Longest Increasing Subsequence

Lab Java Advanced 30 points

Read n integers and print the length of the longest strictly increasing subsequence (O(n²) DP is fine).

Input

n, then n integers.

Output

One integer.

Example

Input

8
10 9 2 5 3 7 101 18

Output

Sample input available Sample output available

Editor

Java

Hints

len[i] = longest increasing subsequence ending at i.

Solution explanation

Each element extends the best subsequence that ends at a smaller earlier element.

Show solution

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = sc.nextInt();
        int[] len = new int[n];
        int best = 0;
        for (int i = 0; i < n; i++) {
            len[i] = 1;
            for (int j = 0; j < i; j++) {
                if (a[j] < a[i]) len[i] = Math.max(len[i], len[j] + 1);
            }
            best = Math.max(best, len[i]);
        }
        System.out.println(best);
    }
}

Output

Answer