Printing the longest Increasing Subsequence

// I can't tell you what it really is,
// I can only tell you what it feels like.
#include "bits/stdc++.h"

using namespace std;

#define int long long
#define F first
#define S second
#define rep(i,a,n)  for (int i = a; i <= n; ++i)
#define fo(i, n)   for (int i = 1; i <= n; ++i)
#define all(v)  v.begin(), v.end()
#define pb push_back
#define P pair < int, int >
#define fast      ios_base::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL);
#define reno(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); }
void err(istream_iterator<string> it) {}

template<typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
    cout << *it << " = " << a << ' ';
    err(++it, args...);
}

const int N = 1e3 + 5;
int v[N], pre[N];
vector < int > let;
void fun(int x) {
	if(x == -1)
		return;
	fun(pre[x]);
	cout << v[x] << ' ';
}
signed main(){
    fast;
    int n;
    cin >> n;
    fo(i, n)
        cin >> v[i];

    fo(i, n) {
    	if(let.empty()) {
        		let.pb(i);
        		pre[i] = -1;
        }
        else if(v[i] < v[let[0]]){
        	let[0] = i;
        	pre[i] = -1;
        }
        else if(v[i] > v[let.back()]) {
            pre[i] = let.back();
            let.pb(i);
        }
        else {
            int lo = 0, hi = let.size(), mid;
            while(lo <= hi) {
                mid = lo + hi >> 1;
                if(v[let[mid]] >= v[i])
                    hi = mid - 1;
                else
                    lo = mid + 1;
            }
            let[hi + 1] = i;
           	if(hi + 1)
           		pre[let[hi+1]] = let[hi];
        }

    }
    fun(let.back());























    return 0;
}