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.
// Importing all important imports
 
import java.awt.Point;
import static java.lang.System.in;
import java.io.BufferedReader;
import java.io.ByteArrayInputStream;
import java.io.DataInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;
import java.nio.file.Files;
import java.nio.file.Paths;
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.Comparator;
import java.util.Date;
import java.util.GregorianCalendar;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.InputMismatchException;
import java.util.LinkedHashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Stack;
import java.util.Queue;
import java.util.Random;
import java.util.regex.Matcher;
import java.util.regex.Pattern;
import java.util.Set;
import java.util.SortedSet;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Vector;
 
 
 
/**
@author
* 
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$$$\    $$$ |                      $$ |              $$  __$$\           
$$$$\  $$$$ |$$\   $$\  $$$$$$$\ $$$$$$\    $$$$$$\  $$ /  \__| $$$$$$\  
$$\$$\$$ $$ |$$ |  $$ |$$  _____|\_$$  _|   \____$$\ $$$$\      \____$$\ 
$$ \$$$  $$ |$$ |  $$ |\$$$$$$\    $$ |     $$$$$$$ |$$  _|     $$$$$$$ |
$$ |\$  /$$ |$$ |  $$ | \____$$\   $$ |$$\ $$  __$$ |$$ |      $$  __$$ |
$$ | \_/ $$ |\$$$$$$  |$$$$$$$  |  \$$$$  |\$$$$$$$ |$$ |      \$$$$$$$ |
\__|     \__| \______/ \_______/    \____/  \_______|\__|       \_______|
* 
*/
 
 
public class Main{
        
        static boolean testcase=false;
        public void solve() throws IOException
        {   
            int n=ni();
            int arr[]=new int[n+1];
            long dp1[]=new long[n+1],dp2[]=new long[n+2];
            for(int i=1;i<=n;i++){
                arr[i]=ni();
            }
            for(int i=1;i<=n;i++){
                dp1[i]=Math.min(dp1[i-1]+1,arr[i]);
            }
            for(int i=n;i>0;i--){
                dp2[i]=Math.min(dp2[i+1]+1,arr[i]);
            }
            long ans=0;
            for(int i=1;i<=n;i++){
            ans=Math.max(ans,Math.min(dp1[i],dp2[i]));
            }
            out.println(ans);
        }
        
        // END OF SOLUTION
        
        public void solveTests(int test) throws IOException
        {
            for(int tc=1;tc<=test;tc++)
                solve();
        }
        
        
        // INPUT OUTPUT TEMPLATE
        static String TESTCASES="";
        static PrintWriter out;
        static int Space;
        
        public static void main(String[] args) throws Exception 
        {
               // generateTestCases(1); 
                long endTime,startTime=System.currentTimeMillis();
                out=new PrintWriter(new OutputStreamWriter(System.out));
               // mytestcases();
                InputStream myinp=TESTCASES.isEmpty() ? System.in : new ByteArrayInputStream(TESTCASES.getBytes());
                //InputStream myinp=System.in;
                init(myinp);
                
                Space=0;
                Main program=new Main();
                if(testcase==true){int test=ni();program.solveTests(test);}
                else program.solve();
                
                out.close();
                endTime=System.currentTimeMillis();
                //printTime("Time: "+(endTime-startTime)+"ms");
        }
        
         // Testcases reader from FILE. If file not found, input is taken from console.
        public static void mytestcases()
        {
            try
            {
            TESTCASES=new String(Files.readAllBytes(Paths.get("C:\\Users\\user\\Desktop\\out.txt")));
            }
            catch(Exception e){TESTCASES="";}
        }
           public static void generateTestCases(int count)
        {
            PrintStream console=System.out;
            try{
            PrintStream out = new PrintStream(new FileOutputStream("C:\\Users\\user\\Desktop\\out.txt"));
            
            System.setOut(out);
            Random r=new Random();
           // System.out.println(count);
            for(int tc=0;tc<count;tc++)
            {
                // generate
                int n=2000;
                int q=30;
                out.println(n+" "+q);
                for(int i=0;i<n;i++)
                {
                  out.print((r.nextInt(10)+1)+" ");
                }
                out.println();
                for(int i=0;i<q;i++)
                {
                    int ty=r.nextInt(4)+1;
                    //while(ty==3)ty=r.nextInt(4)+1;
                    int rr=r.nextInt(n)+1;
                    out.print(ty+" "+(r.nextInt(rr)+1)+" "+rr+" ");
                    if(ty!=4)out.print(r.nextInt(10)+1);
                    out.println();
                }
            }
            System.setOut(console);
            }
            catch(FileNotFoundException fe){System.setOut(console);}
        }
          
