CF1105A Salem and Sticks

Salem gave you $ n $ sticks with integer positive lengths $ a_1, a_2, \ldots, a_n $ . For every stick, you can change its length to any other positive integer length (that is, either shrink or stretch it). The cost of changing the stick's length from $ a $ to $ b $ is $ |a - b| $ , where $ |x| $ means the absolute value of $ x $ . A stick length $ a_i $ is called almost good for some integer $ t $ if $ |a_i - t| \le 1 $ . Salem asks you to change the lengths of some sticks (possibly all or none), such that all sticks' lengths are almost good for some positive integer $ t $ and the total cost of changing is minimum possible. The value of $ t $ is not fixed in advance and you can choose it as any positive integer. As an answer, print the value of $ t $ and the minimum cost. If there are multiple optimal choices for $ t $ , print any of them.

The first line contains a single integer $ n $ ( $ 1 \le n \le 1000 $ ) — the number of sticks. The second line contains $ n $ integers $ a_i $ ( $ 1 \le a_i \le 100 $ ) — the lengths of the sticks.

Print the value of $ t $ and the minimum possible cost. If there are multiple optimal choices for $ t $ , print any of them.

In the first example, we can change $ 1 $ into $ 2 $ and $ 10 $ into $ 4 $ with cost $ |1 - 2| + |10 - 4| = 1 + 6 = 7 $ and the resulting lengths $ [2, 4, 4] $ are almost good for $ t = 3 $ . In the second example, the sticks lengths are already almost good for $ t = 2 $ , so we don't have to do anything.