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.*;
import java.math.*;

public class B {
	public static void main(String[] args) throws IOException {

		/**/
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		/*/
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(new FileInputStream("src/b.in"))));
		/**/
		
		int n = sc.nextInt();
		int[] p = new int[n];
		sc.nextLine();
		String[] sp = sc.nextLine().split(" ");
		for (int i = 0; i < n; i++) {
			p[i] = Integer.parseInt(sp[i])-1;
		}
		int[] left = new int[n*2+1];
		int rsize = 0;
		long currnum = 0;
		int ans = 0;
		long num = 0;
		for (int i = 0; i < n; i++) {
			if (p[i]>=i)
				left[p[i]-i]++;
			else
				rsize++;
			currnum += Math.abs(p[i]-i);
			num += Math.abs(p[i]-i);
		}
		//System.out.println(0+" "+currnum);
		for (int i = 1; i < n; i++) {
			rsize += left[i-1];
			int index = n-i;
			currnum -= n-1-p[index];
			currnum += p[index];
			left[p[index]-index+n]++;
			rsize--;
			currnum += rsize;
			currnum -= n-rsize-1;
			if (currnum < num) {
				num = currnum;
				ans = i;
			}
			//System.out.println(i+" "+currnum);
		}
		System.out.println(num+" "+ans);
	}
}