1585: Mister B and PR Shifts
Description
Some time ago Mister B detected a strange signal from the space, which he started to study.
After some transformation the signal turned out to be a permutation p of length n or its cyclic shift. For the further investigation Mister B need some basis, that's why he decided to choose cyclic shift of this permutation which has the minimum possible deviation.
Let's define the deviation of a permutation p as 
.
Find a cyclic shift of permutation p with minimum possible deviation. If there are multiple solutions, print any of them.
Let's denote id k (0≤k<n) of a cyclic shift of permutation p as the number of right shifts needed to reach this shift, for example:
- k=0: shift p1,p2,... pn,
- k=1: shift pn,p1,... pn-1,
- ...,
- k=n-1: shift p2,p3,... pn,p1.
First line contains single integer n (2≤n≤106) − the length of the permutation.
The second line contains n space-separated integers p1,p2,...,pn (1≤pi≤n)− the elements of the permutation. It is guaranteed that all elements are distinct.
Print two integers: the minimum deviation of cyclic shifts of permutation p and the id of such shift. If there are multiple solutions, print any of them.
3
1 2 3
0 0
3
2 3 1
0 1
3
3 2 1
2 1
In the first sample test the given permutation p is the identity permutation, that's why its deviation equals to 0, the shift id equals to 0 as well.
In the second sample test the deviation of p equals to 4, the deviation of the 1-st cyclic shift (1,2,3) equals to 0, the deviation of the 2-nd cyclic shift (3,1,2) equals to 4, the optimal is the 1-st cyclic shift.
In the third sample test the deviation of p equals to 4, the deviation of the 1-st cyclic shift (1,3,2) equals to 2, the deviation of the 2-nd cyclic shift (2,1,3) also equals to 2, so the optimal are both 1-st and 2-nd cyclic shifts.