Migrated from Lutece 1037 Destroy room

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Description

There are $n$ room number from $1$ to $n$, and there are at most $7$ people in each room. Dave, a leader of all the people, think there is no need using all of those room. so he ask people gathering to some rooms, and destory others.

But he all is a superstitious man. He want the number of people in one room is $4$ or $7$.

It will cost need $|i-j|$ seconds when a person for room $i$ go to room $j$, Dave want to know how to arrange it so people will cost as little as possible.

Input

First has one element $n$.

Second line has $n$ numbers, indicate the number of people in $i_{th}$ room.

$n \leq 100000$

Output

If there is a way to arrang it, output the tot time people gone cost.

If there is no way to make it match the condition,output -1.

Samples

5
2 3 1 0 6

7

2
3 2

-1

Resources

The 13th UESTC Programming Contest Preliminary