Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
 
public class Main {
 
    void solve() throws IOException {
        int N = ni();
        int[] a = new int[N];
        for (int i = 0; i < N; i++) {
            a[i] = ni();
        }
        int[] minright = new int[N];
        minright[N-1] = a[N-1];
        for (int i = N-2; i >=0; i--) {
            minright[i] = Math.min(minright[i+1], a[i]);
        }
        int[] used = new int[N];
        UnionFind uf = new UnionFind(N);
        for (int i = 0; i < N; i++) {
            used[i] = 1;
            if(i < N-1){
                if(a[i] >= minright[i+1]) continue;
            }
            for (int j = i+1; j < N; j++) {
                if(used[j] == 0 && a[i] < a[j]) {
                    used[j] = 1;
                    uf.union(i,j);
                }
            }
        }
        
        long ans = uf.count();
        out.println(ans);
    }
    class UnionFind{
        int[] par;
        UnionFind(int n){
            par = new int[n];
            for (int i = 0; i < n; i++) {
                par[i] = -1;
            }
        }
        int find (int n){
            if(par[n] < 0){
                return n;
            }else{
                return find(par[n]);
            }
        }
        int count (){
            int count = 0;
            for (int i = 0; i < par.length; i++) {
                if(par[i]<0) count++;
            }
            return count;
        }
        boolean union(int a, int b){
            a = find(a);
            b = find(b);
            if(a == b) return false;
            if(par[a] > par[b]){
                int temp = b;
                b = a;
                a = temp;
            }
            par[a] += par[b];
            par[b] = a;
            return true;
        }
        int par(int n){
            return par[n];
        }
        int size(int n){
            return -par[find(n)];
        }
        boolean same(int a, int b){
            return find(a) == find(b);
        }
    }
    final int mod = 1000000007;
    final BigInteger MOD = BigInteger.valueOf(mod);
    int upperBound(ArrayList<Long> list, Long target){
        int i = Collections.binarySearch(list, target, new UpperBoundComparator<Long>());
        return ~i;
    }
    class UpperBoundComparator<T extends Comparable<? super T>> implements Comparator<T>{
        public int compare(T x, T y){
            return (x.compareTo(y) > 0) ? 1 : -1;
        }
    }
    int lowerBound(ArrayList<Long> list, Long target){
        int i = Collections.binarySearch(list, target, new LowerBoundComparator<Long>());
        return ~i;
    }
    class LowerBoundComparator<T extends Comparable<? super T>> implements Comparator<T>{
        public int compare(T x, T y){
            return (x.compareTo(y) >= 0) ? 1 : -1;
        }
    }
    int mul(int x, int y){
        int val = (int)((x * 1L * y) % mod);
        return val>=0 ? val : val+mod;
    }
    int add(int x, int y) {
        x += y;
        if(x < 0) x += mod;
        if(x>=mod) x -= mod;
        return x;
    }
    int sub(int x, int y){
        x = add(x,mod-y);
        if(x < 0) x += mod;
        if(x>=mod) x -= mod;
        return x;
    }
    String ns() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine(), " ");
        }
        return tok.nextToken();
    }
 
    int ni() throws IOException {
        return Integer.parseInt(ns());
    }
 
    long nl() throws IOException {
        return Long.parseLong(ns());
    }
 
    double nd() throws IOException {
        return Double.parseDouble(ns());
    }
 
    String[] nsa(int n) throws IOException {
        String[] res = new String[n];
        for (int i = 0; i < n; i++) {
            res[i] = ns();
        }
        return res;
    }
 
    int[] nia(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = ni();
        }
        return res;
    }
 
    long[] nla(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = nl();
        }
        return res;
    }
 
    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;
 
    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        tok = new StringTokenizer("");
        Main main = new Main();
        main.solve();
        out.close();
    }
}