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].
import java.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;
import static java.lang.Math.*;
 
public class fast implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        
        public int read() {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
            
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
            
            return res * sgn;
        }
        
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
        
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        
        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next() {
            return readString();
        }
        
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    
    class pair implements Comparable<pair>{
        int x,y;
        pair(int xi, int yi){
            x=xi;
            y=yi;
        }
        @Override
        public int compareTo(pair other){
            if(this.x>other.x){return 1;}
            if(this.x<other.x){return -1;}
            if(this.y>other.y){return 1;}
            if(this.y<other.y){return -1;}
            return 0;
        }    
    }
 
    class dist implements Comparable<dist>{
        int x,y,z;
        dist(int xi, int yi, int zi){
            x=xi;
            y=yi;
            z=zi;
        }
        @Override
        public int compareTo(dist other){
            if(this.z>other.z){return 1;}
            if(this.z<other.z){return -1;}
            return 0;
        } 
    } 
    
    public static void main(String args[]) throws Exception {
        new Thread(null, new fast(),"fast",1<<26).start();
    }
    
    public void sortbyColumn(int arr[][], final int col){ 
        // Using built-in sort function Arrays.sort 
        Arrays.sort(arr, new Comparator<int[]>() { 
            
          @Override              
          // Compare values according to columns 
          public int compare(final int[] entry1, final int[] entry2) { 
  
            // To sort in descending order revert  
            // the '>' Operator 
            if (entry1[col] > entry2[col]) 
                return 1; 
            if(entry1[col] < entry2[col])
                return -1;
            return 0;
          } 
        });  // End of function call sort(). 
    }
    
    public void sortbyColumn(long arr[][], final int col){ 
        // Using built-in sort function Arrays.sort 
        Arrays.sort(arr, new Comparator<long[]>() { 
            
          @Override              
          // Compare values according to columns 
          public int compare(final long[] entry1, final long[] entry2) { 
  
            // To sort in descending order revert  
            // the '>' Operator 
            if (entry1[col] > entry2[col]) 
                return 1; 
            if(entry1[col] < entry2[col])
                return -1;
            return 0;
          } 
        });  // End of function call sort(). 
    }
    
    public void sort(int ar[]){
        int n=ar.length;
        Integer arr[]=new Integer[n];
        for(int i=0;i<n;i++){
            arr[i]=ar[i];
        }
        Arrays.sort(arr); 
        for(int i=0;i<n;i++){
            ar[i]=arr[i].intValue();
        }
    }
    
    public void sort(long ar[]){
        int n=ar.length;
        Long arr[]=new Long[n];
        for(int i=0;i<n;i++){
            arr[i]=ar[i];
        }
        Arrays.sort(arr); 
        for(int i=0;i<n;i++){
            ar[i]=arr[i].longValue();
        }
    }
    
    long power(long x, long y, long 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; 
    }
    
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}

    int bing(int dp[], int r, int val){
        int l=0,mid;
        while(l<=r){
            mid=(l+r)>>1;
            if(dp[mid]<val){
                l=mid+1;
            }
            else{
                r=mid-1;
            }
        }return l;
    }

    int lcs(int a[], int n){
        int dp[]=new int[n];
        int len=1;
        dp[0]=a[0];
        for(int i=1;i<n;i++){
            if(a[i]<dp[0]){
                dp[0]=a[i];
            }
            else if(a[i]>dp[len-1]){
                dp[len++]=a[i];
            }
            else{
                dp[bing(dp,len-1, a[i])]=a[i];
            }
        }
        return len;
    }

    public void run(){
        InputReader s = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
        
        int n=s.nextInt(),a[]=new int[n];
        for(int i=0;i<n;i++){
            a[i]=s.nextInt();
        }
        w.println(lcs(a,n));

        w.close();
    }
}