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Byteasar loved to play with building blocks as a child. He used to arrange the blocks into columns of random height and then organize them in the following manner: Byteasar would choose a number and try to arrange the blocks in such a way that some consecutive columns would be of equal height. Furthermore he always tried to achieve this goal in a minimum number of moves possible, where a single move consists in:
However, Byteasar was never quite sure if his sequence of moves was indeed optimal, therefore he has asked you to write a programme that will help him solve the problem.
Write a programme that:
In the first line of the standard input there are two integers, and (), separated by a single space. Each of the following lines contains the height of some column; the line no. contains the integer - the height of the column, ie. the number of blocks it consists of.
The optimal solution should be written out to the standard output, ie. such arrangement of blocks that:
For the input data:
5 3 3 9 2 3 1
the correct result is:
2 3 9 2 2 2
Task author: Tomasz Walen.