HearthStone

Alice loves playing HearthStone! She loves the hero class of Warlock, who can cast the spell named Defile.

When cast, Defile deals $1$ unit of damage to the health of all minions. If any minion dies, Defile will be cast again automatically. Importantly, if two or more minions die simultaneously, it still causes a single Defile cast. That, in turn, may kill other minions, causing Defile to be cast again, and so on.

The health of each minion is a nonnegative integer. A minion dies when their health becomes zero. If a minion dies, it will disappear. It will not die twice.

Now there are $n$ minions. Before casting Defile, Alice can make zero or more steps. In each step, Alice changes a single minion's health by one. That is to say, if the health of a minion is $x$, Alice can change it to $x-1$ or $x+1$.

Alice wants to know the minimum number of steps such that, after these steps, she can cast a single Defile to kill all the minions.

The first line contains a single integer $n$ ($1 \leq n \leq 10^6$).

The next line contains $n$ integers $a\_1, a\_2, \ldots, a\_n$ ($1 \leq a\_i \leq 10^6$), the health of the $n$ minions.

Print one integer: the minimum number of steps before Alice can cast a single Defile to kill all the minions.