Mister B and PR Shifts

2000ms

262144K

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 $\text{[math]}$ .

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, ... p_n,
k = 1: shift p_n, p₁, ... p_n - 1,
...,
k = n - 1: shift p₂, p₃, ... p_n, p₁.

Input:

First line contains single integer n (2 ≤ n ≤ 10⁶) — the length of the permutation.

The second line contains n space-separated integers p₁, p₂, ..., p_n (1 ≤ p_i ≤ n) — the elements of the permutation. It is guaranteed that all elements are distinct.

Output:

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.

Sample Input:

3
1 2 3

Sample Output:

0 0

Sample Input:

3
2 3 1

Sample Output:

0 1

Sample Input:

3
3 2 1

Sample Output:

2 1

Note:

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.

Informação

Provedor Codeforces

Código CF819B