#include <bits/stdc++.h>
using namespace std;
const int MAX_SIZE = 1e6 + 10;
long long arr[MAX_SIZE];
long long prefix[MAX_SIZE];
long long coeff[MAX_SIZE];
void add(int l, int r, long long A, long long k) {
  prefix[l] += A;
  prefix[r + 1] -= k * 1L * (r - l) + A;
  coeff[l + 1] += k;
  coeff[r + 1] -= k;
}
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  memset(prefix, 0, sizeof(prefix));
  memset(coeff, 0, sizeof(coeff));
  for (int i = 0; i < n; i++) {
    if (arr[i] >= (i + 1)) {
      add(0, arr[i] - (i + 1), arr[i] - (i + 1), -1);
      add(arr[i] - i, n - (i + 1), 1, 1);
      add(n - i, n - 1, arr[i] - 1, -1);
    } else {
      add(0, n - (i + 1), (i + 1) - arr[i], 1);
      add(n - i, n - (i + 1) + arr[i], arr[i] - 1, -1);
      add(n - i + arr[i], n - 1, 1, 1);
    }
  }
  prefix[0] += coeff[0];
  for (int i = 1; i < n; i++) {
    coeff[i] += coeff[i - 1];
    prefix[i] += coeff[i];
  }
  for (int i = 1; i < n; i++) {
    prefix[i] += prefix[i - 1];
  }
  long long res = 1e12;
  long long index = n;
  for (int i = 0; i < n; i++) {
    if (prefix[i] < res) {
      index = i;
      res = prefix[i];
    }
  }
  cout << res << " " << index << endl;
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAX_SIZE = 1e6 + 10;
long long arr[MAX_SIZE];
long long prefix[MAX_SIZE];
long long coeff[MAX_SIZE];
void add(int l, int r, long long A, long long k) {
  prefix[l] += A;
  prefix[r + 1] -= k * 1L * (r - l) + A;
  coeff[l + 1] += k;
  coeff[r + 1] -= k;
}
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  memset(prefix, 0, sizeof(prefix));
  memset(coeff, 0, sizeof(coeff));
  for (int i = 0; i < n; i++) {
    if (arr[i] >= (i + 1)) {
      add(0, arr[i] - (i + 1), arr[i] - (i + 1), -1);
      add(arr[i] - i, n - (i + 1), 1, 1);
      add(n - i, n - 1, arr[i] - 1, -1);
    } else {
      add(0, n - (i + 1), (i + 1) - arr[i], 1);
      add(n - i, n - (i + 1) + arr[i], arr[i] - 1, -1);
      add(n - i + arr[i], n - 1, 1, 1);
    }
  }
  prefix[0] += coeff[0];
  for (int i = 1; i < n; i++) {
    coeff[i] += coeff[i - 1];
    prefix[i] += coeff[i];
  }
  for (int i = 1; i < n; i++) {
    prefix[i] += prefix[i - 1];
  }
  long long res = 1e12;
  long long index = n;
  for (int i = 0; i < n; i++) {
    if (prefix[i] < res) {
      index = i;
      res = prefix[i];
    }
  }
  cout << res << " " << index << endl;
  return 0;
}

```