819_B. Mister B and PR Shifts_36791
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.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakhar17252
 */
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);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        long[] sum = new long[1000010];
        long[] df = new long[1000010];
        long[] res = new long[1000010];
        int n;
        int[] p = new int[1000010];

        private void add(int lf, int rg, int k, int b) {
            if (lf > rg) return;
            sum[lf] += b;
            df[lf] += k;

            sum[rg + 1] -= b + (long) k * (rg - lf);
            df[rg] -= k;
        }

        private void calc() {
            long curdf = 0;
            for (int i = 0; i < n; i++) {
                sum[i] += curdf;
                curdf += df[i];
            }

            long cursm = 0;
            for (int i = 0; i < n; i++) {
                cursm += sum[i];
                res[i] += cursm;
            }
        }

        private int solver() {
            Arrays.fill(sum, 0);
            Arrays.fill(res, 0);
            Arrays.fill(df, 0);
            for (int i = 0; i < n; i++) {
                int c1 = i + 1, p1 = 0;
                int c2 = n, p2 = p1 + c2 - c1;
                int c3 = i, p3 = p2 + c3;

                if (p[i] <= c3) {
                    add(p1, p2, 1, c1 - p[i]);
                    add(p2 + 1, p2 + p[i], -1, p[i] - 1);
                    add(p2 + p[i] + 1, p3, 1, 1);
                } else {
                    add(p1, p1 + p[i] - c1, -1, p[i] - c1);
                    add(p1 + p[i] - c1 + 1, p2, 1, 1);
                    add(p2 + 1, p3, -1, p[i] - 1);
                }
            }

            calc();

            int ans = 0;
            for (int i = 0; i < n; i++) {
                if (res[ans] > res[i]) ans = i;
            }
            return ans;

        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {

            n = in.nextInt();

            for (int i = 0; i < n; i++) {
                p[i] = in.nextInt();
            }
            int ans = solver();
            out.println(res[ans] + " " + ans);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}


3
1 2 3
 3
3 2 1
 3
2 3 1
 10
2 5 10 3 6 4 9 1 8 7
 108
1 102 33 99 6 83 4 20 61 100 76 71 44 9 24 87 57 2 81 82 90 85 12 30 66 53 47 36 43 29 31 64 96 84 77 23 93 78 58 68 42 55 13 70 62 19 92 14 10 65 63 75 91 48 11 105 37 50 32 94 18 26 52 89 104 106 86 97 80 95 17 72 40 22 79 103 25 101 35 51 15 98 67 5 34 69 54 27 45 88 56 16 46 60 74 108 21 41 73 39 107 59 3 8 28 49 7 38
 4
4 2 1 3
 10
10 1 9 2 8 3 7 4 6 5
 10
2 7 10 1 6 3 4 8 9 5
 10
1 2 3 4 6 5 7 9 10 8
 4
4 2 3 1
 4
3 1 4 2
 10
2 3 10 5 4 8 6 9 7 1
 10
1 2 10 9 7 4 8 3 6 5
 4
1 3 4 2
 4
3 1 2 4
 10
2 1 10 5 8 4 9 3 7 6
 4
3 4 1 2
 10
1 8 10 6 2 4 9 3 7 5
 4
4 1 3 2
 10
1 6 10 7 9 5 3 8 4 2
 10
2 4 10 3 9 1 5 7 8 6
 4
2 4 3 1
 4
2 3 1 4
 4
3 4 2 1
 10
1 7 10 6 5 2 3 8 9 4
 10
1 5 10 8 4 3 9 2 7 6
 4
3 2 4 1
 10
2 6 10 1 9 7 4 8 5 3
 4
2 3 4 1
 4
3 2 1 4
 2
1 2
 10
1 3 10 9 4 7 5 8 6 2
 4
4 3 1 2
 10
1 9 10 5 6 7 3 8 4 2
 2
2 1
 4
1 4 3 2
 4
2 1 4 3
 4
1 3 2 4
 4
4 1 2 3
 4
1 4 2 3
 10
1 10 9 5 3 2 4 7 8 6
 4
1 2 3 4
 10
1 4 10 8 9 2 3 6 7 5
 4
4 3 2 1
 4
2 1 3 4
 4
1 2 4 3
 4
2 4 1 3
 10
1 5 10 9 4 3 9 2 7 6
 4
3 2 4 2
 4
3 2 2 4
 4
1 2 4 1
 10
1 7 10 10 5 2 3 8 9 4
 4
1 3 3 4
 10
1 4 10 8 9 2 3 6 7 9
 4
4 3 1 3
 10
1 2 5 4 6 5 7 9 10 8
 10
2 4 10 6 9 1 5 7 8 6
 4
1 4 4 2
 4
1 4 2 4
 3
1 3 3

0 0
 2 1
 0 1
 28 0
 3428 30
 2 3
 24 7
 20 7
 6 0
 4 1
 4 1
 14 1
 26 5
 2 1
 2 3
 28 0
 0 2
 24 6
 2 3
 24 4
 28 0
 2 1
 4 0
 2 2
 26 6
 26 6
 2 1
 28 1
 0 1
 4 0
 0 0
 22 1
 2 2
 26 1
 0 1
 4 0
 4 0
 2 0
 0 3
 4 0
 20 7
 0 0
 20 5
 4 1
 2 0
 2 0
 2 2
 25 6
 3 1
 3 0
 2 1
 22 6
 1 0
 24 5
 3 2
 8 0
 25 5
 3 1
 3 0
 1 0
