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10057
A mid-summer night’s dream
This is year 2200AD. Science has progressed a lot in two hundred years. Two hundred years is mentioned
here because this problem is being sent back to 2000AD with the help of time machine. Now it is possible
to establish direct connection between man and computer CPU. People can watch other peoples dream
on 3D displayer (That is the monitor today) as if they were watching a movie.
One problem in
this century is that people have become so dependent on computers that their analytical ability is
approaching zero. Computers can now read problems and solve them automatically. But they can solve
only difficult problems. There are no easy problems now. Our chief scientist is in great trouble as he
has forgotten the number of his combination lock. For security reasons computers today cannot solve
combination lock related problems. In a mid-summer night the scientist has a dream where he sees a
lot of unsigned integer numbers flying around. He records them with the help of his computer, Then
he has a clue that if the numbers are (X1, X2, …, Xn) he will have to find an integer number A (This
A is the combination lock code) such that
(|X1 −A| + |X2 −A| + . . . + |Xn −A|)
is minimum.
Input
Input will contain several blocks. Each block will start with a number n (0 < n ≤1000000) indicating
how many numbers he saw in the dream. Next there will be n numbers. All the numbers will be less
that 65536. The input will be terminated by end of file.
Output
For each set of input there will be one line of output. That line will contain the minimum possible
value for A. Next it will contain how many numbers are there in the input that satisfy the property
of A (The summation of absolute deviation from A is minimum). And finally you have to print how
many possible different integer values are there for A (these values need not be present in the input).
These numbers will be separated by single space.
Sample Input
2
10
10
4
1
2
2
4
Sample Output
10 2 1
2 2 1