Limak is a little bear who loves to play. Today he is playing by destroying block towers. He built n towers in a row. The i-th tower is made of hi identical blocks. For clarification see picture for the first sample.

Limak will repeat the following operation till everything is destroyed.

Block is called internal if it has all four neighbors, i.e. it has each side (top, left, down and right) adjacent to other block or to the floor. Otherwise, block is boundary. In one operation Limak destroys all boundary blocks. His paws are very fast and he destroys all those blocks at the same time.

Limak is ready to start. You task is to count how many operations will it take him to destroy all towers.

Input

The first line contains single integer n (1 ≤ n ≤ 105).

The second line contains n space-separated integers h1, h2, ..., hn (1 ≤ hi ≤ 109) — sizes of towers.

Output

Print the number of operations needed to destroy all towers.

Examples

Input

6
2 1 4 6 2 2


Output

3


Input

7
3 3 3 1 3 3 3


Output

2

Note

The picture below shows all three operations for the first sample test. Each time boundary blocks are marked with red color. 

<image> After first operation there are four blocks left and only one remains after second operation. This last block is destroyed in third operation.
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

/**
 * Created by Snayde on 05.01.2015.
 */
public class Main {

    public static void solve() {
        int n = IO.readInt();

        int[] h = new int[n];
        for (int index = 0; index < n; ++index) {
            h[index] = IO.readInt();
        }

        int[] s = new int[n];
        s[0] = 1;
        s[n - 1] = 1;
        for (int index = 1; index < n - 1; ++index) {
            s[index] = Math.min(s[index - 1] + 1, h[index]);
        }
        for (int index = n - 2; index > 0; --index) {
            s[index] = Math.min(s[index + 1] + 1, s[index]);
        }

        int max = -1;
        for (int ss : s) {
            max = Math.max(ss, max);
        }
        IO.println(max);
    }

    // Input/Output ================================
    public static class IO {

        private static Scanner scanner;
        private static PrintWriter writer;

        public static void setUp(InputStream in, OutputStream out) {
            scanner = new Scanner(new java.io.BufferedInputStream(in));
            writer = new PrintWriter(out);
        }

        public static boolean isEmpty() {
            return !scanner.hasNext();
        }

        public static boolean hasNextLine() {
            return scanner.hasNextLine();
        }

        public static String readLine() {
            String line;
            try {
                line = scanner.nextLine();
            } catch (Exception e) {
                line = null;
            }
            return line;
        }

        public static String readString() {
            return scanner.next();
        }

        public static int readInt() {
            return scanner.nextInt();
        }

        public static double readDouble() {
            return scanner.nextDouble();
        }

        public static float readFloat() {
            return scanner.nextFloat();
        }

        public static long readLong() {
            return scanner.nextLong();
        }

        public static char readChar() {
            return scanner.findInLine("[^\\s]").charAt(0);
        }

        public static void print(Object o) {
            writer.print(o);
            writer.flush();
        }

        public static void println(Object o) {
            writer.println(o);
            writer.flush();
        }
    }

    // Algorithms ================================

    private static class Algo {

        private static int binSearch(int[] array, int n, int lo, int hi) {
            if (lo > hi) {
                return lo;
            }

            int mid = lo + (hi - lo) / 2;
            int cmp = (int) Math.signum(n - array[mid]);
            if (cmp < 0) {
                return binSearch(array, n, lo, mid - 1);
            } else if (cmp == 0) {
                return mid;
            } else {
                return binSearch(array, n, mid + 1, hi);
            }
        }

        private static void permutations(int n) {
            int[] p = new int[n];
            for (int index = 0; index < n; ++index) {
                p[index] = index + 1;
            }

            while (true) {
                IO.println(Arrays.toString(p));

                int k = n - 1;
                while (k > 0) {
                    if (p[k] < p[k - 1]) {
                        k--;
                    }
                    else {
                        break;
                    }
                }
                if (k == 0) {
                    break;
                }
                int j = n - 1;
                while (p[j] < p[k - 1]) {
                    j--;
                }

                int t = p[j];
                p[j] = p[k - 1];
                p[k - 1] = t;

                int i = 0;
                while (k + i < n - 1 - i) {
                    t = p[k + i];
                    p[k + i] = p[n - i - 1];
                    p[n - i - 1] = t;
                    i++;
                }
            }
        }

        private static final boolean isPrime(int number) {
            if (number <= 1) {
                return false;
            }
            if (number <= 3) {
                return true;
            }
            if (number % 2 == 0 || number % 3 == 0) {
                return false;
            }
            int i = 5;
            while (i * i <= number) {
                if (number % i == 0 || number % (i + 2) == 0) {
                    return false;
                }
                i += 6;
            }
            return true;
        }

        private static boolean isPalindrome(int number) {
            int n = number;
            int reverse = 0;
            while (n > 0) {
                reverse *= 10;
                reverse += (n % 10);
                n /= 10;
            }
            return reverse == number;
        }

        public static int gcd(int a,int b) {
            while (b != 0) {
                int tmp = a % b;
                a = b;
                b = tmp;
            }
            return a;
        }
    }

    public static final void main(String[] args) {
        IO.setUp(System.in, System.out);
        /*
        try {
            IO.setUp(new FileInputStream("encode.in"), new FileOutputStream("encode.out"));
        } catch (FileNotFoundException e) {
            e.printStackTrace();
            return;
        }
        */
        solve();
    }
}
