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 \le k \lt 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 \le n \le 106) - the length of the permutation.

The second line contains n space-separated integers p1,p2,...,pn (1 \le pi \le 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.

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.