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 = 1000000;
int countDiff[MAXN * 3];
int nums[MAXN];
int nNums;
int shifts;
long long minDiff;
long long diffs[MAXN];
int countNegative;
void handleShift(int n) {
  int ind = nNums - n;
  int former = nums[ind] - nNums;
  int latter = nums[ind];
  countDiff[nums[ind] + nNums - ind - 2]--;
  countDiff[nums[ind] + nNums - ind - 2 + nNums]++;
  long long currResult = diffs[n - 1];
  currResult += abs(latter) - abs(former);
  if (former < 0) {
    countNegative--;
  }
  countNegative += countDiff[nNums - 2 + n];
  currResult += countNegative;
  currResult -= (nNums - countNegative);
  diffs[n] = currResult;
  if (diffs[n] < minDiff) {
    minDiff = diffs[n];
    shifts = n;
  }
}
int main() {
  scanf("%d", &nNums);
  for (int i = 0; i < nNums; i++) {
    scanf("%d", nums + i);
    int diff = nums[i] - (i + 1);
    minDiff += abs(diff);
    countDiff[diff + (nNums - 1)]++;
    if (diff < 0) {
      countNegative++;
    }
  }
  diffs[0] = minDiff;
  for (int i = 1; i < nNums; i++) {
    handleShift(i);
  }
  cout << minDiff << ' ' << shifts << endl;
  return 0;
}
