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.io.InputStream;

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

    static class TaskB {
        int[] P;
        int[] D;
        int[] DF;
        long[] SUM;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            P = new int[N];
            for (int i = 0; i < N; i++) {
                P[i] = in.nextInt() - 1;
            }
            D = new int[N];
            DF = new int[N + 1];
            SUM = new long[N + 1];

            for (int k = 0; k < N; k++) {
                if (P[k] >= k) {
                    add(0, P[k] - k, P[k] - k, -1);
                    add(P[k] - k + 1, N - k - 1, 1, 1);
                    add(N - k, N - 1, P[k], -1);
                } else {
                    add(0, N - k - 1, k - P[k], 1);
                    add(N - k, N - k + P[k], P[k], -1);
                    add(N - k + P[k] + 1, N - 1, 1, 1);
                }
            }

            long cur_val = 0, cur_incr = 0;
            for (int j = 0; j < N; ++j) {
                cur_val += SUM[j];
                cur_incr += DF[j];
                cur_val += cur_incr;
                SUM[j] = cur_val;
            }
            int ans = 0;
            for (int i = 0; i < N; i++) {
                if (SUM[ans] > SUM[i]) {
                    ans = i;
                }
            }

            out.println(SUM[ans] + " " + ans);

        }

        private void add(int left, int right, int b, long k) {
            if (left > right) return;

            SUM[left] += b;
            SUM[right + 1] -= b;
            SUM[right + 1] -= k * (right - left);

            DF[left + 1] += k; //
            DF[right + 1] -= k;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}

