Информатика

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Дана блок-схема алгоритма. Какое целое положительное число w необходимо подать на вход, чтобы после завершения алгоритма получилось значение s ? В ответе укажите целое число. Примечание. Операция mod вычисляет остаток от деления первого аргумента на второй. Операция div вычисляет частное от целочисленного деления первого аргумента на второй.

Little Lidia likes playing with numbers. Today she has a positive integer n, and she wants to decompose it to the product of positive integers.

Because Lidia is little, she likes to play with numbers with little difference. So, all numbers in decomposition should differ by at most one. And of course, the product of all numbers in the decomposition must be equal to n. She considers two decompositions the same if and only if they have the same number of integers and there is a permutation that transforms the first one to the second one.
Write a program that finds all decompositions, which little Lidia can play with today.

Input
The only line of the input contains a single integer n (1 ≤ n ≤ 10¹⁸).

Output
In first line output the number of decompositions of n, or −1 if this number is infinite. If number of decompositions is finite, print all of them one per line. In each line first print number ki of elements in decomposition. Then print ki integers in this decomposition in any order. Don’t forget that decompositions which are different only in order of elements are considered the same.
 

Input	Output
12	3 1 12 3 2 3 2 2 4 3
1	-1

In the second example 1 can be represented as product of any number of ones.

There is an urban myth that Peter the Great wanted to make a rectangular channel-grid engineering masterpiece not only from Vasilyevskiy island, but also from Kotlin island (where the town of Kronstadt is located nowadays).

The following mathematical model was (allegedly) presented to the tsar. The island is considered a rectangular grid h cells high and w cells wide. Each cell is dry land initially but can become water.

Technologies of those days allowed engineers to dig a channel across the entire island. In that case an entire row or an entire column of cells became water. If some of these cells already were water, their status did not change.
Your task is to propose a plan of the island which has exactly n connected components of dry land cells.

Input
The only line of the input contains three integers h, w, and n — grid’s height, width and the desired number of connected components (1 ≤ h, w ≤ 100; 1 ≤ n ≤ 10⁹ )

Output
If there is no valid plan containing n connected components, output a single word “Impossible”. Otherwise output h lines of length w depicting the plan. Dot (‘.’) represents a dry land cell, hash (‘#’) represents a water cell.
 

Input	Output
3 5 4	..#.. ##### ..#..
2 1 1	# .
5 3 10	Impossible

There are two kinds of sounds in spoken languages: vowels and consonants. Vowel is a sound, produced with an open vocal tract; and consonant is pronounced in such a way that the breath is at least partly obstructed. For example, letters a and o are used to express vowel sounds, while letters b and p are the consonants (e.g. bad, pot).

Some letters can be used to express both vowel and consonant sounds: for example, y may be used as a vowel (e.g. silly) or as a consonant (e.g. yellow). The letter w, usually used as a consonant (e.g. wet) could produce a vowel after another vowel (e.g. growth) in English, and in some languages (e.g. Welsh) it could be even the only vowel in a word.
In this task, we consider y and w as vowels, so there are seven vowels in English alphabet: a, e, i, o, u, w and y, all other letters are consonants.

Let’s define the consonant fencity of a string as the number of pairs of consecutive letters in the string which both are consonants and have different cases (lowercase letter followed by uppercase or vice versa). For example, the consonant fencity of a string CoNsoNaNts is 2, the consonant fencity of a string dEsTrUcTiOn is 3 and the consonant fencity of string StRenGtH is 5.

You will be given a string consisting of lowercase English letters. Your task is to change the case of some letters in such a way that all equal letters will be of the same case (that means, no letter can occur in resulting string as both lowercase and uppercase), and the consonant fencity of resulting string is maximal.

Input
The only line of the input contains non-empty original string consisting of no more than 10⁶ lowercase English letters.

Output
Output the only line: the input string changed to have maximum consonant fencity.
 

Input	Output
consonants	CoNsoNaNts
destruction	dEsTrUcTiOn
strength	StRenGtH

Anna has just finished her course project. She has a lot of seven-segment LED displays as leftovers and a small power source. Each display consumes power proportionally to the number of lit segments, e.g. ‘9’ consumes twice more power than ‘7’.


Anna wonders what is the maximum possible sum of digits she is able to achieve, if her power source is able to light n segments, and she wants to light exactly n segments.
Input
The single line of the input contains one integer n — the number of segments that should be lit (2 ≤ n ≤ 10⁶ ).
Output
Output a single integer — the maximum possible sum of digits that can be displayed simultaneously.

Input	Output
4	4
7	11
6	14

In the first example, a single ‘4’ should be displayed (‘7’ has greater value, but has only three segments). In the second example ‘4’ and ‘7’ should be displayed, in the third one — two ‘7’s.

Дано корректное математическое выражение, состоящее из переменных, обозначаемых строчными латинскими буквами, инфиксных бинарных операций и круглых скобок для группировки подвыражений. Все операции имеют ассоциативность слева направо и приоритеты, указанные в таблице:
 

Приоритет	Операции
1 (наибольший)	*, /
2	+, -
3	&
4	^
5 (наименьший)	|

Требуется удалить из выражения все лишние пары скобок, не влияющие на порядок операций в нём (операции трактовать абстрактно, без какого-либо математического смысла, опираясь только на формальный порядок операций). Приоритет определяет, в каком порядке выполняются операции в цепочке, а ассоциативность определяет направление вычислений в цепочке операций одного приоритета.
 

Ввод	Вывод	Замечания
a+(b*c)	a+b*c	(у ‘*’ приоритет выше, чем у ‘+’, поэтому она и так выполняется первой,- скобки лишние);
((a+b)+(c+d))	a+b+(c+d)	(Скобки вокруг всего выражения допустимы, но никогда не влияют на порядок вычисления внутри. Поскольку ассоциативность всех операций слева направо, первые внутренние скобки лишние, а вторые – нет, без них выражение было бы эквивалентно (((a+b)+c)+d));
((a)+b)&c^d	a+b&c^d	(скобки вокруг переменной всегда лишние).
(((a)&b^c|((d))))	a&b^c|d
a	a

Формат входного файла:
Одна строка, содержащая исходное математическое выражение не длиннее 100 символов.
Формат выходного файла:
Одна строка с математическим выражением без лишних скобок.

Примеры

№	Входные данные	Выходные данные
1	2	11 10 01 00