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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
public class d {
    public static void main(String[] args) throws IOException {
  //     Scanner s = new Scanner(System.in);
   BufferedReader s=new BufferedReader(new InputStreamReader(System.in));
        //       String[] st=s.readLine().trim().split("\\s+");
        //      a[i]=Integer.parseInt(st[i]);
        //      Integer.parseInt(s.readLine().trim().split("\\s+");
        StringBuilder sb = new StringBuilder();
       int n=Integer.parseInt(s.readLine().trim().split("\\s+")[0]);
       long[] a=new long[n];
       String[] st=s.readLine().trim().split("\\s+");
       for(int i=0;i<n;i++){
           a[i]=Integer.parseInt(st[i]);
       }
        long[] ans=new long[n];long l=0;long r=0;
       for(int i=0;i<n;i++){
           ans[i]=Math.min(l+1,a[i]);
           l=ans[i];
       }long max=0;
       for(int i=n-1;i>=0;i--){
           ans[i]=Math.min(ans[i],r+1);
           r=ans[i];
           max=Math.max(max,ans[i]);
       }
        System.out.println(max);
    }
    static String lexographicallysmallest(String s) {
        if (s.length() % 2 == 1) return s;
        String s1 =lexographicallysmallest(s.substring(0, s.length()/2));
        String s2 = lexographicallysmallest(s.substring(s.length()/2, s.length()));
        if (s1.compareTo(s2)<0) return s1 + s2;
        else return s2 + s1;
    }
    public static int countSetBits(int n)
    {
        return (BitsSetTable256[n & 0xff]
                + BitsSetTable256[(n >> 8) & 0xff]
                + BitsSetTable256[(n >> 16) & 0xff]
                + BitsSetTable256[n >> 24]);
    }
    static int[] BitsSetTable256 ;
    public static void initialize(int n)
    {
        BitsSetTable256[0] = 0;
        for (int i = 0; i <=Math.pow(2,n); i++) {
            BitsSetTable256[i] = (i & 1) + BitsSetTable256[i / 2];
        }
    }
    static void dfs(int i,int val,ArrayList<Integer>[] adj){
    }

    static  void computeLPSArray(String pat, int M, int lps[]) {
        int len = 0;
        int i = 1;
        lps[0] = 0;
        while (i < M) {
            if (pat.charAt(i) == pat.charAt(len)) {
                len++;
                lps[i] = len;
                i++;
            }
            else
            {
                if (len != 0) {
                    len = lps[len - 1];
                }
                else
                {
                    lps[i] = len;
                    i++;
                }
            }
        }
    }
    static boolean isPrime(int n) {
        if (n <= 1) return false;
        if (n <= 3) return true;

        if (n % 2 == 0 || n % 3 == 0) return false;

        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }
    static long powerwithmod(long  x, long y, int p) {
        long  res = 1;
        x = x % p;
        while (y > 0) {
            if ((y & 1) == 1)
                res = (res * x) % p;
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }
    static long  powerwithoutmod(long x, int y) {
        long  temp;
        if( y == 0)
            return 1;
        temp = powerwithoutmod(x, y/2);
        if (y%2 == 0)
            return temp*temp;
        else
        {
            if(y > 0)
                return x * temp * temp;
            else
                return (temp * temp) / x;
        }
    }
    static void fracion(double x) {
        String a = "" + x;
        String spilts[] = a.split("\\."); // split using decimal
        int b = spilts[1].length(); // find the decimal length
        int denominator = (int) Math.pow(10, b); // calculate the denominator
        int numerator = (int) (x * denominator); // calculate the nerumrator Ex
        // 1.2*10 = 12
        int gcd = (int) gcd((long) numerator, denominator); // Find the greatest common
        // divisor bw them
        String fraction = "" + numerator / gcd + "/" + denominator / gcd;
        // System.out.println((denominator/gcd));
        long x1 = modInverse(denominator / gcd, 998244353);
        //  System.out.println(x1);
        System.out.println((((numerator / gcd) % 998244353 * (x1 % 998244353)) % 998244353));
    }
    static int bfs(int i1, ArrayList<Integer>[] h, int[] vis, int n,int val1) {
        Queue<Integer> q = new LinkedList<Integer>();
        q.add(i1);Queue<Integer> aq=new LinkedList<Integer>();
        aq.add(0);
        while(!q.isEmpty()){
            int i=q.poll();
            int val=aq.poll();
            if(i==n){
                return val;
            }
            if(h[i]!=null){
                for(Integer j:h[i]){
                    if(vis[j]==0){
                        q.add(j);vis[j]=1;
                        aq.add(val+1);}
                }
            }
        }return -1;
    }
    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    static long modInverse(long a, int m)
    {
        return (powerwithmod(a, m - 2, m));
    }
    static int MAXN;
    static int[] spf;
    static void sieve() {
        spf[1] = 1;
        for (int i=2; i<MAXN; i++)
            spf[i] = i;
        for (int i=4; i<MAXN; i+=2)
            spf[i] = 2;
        for (int i=3; i*i<MAXN; i++)
        {
            if (spf[i] == i)
            {
                for (int j=i*i; j<MAXN; j+=i)

                    if (spf[j]==j)
                        spf[j] = i;
            }
        }
    }
    static ArrayList<Integer> getFactorizationUsingSeive(int x) {
        ArrayList<Integer> ret = new ArrayList<Integer>();
        while (x != 1)
        {
            ret.add(spf[x]);
            x = x / spf[x];
        }
        return ret;
    }
   static long[] fac ;
     static void calculatefac(int mod){
         fac[0]=1;
        for (int i = 1 ;i <= MAXN; i++)
            fac[i] = fac[i-1] * i % mod;
     }
      static long nCrModPFermat(int n, int r, int mod) {
         if (r == 0)
            return 1;
        fac[0] = 1;
        return (fac[n]* modInverse(fac[r], mod)
                % mod * modInverse(fac[n-r], mod)
                                    % mod) % mod;
    } }
class Student {
    long  l;long r;int x;
    public Student(long l, long r) {
        this.l = l;
        this.r = r;this.x=x;
    }

    public String toString()
    {
        return this.l+" ";
    }
}
class Sortbyroll implements Comparator<Student>
{

    public int compare(Student a, Student b){
      if(a.l<b.l) return 1;
      else if(a.l==b.l){
          if(a.r==b.r){
              return 0;
          }
          if(a.r<b.r) return -1;
          return 1;}
      return -1;  }
}