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 Main {
    class Reader {
        BufferedReader in;

        Reader() throws IOException {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        Reader(String name) throws IOException {
            in = new BufferedReader(new FileReader(name));
        }

        StringTokenizer tokin = new StringTokenizer("");

        String next() throws IOException {
            if (!tokin.hasMoreTokens())
                tokin = new StringTokenizer(in.readLine());
            return tokin.nextToken();
        }

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

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }

    long MOD(long a) {
        if (a < 0)
            a = -a;
        return a;
    }

    void slave() throws IOException {
        Reader in = new Reader();
        int n = in.nextInt();
        long arr[] = new long[n];
        long d[] = new long[n];
        long c[] = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
        }
        for (int i = 0; i < n; i++) {
            long a = arr[i];
            if (n - i < n)
                c[n - i] += MOD(a - 1) - MOD(a - n);
            if (a - i - 1 > -1)
                d[(int) (a - i - 1)] += 2;
            else
                d[(int) (n + a - i - 1)] += 2;
            if (n - i < n)
                d[n - i] += -2;
        }
        long sum1 = 0;
        long sum2 = 0;
        for (int i = 0; i < n; i++) {
            sum1 += MOD(arr[i] - i - 1);
        }
        for (int i = 0; i < n - 1; i++) {
            sum2 += MOD(arr[i] - i - 2);
        }
        sum2 += MOD(arr[n - 1] - 1);
        d[0] = sum2 - sum1 - c[1];
        long min = sum1;
        long mink = 0;
        long cur = sum1;
        long de = d[0];
        //System.out.println(sum1);
        for (int k = 1; k < n; k++) {
            cur += c[k] + de;
            de += d[k];
            if (cur < min) {
                min = cur;
                mink = k;
            }
            //System.out.println(cur);
        }
        System.out.print(min + " " + mink);
    }

    public static void main(String args[]) throws IOException {
        new Main().slave();
    }
}
