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 $*p*_{1}, *p*_{2}, ... *p*_{*n*}$,
• $*k* = 1$: shift $*p*_{*n*}, *p*_{1}, ... *p*_{*n* - 1}$,
• ...,
• $*k* = *n* - 1$: shift $*p*_{2}, *p*_{3}, ... *p*_{*n*}, *p*_{1}$.

Input

First line contains single integer $*n*$ ($2 ≤ *n* ≤ 10^{6}$) — the length of the permutation.

The second line contains $*n*$ space-separated integers $*p*_{1}, *p*_{2}, ..., *p*_{*n*}$ ($1 ≤ *p*_{*i*} ≤ *n*$) — 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.

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.