#include <bits/stdc++.h>
using namespace std;
inline int read() {
  char ch = getchar();
  int x = 0, f = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while ('0' <= ch && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int b[2000010], a[2000010];
int main() {
  int n = read();
  long long res = 0, ans = 0, ans1 = 0;
  int change = 0;
  for (int i = (1); i <= (n); i++) a[i] = read();
  for (int i = (1); i <= (n); i++) {
    if (a[i] >= i) {
      res += a[i] - i;
      change--;
      b[a[i] - i]++;
    } else {
      res += i - a[i];
      change++;
      b[a[i] - i + n]++;
    }
  }
  ans = res;
  for (int i = (1); i <= (n - 1); i++) {
    change += b[i - 1];
    change += b[i - 1];
    res += abs(a[n - i + 1] - 1) - abs(a[n - i + 1] - n) + 1;
    change -= 2;
    res += change;
    if (res < ans) ans = res, ans1 = i;
  }
  cout << ans << " " << ans1 << endl;
  return 0;
}

### Prompt

In cpp, your task is to solve 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;
inline int read() {
  char ch = getchar();
  int x = 0, f = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while ('0' <= ch && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int b[2000010], a[2000010];
int main() {
  int n = read();
  long long res = 0, ans = 0, ans1 = 0;
  int change = 0;
  for (int i = (1); i <= (n); i++) a[i] = read();
  for (int i = (1); i <= (n); i++) {
    if (a[i] >= i) {
      res += a[i] - i;
      change--;
      b[a[i] - i]++;
    } else {
      res += i - a[i];
      change++;
      b[a[i] - i + n]++;
    }
  }
  ans = res;
  for (int i = (1); i <= (n - 1); i++) {
    change += b[i - 1];
    change += b[i - 1];
    res += abs(a[n - i + 1] - 1) - abs(a[n - i + 1] - n) + 1;
    change -= 2;
    res += change;
    if (res < ans) ans = res, ans1 = i;
  }
  cout << ans << " " << ans1 << endl;
  return 0;
}

```