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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 |