sweep Line for intersection

#include <bits/stdc++.h>
#define MAX 600007

using namespace std;
typedef pair<int, int> pii;
typedef long long ll;

int maior[4*MAX], idx[4*MAX], acum[4*MAX];

struct rect{
    int x;
    int ini, end;
    int type;

    rect(int _x, int _ini, int _end, int _type): x(_x), ini(_ini), end(_end), type(_type) {}
};

bool compare(rect a, rect b){
    if(a.x == b.x) return a.type < b.type;
    return a.x < b.x;
}

void build(int id, int l, int r){
    if(l == r) idx[id] = l;
    else{
        int mid = (l+r)/2;
        build(2*id, l, mid);
        build(2*id+1, mid+1, r);

        idx[id] = (maior[id] == maior[2*id]) ? idx[2*id]:idx[2*id+1];

    }
}
void add(int id, int val){
    maior[id] += val;
    acum[id] += val;
}
void update(int id, int l, int r, int x, int y, int val){
    if(r < x || y < l) return;
    else if(x <= l && r <= y) add(id, val);
    else{
        int mid = (l+r)/2;
        add(2*id, acum[id]);
        add(2*id+1, acum[id]);
        acum[id] = 0;

        update(2*id, l, mid, x, y, val);
        update(2*id+1, mid+1, r, x, y, val);

        maior[id] = max(maior[2*id], maior[2*id+1]);
        idx[id] = (maior[id] == maior[2*id]) ? idx[2*id]:idx[2*id+1];
    }
}

// val - index
pii query(int id, int l, int r, int x, int y){
    if(r < x || y < l) return make_pair(0, 0);
    else if(x <= l && r <= y) return make_pair(maior[id], idx[id]);
    else{
        int mid = (l+r)/2;
        add(2*id, acum[id]);
        add(2*id+1, acum[id]);
        acum[id] = 0;

        return max(query(2*id, l, mid, x, y),
                   query(2*id+1, mid+1, r, x, y));
    }
}
void print(int sz){
    for(int i = 1; i <= 4*sz; i++) cout << idx[i] << " \n"[i == 4*sz];
    for(int i = 1; i <= 4*sz; i++) cout << maior[i] << " \n"[i == 4*sz];
}
map<ll, int> compress, descompress;
vector<ll> vals;
vector<rect> arr;
int main(){
    int n; scanf("%d", &n);
    for(int i = 0; i < n; i++){
        ll x1, y1, x2, y2; scanf("%lld %lld %lld %lld", &x1, &y1, &x2, &y2);
        arr.emplace_back(x1, y1, y2, 0);
        arr.emplace_back(x2, y1, y2, 1);
        vals.push_back(x1);
        vals.push_back(x2);
        vals.push_back(y1);
        vals.push_back(y2);
    }

    sort(vals.begin(), vals.end());
    sort(arr.begin(), arr.end(), compare);
    int cnt = 0;
    for(int i = 0; i < vals.size(); i++) {
        if(!compress.count(vals[i])) {
            compress[vals[i]] = cnt;
            descompress[cnt++] = vals[i];
        }
    }

    pii ans = make_pair(-1, -1);
    build(1, 0, cnt);
    //print(cnt);
    for(int i = 0; i < arr.size(); i++){

        rect atual = arr[i];
        //cout << atual.x << " (" << atual.ini << ", " << atual.end << ") #" << atual.type << endl;
        //cout << "virou -> " << atual.x << " (" << compress[atual.ini] << ", " << compress[atual.end] << ") #" << atual.type << endl;
        if(atual.type == 0) {
            update(1, 0, cnt, compress[atual.ini], compress[atual.end], 1);
            //print(cnt);
            pii encontro = query(1, 0, cnt, 0, cnt);
            if(encontro.first >= n-1) {
                //cout << "#" << encontro.first << " " << encontro.second << endl;
                ans = make_pair(atual.x, descompress[encontro.second]);
                break;
            }
        }else update(1, 0, cnt, compress[atual.ini], compress[atual.end], -1);

        //cout << query(1, 1, cnt, 1, cnt).first << " " << query(1, 1, cnt, 1, cnt).second << endl;
    }

    printf("%d %d\n", ans.first, ans.second);
    return 0;
}