Problem 1: Longest Increasing Subsequence

Problem Statement: Given an array of integers, find the length of the longest strictly increasing subsequence.

Input

First line contains an integer n, the number of elements. The next line has n space-separated integers.

Output

Print the length of the longest increasing subsequence.

Examples


Input:
8
10 9 2 5 3 7 101 18

Output:
4

Solution Explanation

Method 1: Use an O(n log n) algorithm by maintaining a temporary list of potential sequence ends and using binary search to update this list. Method 2: Apply dynamic programming with O(n^2) time by comparing each element with all previous elements and tracking the maximum subsequence length ending at each position.

Solution in C++


#include 
#include 
#include 
using namespace std;

int main(){
    int n; 
    cin >> n;
    vector arr(n);
    for (int i = 0; i < n; i++) {
        cin >> arr[i];
    }
    vector lis;
    for (int x : arr) {
        auto it = lower_bound(lis.begin(), lis.end(), x);
        if(it == lis.end()) {
            lis.push_back(x);
        } else {
            *it = x;
        }
    }
    cout << lis.size();
    return 0;
}