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.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author OmarYasser
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(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, Scanner sc, PrintWriter out) {
            int n = sc.nextInt();
            int MAX = (int) 1e6 + n + 1234;

            long[] cum = new long[MAX];
            long[] instant = new long[MAX];
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt() - 1;
                if (i > a[i]) {
                    int distToN = n - i - 1;
                    if (distToN != 0) {
                        cum[1]++;
                        cum[distToN + 1]--;
                    }
                    if (a[i] != 0)
                        cum[n - i + a[i] + 1] += 2;
                } else if (i < a[i]) {
                    int distToNum = a[i] - i;
                    cum[1]--;
                    cum[distToNum + 1]++;
                    if (a[i] != n - 1) {
                        cum[distToNum + 1]++;
                        cum[n - i]--;
                    }
                } else {
                    if (i != n - 1) {
                        cum[1]++;
                        cum[n - i]--;

                    }
                }
                instant[n - i] += (a[i] - Math.abs(a[i] - (n - 1)));
                if (a[i] == 0) {
                    cum[n - i + 1] += 1;
                } else {
                    cum[n - i + 1] -= 1;
                }
            }

            for (int i = 1; i < cum.length; i++) {
                cum[i] = cum[i] + cum[i - 1];
            }
            long best = 0, cycle = 0;
            for (int i = 0; i < n; i++)
                best += Math.abs(a[i] - i);


            long bestOfBest = best;
            for (int i = 1; i < n; i++) {
                long here = best + cum[i] + instant[i];
                if (here < bestOfBest) {
                    bestOfBest = here;
                    cycle = i;
                }
                best = here;
            }
            out.println(bestOfBest + " " + cycle);
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader f) {
            br = new BufferedReader(f);
        }

        public String next() {
            while (st == null || !st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                }
            return st.nextToken();
        }

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

    }
}

