A11007 | 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.