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 <image>.

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, ... pn, 
  * k = 1: shift pn, p1, ... pn - 1, 
  * ..., 
  * k = n - 1: shift p2, p3, ... pn, 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, ..., pn (1 ≤ pi ≤ 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.
#include <bits/stdc++.h>
using namespace std;
long long mod = 1000000007LL;
long long base = 37;
long long large = 1000000000000000000LL;
long long labs(long long x) {
  if (x < 0) return -x;
  return x;
}
int main() {
  int n;
  cin >> n;
  vector<long long> p(n, 0);
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    p[i]--;
  }
  long long s = 0;
  for (int i = 0; i < n; i++) s += labs(p[i] - i);
  long long ans = s;
  vector<long long> adj;
  long long cnt = 0;
  vector<long long> eve(n + 1, 0);
  for (int i = 0; i < n; i++) {
    if (p[i] <= i) {
      cnt++;
      eve[n - i + p[i]]++;
    } else {
      eve[p[i] - i]++;
    }
  }
  int k = 0;
  for (int i = 1; i < n; i++) {
    s -= labs(p[n - i] - (n - 1));
    s += p[n - i];
    cnt--;
    s += cnt;
    s -= (1LL * (n - 1) - cnt);
    cnt += eve[i];
    if (s < ans) {
      ans = s;
      k = i;
    }
  }
  cout << ans << " " << k << endl;
  return 0;
}
