Задачи
Явная формула
Явная формула
Рассмотрим \textbf{10} булевых переменных \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}. Рассмотрим все возможные пары и тройки разных переменных из этих десяти (всего существует \textbf{45} пар и \textbf{120} троек). Вычислите количество пар и троек, у которых хотя бы одна переменная установлена в \textbf{1}. Установим \textbf{f(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)} = \textbf{1} если это количество нечетно и \textbf{f(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)} = \textbf{0} если количество четно.
Рассмотрим явную формулу, которая реализует функцию \textbf{f(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)}:
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\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})
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В указанной формуле через V обозначено \textit{логическое или} \textbf{(or)}, через обозначено \textit{исключающее или} (\textbf{xor}). В языках C++ и Java эти бинарные операции обозначаются "\textbf{||}" и "\textbf{^}".
По заданным числам \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} следует найти значение \textbf{f(x_1, x_2, ..., x_10)}.
\InputFile
Содержит \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}. Каждое из них равно \textbf{0} или \textbf{1}.
\OutputFile
Вывести единственное значение \textbf{f(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)}.
Входные данные #1
1 0 0 1 0 0 1 0 0 1
Выходные данные #1
0