A12291. 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.