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.*;
//import java.util.*;

public class ranjan {

    public static Reader cin;
    public static PrintWriter cout;
    public static final long bil = (long)1e9+7;
    public static void main(String[] arg) throws IOException {
        //input / output variables
        if(arg.length == 0)
            cin = new Reader(System.in);
        else
            cin = new Reader(new FileInputStream(new File("in"+arg[0]+".txt")));
        cout = new PrintWriter(new BufferedOutputStream(System.out));
        //input
        int n = cin.nextInt();
        int[] h = new int[n];
        for(int i=0;i<n;i++)
            h[i] = cin.nextInt();
        int[] destroyTimeL = new int[n];
        int[] destroyTimeR = new int[n];

        destroyTimeL[0] = 1;
        destroyTimeR[n-1] = 1;
        for(int i=1;i<n;i++)
            destroyTimeL[i] = Math.min(destroyTimeL[i-1]+1,h[i]);
        for(int i=n-2;i>=0;i--)
            destroyTimeR[i] = Math.min(destroyTimeR[i+1]+1,h[i]);

        int ans = -1;
        for(int i=0;i<n;i++)
            ans = Math.max(ans,Math.min(destroyTimeL[i],destroyTimeR[i]));
        cout.print(ans);
        //end
        cout.print("\n");
        cout.close();
    }


    static <T> void reverseArray(T intArray[], int size) 
    { 
        int i;
        T temp; 
        for (i = 0; i < size / 2; i++) { 
            temp = intArray[i]; 
            intArray[i] = intArray[size - i - 1]; 
            intArray[size - i - 1] = temp; 
        }  
    }



    private static class Pair<U,V>{
        public U a;
        public V b;
        public Pair(U a,V b)
        {
            this.a = a;
            this.b = b;
        }	
    }

    //useful functions 
/*   public static void seive(int size)
    {
        prime[0] = prime[1] = false;
        int p = 2;
        while(p*p<= size)
        {
            if(prime[p])
            {
                for(int i=p*p;i<size;i += p)

                    prime[i] = false;
            }
            p++;
        }
    }
    public static long mod_pow(long x,long n,long mod) {
        long res=1;
        while(n>0) {
            if((n&1)==1)res=res*x%mod;
            x=x*x%mod;
            n>>=1;
        }
        return res;
    }
    public static int gcd(int n1, int n2) 
    {
        int r;
        while (n2 != 0) 
        {
            r = n1 % n2;
            n1 = n2;
            n2 = r;
        }
        return n1;
    }

    public static int lcm(int n1, int n2) 
    {
        int answer = (n1 * n2) / (gcd(n1, n2));
        return answer;
    }
*/

    //Fast Reading classes
    static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 

        public Reader(InputStream is) 
        { 
            din = new DataInputStream(is); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 

        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 

        public String nextLine() throws IOException 
        { 
            byte[] buf = new byte[1024]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 

        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 

            if (neg) 
                return -ret; 
            return ret; 
        } 

        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 

        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 

            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 

            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 

            if (neg) 
                return -ret; 
            return ret; 
        } 

        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 

        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 

        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
}
