B"Polycarp likes arithmetic progressions. A sequence [a_1, a_2, ... , a_n] is called an arithmetic progression if for each i ( 1 <= i < n ) the value a_{i+1} - a_i is the same. For example, the sequences [42] , [5, 5, 5] , [2, 11, 20, 29] and [3, 2, 1, 0] are arithmetic progressions, but [1, 0, 1] , [1, 3, 9] and [2, 3, 1] 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 [b_1, b_2, ... , b_n] . 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 b becomes 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 (1 <= n <= 100 ,000) -- the number of elements in b . The second line contains a sequence b_1, b_2, ... , b_n (1 <= b_i <= 10^{9}) . 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). In the first example Polycarp should increase the first number on 1 , decrease the second number on 1 , increase the third number on 1 , and the fourth number should left unchanged. So, after Polycarp changed three elements by one, his sequence became equals to [25, 20, 15, 10] , which is an arithmetic progression. I"...