Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode). 
    
    
      
    procedure bubbleSortGraph()  
        build a graph G with n vertices and 0 edges  
        repeat  
            swapped = false  
            for i = 1 to n - 1 inclusive do:  
                if a[i] > a[i + 1] then  
                    add an undirected edge in G between a[i] and a[i + 1]  
                    swap( a[i], a[i + 1] )  
                    swapped = true  
                end if  
            end for  
        until not swapped   
        /* repeat the algorithm as long as swapped value is true. */   
    end procedure  
    

For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.

Input

The first line of the input contains an integer n (2 ≤ n ≤ 105). The next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n).

Output

Output a single integer — the answer to the problem. 

Examples

Input

3
3 1 2


Output

2

Note

Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
100
36 48 92 87 28 85 42 10 44 41 39 3 79 9 14 56 1 16 46 35 93 8 82 26 100 59 60 2 96 52 13 98 70 81 71 94 54 91 17 88 33 30 19 50 18 73 65 29 78 21 61 7 99 97 45 89 57 27 76 11 49 72 84 69 43 62 4 22 75 6 66 83 38 34 86 15 40 51 37 74 67 31 20 63 77 80 12 53 5 25 58 90 68 24 64 23 95 32 55 47
 5
4 2 1 3 5
 10
1 9 8 10 2 3 4 6 5 7
 50
12 24 42 43 36 3 40 29 7 34 10 13 28 9 35 23 25 21 19 4 20 18 11 38 41 48 6 46 33 17 31 37 2 30 32 44 45 5 47 49 16 15 50 27 26 14 39 22 1 8

16
 3
 6
 13


import java.io.*;
import java.util.*;

public class Main {
    static BufferedReader br;
       //static  long mod  = 1000
    static HashSet<Integer> p  = new HashSet<>();
    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        int tc = 1;
     //   tc = cinI();

        //  sieve();
        while (tc-- > 0) {
          //  int[] npqr=  readArray(4,0,1);
            int n  =cinI();
            long[] arr = readArray(n,0);

          //  long[] pqr = new long[3];
            long[] dp =new long[n+1];
            for(int i=0;i<n;i++){
                long correct =  arr[i]-1;
                long current = i;
                if(correct<current){
                    dp[i+1]=dp[i]+(current-correct);
                 //   System.out.println(arr[i]+ " "+dp[i+1]);
                    continue;
                }
                dp[i+1]=dp[i];
            }
            System.out.println(dp[n]);

        }
    }

    public static void sieve(){
         int[] pf = new int[100000+1];
        //0 prime //1 not prime
        pf[0]=1;
        pf[1]=1;
        for(int j=2;j<pf.length;j++){

            if(pf[j]==0 && ((long)j*j<pf.length)){
                for(int k=j*j;k<pf.length;k+=j){
                    pf[k]=1;
                }
            }
        }
        for(int j=2;j<pf.length;j++){
          if(pf[j]==0){
              p.add(j);
          }

        }
    }






    public  static  int[] readArray(int n,int x ,int z)throws Exception{
        int[] arr= new int[n];
        String[] ar= cinA();
        for(int i =x ;i<n+x;i++){
            arr[i]=getI(ar[i-x]);
        }
        return arr;
    }
      public  static  long[] readArray(int n,int x )throws Exception{
        long[] arr= new long[n];
        String[] ar= cinA();
        for(int i =x ;i<n+x;i++){
            arr[i]=getI(ar[i-x]);
        }
        return arr;
      }

    public static void arrinit(String[] a,long[] b)throws Exception{
        for(int i=0;i<a.length;i++){
            b[i]=Long.parseLong(a[i]);
        }
    }
    public  static HashSet<Integer>[]  Graph(int n,int edge,int directed)throws Exception{
        HashSet<Integer>[] tree=  new HashSet[n];

        for(int j=0;j<edge;j++){

            String[] uv = cinA();
            int u = getI(uv[0]);
            int v = getI(uv[1]);
            if(directed==0){

                tree[v].add(u);
            }
            tree[u].add(v);
        }
        return tree;
    }
    public static void arrinit(String[] a,int[] b)throws Exception{
        for(int i=0;i<a.length;i++){
            b[i]=Integer.parseInt(a[i]);
        }
    }


    static double findRoots(int a, int b, int c) {
        // If a is 0, then equation is not
        //quadratic, but linear


        int d = b * b - 4 * a * c;
        double sqrt_val = Math.sqrt(Math.abs(d));


        // System.out.println("Roots are real and different \n");

        return Math.max((double) (-b + sqrt_val) / (2 * a),
                (double) (-b - sqrt_val) / (2 * a));


    }

    public static String cin() throws Exception {
        return br.readLine();
    }

    public static String[] cinA() throws Exception {
        return br.readLine().split(" ");
    }
    public static String[] cinA(int x) throws Exception{
        return br.readLine().split("");
    }

    public static String ToString(Long x) {
        return Long.toBinaryString(x);
    }

    public static void cout(String s) {
        System.out.println(s);
    }

    public static Integer cinI() throws Exception {
        return Integer.parseInt(br.readLine());
    }

    public static int getI(String s) throws Exception {
        return Integer.parseInt(s);
    }

    public static long getL(String s) throws Exception {
        return Long.parseLong(s);
    }

    public static long max(long a, long b) {
        return Math.max(a, b);
    }

    public static void coutI(int x) {
        System.out.println(String.valueOf(x));
    }

    public static void coutI(long x) {
        System.out.println(String.valueOf(x));
    }

    public static Long cinL() throws Exception {
        return Long.parseLong(br.readLine());
    }

    public static void arrInit(String[] arr, int[] arr1) throws Exception {
        for (int i = 0; i < arr.length; i++) {
            arr1[i] = getI(arr[i]);
        }

    }
}

class range {
    int l;
    int r;
    int diff;

    public range(int l, int r, int diff) {
        this.l = l;
        this.r = r;
        this.diff = diff;
    }
}

class sortRange implements Comparator<range> {


    @Override
    public int compare(range range, range t1) {
        if (range.diff != t1.diff)
            return t1.diff - range.diff;
        return range.l - t1.l;

    }}
class Diag{

    int c0;
    int c1;
    public Diag(int c0,int c1){
        this.c0=c0;
        this.c1=c1;
    }
}