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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

/*
 public class _823D {

 }

 */

public class _823D
{
	public void solve() throws FileNotFoundException
	{
		InputStream inputStream = System.in;

		InputHelper inputHelper = new InputHelper(inputStream);

		PrintStream out = System.out;

		// actual solution
		int n = inputHelper.readInteger();

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

		long[] s = new long[n + 1];

		long[] d = new long[n + 1];

		for (int i = 1; i <= n; i++)
		{
			p[i] = inputHelper.readInteger();
		}

		for (int i = 1; i <= n; i++)
		{
			if (p[i] >= i)
			{
				ap(0, p[i] - i, -1, p[i] - i + 1, s, d);
				ap(p[i] - i + 1, 1, 1, n - p[i], s, d);
				ap(n - i + 1, p[i] - 1, -1, i - 1, s, d);
			}
			else if (p[i] < i)
			{
				ap(0, i - p[i], 1, n - i + 1, s, d);
				ap(n - i + 1, p[i] - 1, -1, p[i], s, d);
				ap(n - i + 1 + p[i], 1, 1, i - 1 - p[i], s, d);
			}
		}

		long rk = d[0];

		long ans = 0;

		long min = s[0];

		for (int i = 1; i < n; i++)
		{
			s[i] += (s[i - 1] + rk);

			if (min > s[i])
			{
				min = s[i];
				ans = i;
			}
			rk += d[i];
		}

		System.out.println(min + " " + ans);
		// end here
	}

	void ap(int ind, long a, long k, int l, long[] s, long[] d)
	{
		s[ind] += a;
		d[ind] += k;

		s[ind + l] -= (a + (l - 1) * k);
		d[ind + l - 1] -= k;
	}

	public static void main(String[] args) throws FileNotFoundException
	{
		(new _823D()).solve();
	}

	class InputHelper
	{
		StringTokenizer tokenizer = null;
		private BufferedReader bufferedReader;

		public InputHelper(InputStream inputStream)
		{
			InputStreamReader inputStreamReader = new InputStreamReader(
					inputStream);
			bufferedReader = new BufferedReader(inputStreamReader, 16384);
		}

		public String read()
		{
			while (tokenizer == null || !tokenizer.hasMoreTokens())
			{
				try
				{
					String line = bufferedReader.readLine();
					if (line == null)
					{
						return null;
					}
					tokenizer = new StringTokenizer(line);
				}
				catch (IOException e)
				{
					e.printStackTrace();
				}
			}

			return tokenizer.nextToken();
		}

		public Integer readInteger()
		{
			return Integer.parseInt(read());
		}

		public Long readLong()
		{
			return Long.parseLong(read());
		}
	}
}