#include <bits/stdc++.h>
using namespace std;
const int MAX = 1000005;
long long res[MAX], a[MAX], b[MAX];
void add(int l, int r, int x, int y) {
  a[l] += x;
  a[r] -= x + y * (r - l);
  b[l] += y;
  b[r] -= y;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  for (int from = 0; from < n; from++) {
    int to;
    cin >> to;
    to--;
    if (from <= to) {
      add(0, to - from + 1, to - from, -1);
      add(to - from + 1, n - from, 1, 1);
      add(n - from, n, to, -1);
    } else {
      add(0, n - from, from - to, 1);
      add(n - from, n - from + to + 1, to, -1);
      add(n - from + to + 1, n, 1, 1);
    }
  }
  long long val = 0, step = 0;
  for (int i = 0; i < n; i++) {
    val += a[i];
    step += b[i];
    res[i] = val;
    val += step;
  }
  int mn = min_element(res, res + n) - res;
  cout << res[mn] << " " << mn << "\n";
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 = 1000005;
long long res[MAX], a[MAX], b[MAX];
void add(int l, int r, int x, int y) {
  a[l] += x;
  a[r] -= x + y * (r - l);
  b[l] += y;
  b[r] -= y;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  for (int from = 0; from < n; from++) {
    int to;
    cin >> to;
    to--;
    if (from <= to) {
      add(0, to - from + 1, to - from, -1);
      add(to - from + 1, n - from, 1, 1);
      add(n - from, n, to, -1);
    } else {
      add(0, n - from, from - to, 1);
      add(n - from, n - from + to + 1, to, -1);
      add(n - from + to + 1, n, 1, 1);
    }
  }
  long long val = 0, step = 0;
  for (int i = 0; i < n; i++) {
    val += a[i];
    step += b[i];
    res[i] = val;
    val += step;
  }
  int mn = min_element(res, res + n) - res;
  cout << res[mn] << " " << mn << "\n";
  return 0;
}

```