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;
const int maxN = 1e6 + 9, maxV = 20, MOD = 1e9 + 7, LG = 11, BASE = 29;
int n, arr[maxN];
long long dp[maxN];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    arr[i]--;
  }
  priority_queue<int, vector<int>, greater<int>> pq;
  long long rela = n, tot = 0, investors = 0;
  for (int i = 0; i < n; i++) {
    if (i - arr[i] <= 0) {
      investors++;
    } else {
      pq.push(i - arr[i] + (int)rela);
    }
    tot += abs(i - arr[i]);
  }
  dp[0] = tot;
  int ans = 0;
  for (int i = 1; i < n; i++) {
    rela++;
    investors--;
    dp[i] = dp[i - 1] + investors - pq.size() - arr[i - 1];
    while (pq.size() && pq.top() == rela) {
      investors++;
      pq.pop();
    }
    if (arr[i - 1] < n - 1) {
      dp[i] += n - 1 - arr[i - 1];
      pq.push(n - 1 - arr[i - 1] + (int)rela);
    } else
      investors++;
    if (dp[ans] > dp[i]) ans = i;
  }
  cout << dp[ans] << ' ' << (n - ans) % n << '\n';
}