          
        // Just to print time, not to use anywhere else
        public static void printTime(Object ...obj){if(TESTCASES.length()!=0)System.err.println(Arrays.deepToString(obj));}
        static InputStream is;
        static BufferedReader brr;
        protected static byte[] inbuf = new byte[1024];
        static int lbuffer = 0, pbuffer = 0;
        public static void init(InputStream input) {is=input;brr=new BufferedReader(new InputStreamReader(input));}
        // Fundamental
        protected static int rb(){if(lbuffer == -1)throw new InputMismatchException();if(pbuffer >= lbuffer){pbuffer = 0;try { lbuffer = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }if(lbuffer <= 0)return -1;}return inbuf[pbuffer++];}       
        protected static String line() throws IOException{return brr.readLine();}   
        protected static boolean isSpace(int c) { return !(c >= 33 && c <= 126); }
        protected static int skip(){ int b; while((b = rb()) != -1 && isSpace(b)); return b; }
        // Inputs
        protected static double nd() throws IOException { return Double.parseDouble(ns()); }
        protected static char nc() { return (char)skip(); }
        protected static String ns() throws IOException{if(Space==1)return line();int b = skip();StringBuilder sb = new StringBuilder();while(!(isSpace(b))){ sb.appendCodePoint(b);b = rb();}return sb.toString();}
        protected static char[] nca(int n){char[] buf = new char[n];int b = skip(), p = 0;while(p < n && !(isSpace(b))){buf[p++] = (char)b;b = rb();} return n == p ? buf : Arrays.copyOf(buf, p);}
        protected static int[] nia(int n) throws IOException{int[] a = new int[n];for(int i = 0;i < n;i++)a[i] = ni();return a;}
        protected static int[][] niaindex(int n) throws IOException{int ea[][]=new int[n][2];for(int i=0;i<n;i++){ea[i][0]=ni();ea[i][1]=i;}return ea;}
        protected static long[] nla(int n) throws IOException{long[] a = new long[n];for(int i = 0;i < n;i++)a[i] = nl();return a;}
        protected static long[][] nlaindex(int n) throws IOException{long ea[][]=new long[n][2];for(int i=0;i<n;i++){ea[i][0]=ni();ea[i][1]=i;}return ea;}
        protected static String[] nsa(int n) throws IOException{String[] a = new String[n];for(int i = 0;i < n;i++)a[i] = ns();return a;    }
        protected static double[] nda(int n) throws IOException{double[] a = new double[n];for(int i = 0;i < n;i++)a[i] = nd();return a;}
        protected static int ni() throws IOException{if(Space==1)return Integer.parseInt(line());int num=0,b;boolean minus = false;while((b = rb())!= -1 && !((b>='0'&&b<='9') || b =='-'));if(b =='-'){minus=true;b = rb();    }while(true){if(b >= '0' && b <= '9'){num = num * 10 + (b - '0');}else{return minus ? -num : num;}b = rb();}}  
        protected static long nl() throws IOException{if(Space==1)return Long.parseLong(line());long num = 0;int b;boolean minus = false;while((b = rb()) != -1 && !((b >= '0' && b <= '9') || b == '-'));if(b == '-'){   minus = true;b = rb();}while(true){if(b >= '0' && b <= '9'){num = num * 10 + (b - '0');}else{return minus ? -num : num;}b = rb();}}
        // Outputs
        public static void pln(){out.println();}
        public static void ps(String s){out.print(s);}
        public static void pi(int s){out.print(s);}
        public static void pl(long s){out.print(s);}
        public static void pd(double s){out.print(s);}
        public static void psp(){out.print(" ");}
        public static void parr(int s[]){out.println(Arrays.toString(s));}
        public static void parr(String s[]){out.println(Arrays.toString(s));}
        public static void parr(long s[]){out.println(Arrays.toString(s));}        
        public static void parr2(int s[][]){for(int i=0;i<s.length;i++)out.println(Arrays.toString(s[i]));}
        public static void parr2(long s[][]){for(int i=0;i<s.length;i++)out.println(Arrays.toString(s[i]));}
        public static void parr2(String s[][]){for(int i=0;i<s.length;i++)out.println(Arrays.toString(s[i]));}
        
}   
 