Polycarp likes arithmetic progressions. A sequence [a1,a2,…,an]
are not.
It follows from the definition that any sequence of length one or two is an arithmetic progression.
Polycarp found some sequence of positive integers [b1,b2,…,bn]
. He agrees to change each element by at most one. In the other words, for each element there are exactly three options: an element can be decreased by 1, an element can be increased by 1, an element can be left unchanged.
Determine a minimum possible number of elements in b
which can be changed (by exactly one), so that the sequence bbecomes an arithmetic progression, or report that it is impossible.
It is possible that the resulting sequence contains element equals 0
.
The first line contains a single integer n
.
The second line contains a sequence b1,b2,…,bn
(1≤bi≤109).
If it is impossible to make an arithmetic progression with described operations, print -1. In the other case, print non-negative integer — the minimum number of elements to change to make the given sequence becomes an arithmetic progression. The only allowed operation is to add/to subtract one from an element (can't use operation twice to the same position).
4 24 21 14 10
3
2 500 500
0
3 14 5 1
-1
5 1 3 6 9 12
1
In the first example Polycarp should increase the first number on 1
, which is an arithmetic progression.
In the second example Polycarp should not change anything, because his sequence is an arithmetic progression.
In the third example it is impossible to make an arithmetic progression.
In the fourth example Polycarp should change only the first element, he should decrease it on one. After that his sequence will looks like [0,3,6,9,12]