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.
import java.io.*;
import java.util.*;

public class CF819B {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine());
		int[] pp = new int[n];
		for (int i = 0; i < n; i++)
			pp[i] = Integer.parseInt(st.nextToken()) - 1;
		long sum = 0;
		int inc = 0;
		int[] zz = new int[n];
		for (int i = 0; i < n; i++)
			if (pp[i] > i) {
				int d = pp[i] - i;
				sum += d;
				zz[n - d]++;
				inc++;
			} else if (pp[i] < i) {
				int d = i - pp[i];
				sum += d;
				zz[d]++;
			} else
				zz[0]++;
		long min = Long.MAX_VALUE;
		int i_ = -1;
		for (int i = 0; i < n; i++) {	// left-shift pp[i] to index 0
			if (min > sum) {
				min = sum;
				i_ = i;
			}
			inc--;
			sum -= pp[i];
			sum += n - 1 - pp[i];
			inc += zz[i];
			sum += inc;
			sum -= n - 1 - inc;
		}
		System.out.println(min + " " + (i_ == 0 ? 0 : n - i_));
	}
}
