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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author vikas.k
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();

            int[] a = new int[n + 1];

            int cntNegative = 0;
            int cntPositive = 0;

            ArrayList<Integer>[] positive = new ArrayList[n + 1];
            for (int i = 0; i <= n; i++) {
                positive[i] = new ArrayList<>();
            }

            long diff = 0;
            for (int i = 1; i <= n; i++) {
                a[i] = in.nextInt();

                if (a[i] > i) {
                    cntPositive++;
                    positive[a[i] - i].add(a[i]);
                } else {
                    cntNegative++;
                }
                diff += Math.abs(a[i] - i);
            }

            long mn = diff;
            int id = 0;

            for (int i = 1; i < n; i++) {
                int j = n - i + 1;
//            out.print(j+" "+diff+" ");
                diff = diff - Math.abs(a[j] - n) + a[j];
//            out.println(diff);
                cntPositive++;
                cntNegative--;
                if (i + a[j] - 1 < n) positive[i + a[j] - 1].add(a[j]);

                diff = diff + cntNegative - cntPositive;

//            out.println(diff +" "+ cntNegative +" "+ cntPositive);
//            out.println(positive[i]);
//            out.println();

                for (Integer e : positive[i]) {
                    cntPositive--;
                    cntNegative++;
                }

                if (diff < mn) {
                    mn = diff;
                    id = i;
                }
            }

            out.println(mn + " " + id);

        }

    }

    static class FastScanner {
        private BufferedReader bufferedReader;
        private StringTokenizer stringTokenizer;

        public FastScanner(InputStream inputStream) {
            bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String next() {
            if (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

