf{x_10}) (\textbf{x_2} V \textbf{x_7} V \textbf{x_8}) (\textbf{x_2} V \textbf{x_7} V \textbf{x_9}) (\textbf{x_2} V \textbf{x_7} V \textbf{x_10}) (\textbf{x_2} V \textbf{x_8} V \textbf{x_9}) (\textbf{x_2} V \textbf{x_8} V \textbf{x_10}) (\textbf{x_2} V \textbf{x_9} V \textbf{x_10}) (\textbf{x_3} V \textbf{x_4} V \textbf{x_5}) (\textbf{x_3} V \textbf{x_4} V \textbf{x_6}) (\textbf{x_3} V \textbf{x_4} V \textbf{x_7}) (\textbf{x_3} V \textbf{x_4} V \textbf{x_8}) (\textbf{x_3} V \textbf{x_4} V \textbf{x_9}) (\textbf{x_3} V \textbf{x_4} V \textbf{x_10}) (\textbf{x_3} V \textbf{x_5} V \textbf{x_6}) (\textbf{x_3} V \textbf{x_5} V \textbf{x_7}) (\textbf{x_3} V \textbf{x_5} V \textbf{x_8}) (\textbf{x_3} V \textbf{x_5} V \textbf{x_9}) (\textbf{x_3} V \textbf{x_5} V \textbf{x_10}) (\textbf{x_3} V \textbf{x_6} V \textbf{x_7}) (\textbf{x_3} V \textbf{x_6} V \textbf{x_8}) (\textbf{x_3} V \textbf{x_6} V \textbf{x_9}) (\textbf{x_3} V \textbf{x_6} V \textbf{x_10}) (\textbf{x_3} V \textbf{x_7} V \textbf{x_8}) (\textbf{x_3} V \textbf{x_7} V \textbf{x_9}) (\textbf{x_3} V \textbf{x_7} V \textbf{x_10}) (\textbf{x_3} V \textbf{x_8} V \textbf{x_9}) (\textbf{x_3} V \textbf{x_8} V \textbf{x_10}) (\textbf{x_3} V \textbf{x_9} V \textbf{x_10}) (\textbf{x_4} V \textbf{x_5} V \textbf{x_6}) (\textbf{x_4} V \textbf{x_5} V \textbf{x_7}) (\textbf{x_\{4 \}}V \textbf{x_5} V \textbf{x_8}) (\textbf{x_4} V \textbf{x_5} V \textbf{x_9}) (\textbf{x_4} V \textbf{x_5} V \textbf{x_10}) (\textbf{x_4} V \textbf{x_6} V \textbf{x_7}) (\textbf{x_4} V \textbf{x_6} V \textbf{x_8}) (\textbf{x_4} V \textbf{x_6} V \textbf{x_9}) (\textbf{x_4} V \textbf{x_6} V \textbf{x_10}) (\textbf{x_4} V \textbf{x_7} V \textbf{x_8}) (\textbf{x_4} V \textbf{x_7} V \textbf{x_9}) (\textbf{x_4} V \textbf{x_7} V \textbf{x_10}) (\textbf{x_4} V \textbf{x_8} V \textbf{x_9}) (\textbf{x_4} V \textbf{x_8} V \textbf{x_10}) (\textbf{x_4} V \textbf{x_9} V \textbf{x_10}) (\textbf{x_5} V \textbf{x_6} V \textbf{x_7}) (\textbf{x_5} V \textbf{x_6} V \textbf{x_8}) (\textbf{x_5} V \textbf{x_6} V \textbf{x_9}) (\textbf{x_5} V \textbf{x_6} V \textbf{x_10}) (\textbf{x_5} V \textbf{x_7} V \textbf{x_8}) (\textbf{x_5} V \textbf{x_7} V \textbf{x_9}) (\textbf{x_5} V \textbf{x_7} V \textbf{x_10}) (\textbf{x_5} V \textbf{x_8} V \textbf{x_9}) (\textbf{x_5} V \textbf{x_8} V \textbf{x_10}) (\textbf{x_5} V \textbf{x_9} V \textbf{x_10}) (\textbf{x_6} V \textbf{x_7} V \textbf{x_8}) (\textbf{x_6} V \textbf{x_7} V \textbf{x_9}) (\textbf{x_6} V \textbf{x_7} V \textbf{x_10}) (\textbf{x_6} V \textbf{x_8} V \textbf{x_9}) (\textbf{x_6} V \textbf{x_8} V \textbf{x_10}) (\textbf{x_6} V \textbf{x_9} V \textbf{x_10}) (\textbf{x_7} V \textbf{x_8} V \textbf{x_9}) (\textbf{x_7} V \textbf{x_8} V \textbf{x_10}) (\textbf{x_7} V \textbf{x_9} V \textbf{x_10}) (\textbf{x_8} V \textbf{x_9} V \textbf{x_10}) \includegraphics{https://static.e-olymp.com/content/7e/7e838c0f60f64deef9d13ec9a874ce43b20530ea.jpg} У зазначеній формулі через V позначено \textit{логічне або} \textbf{(or)}, через позначено \textit{виключаєче або} (\textbf{xor}). В мовах C++ та Java ці бінарні операції позначаються "\textbf{||}" та "\textbf{^}". За заданими числами \textbf{x_1},\textbf{ x_2},\textbf{ x_3},\textbf{ x_4},\textbf{ x_5},\textbf{ x_6},\textbf{ x_7},\textbf{ x_8},\textbf{ x_9},\textbf{ x_10} слід знайти значення \textbf{f(x_1, x_2, ..., x_10)}. \InputFile Містить \textbf{10} чисел \textbf{x_1},\textbf{ x_2},\textbf{ x_3},\textbf{ x_4},\textbf{ x_5},\textbf{ x_6},\textbf{ x_7},\textbf{ x_8},\textbf{ x_9} и \textbf{x_10}. Кожне з них дорівнює \textbf{0} або \textbf{1}. \OutputFile Вивести єдине значення \textbf{f(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)}.
Ліміт часу 1 секунда
Ліміт використання пам'яті 256 MiB
Вхідні дані #1
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Вихідні дані #1
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Автор Mikhail Dvorkin, Georgiy Korneev