CF819B.Mister B and PR Shifts

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 $p_{2},p_{3},...\ p_{n},p_{1}$ .

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.

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.