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 + 10;
int p[maxn], n;
struct Node {
  int i, v;
  Node(int pi = 0, int pv = 0) {
    i = pi;
    v = pv;
  }
  bool operator<(Node a) const { return v < a.v || (v == a.v && i < a.i); }
};
priority_queue<int, vector<int>, greater<int> > q;
int pointer;
int s1size;
long long cur, bestv, bestk;
int main() {
  scanf("%d", &n);
  bestk = cur = 0;
  s1size = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", p + i);
    cur += abs(p[i] - i);
    if (p[i] <= i)
      s1size++;
    else
      q.push(p[i] - i);
  }
  bestv = cur;
  pointer = n;
  for (int k = 1; k < n; k++) {
    s1size--;
    cur += p[pointer] - 1LL - (n - p[pointer]);
    cur += s1size - 0LL - q.size();
    q.push(k + p[pointer] - 1);
    if (!--pointer) pointer = n;
    for (int d = q.top(); q.size() && d == k; d = q.top()) {
      q.pop();
      s1size++;
    }
    if (cur < bestv) {
      bestk = k;
      bestv = cur;
    }
  }
  printf("%I64d %d\n", bestv, bestk);
}
