Solve in Python:
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 $\sum_{i = 1}^{i = n}|p [ i ] - i|$.

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.


-----Examples-----
Input
3
1 2 3

Output
0 0

Input
3
2 3 1

Output
0 1

Input
3
3 2 1

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.
n = int(input())
a = list(map(int, input().split()))
t = [0] * 2 * n
s = 0
for i in range(n):
    d = a[i] - i - 1
    s += abs(d)
    if d > 0: t[d] += 1
p = sum(t)
r = (s, 0)
for i in range(1, n):
    d = a[n - i] - 1
    s += d - p << 1
    t[d + i] += d > 0
    p += (d > 0) - t[i]
    if s < r[0]: r = (s, i)
print(*r)