Problem:
Score : 800 points

Problem Statement

There are N lines in the xy-plane. The i-th line is represented by A_ix+B_iy=C_i.
Any two lines among the N+2 lines, the above N lines plus the x-axis and y-axis, cross each other at exactly one point.

For each pair 1 \leq i < j \leq N, there is a car at the cross point of the i-th and j-th lines.
Even where three or more lines intersect at a point, a car is individually placed for each pair of lines.
That is, there will be k(k-1)/2 cars placed at the intersection of k lines.

Those cars are already very old, and can only be moved parallel to the x-axis or y-axis.

Takahashi will hold an exhibition of antique cars at a place on the xy-plane.
In order to avoid damaging the half-broken cars too much, he will select the place of the exhibition so that the total distance covered will be minimized when all the cars are moved to the place.
If such a place is not uniquely determined, among the places that satisfy the condition above, the place with the minimum x-coordinate will be selected.
If the place is still not uniquely determined, among the places that satisfy the two conditions above, the place with the minimum y-coordinate will be selected.

Find the place of the exhibition that will be selected.

Constraints

2 \leq N \leq 4 × 10^4

1 \leq |A_i|,|B_i| \leq 10^4(1 \leq i \leq N)

0 \leq |C_i| \leq 10^4(1 \leq i \leq N)

No two given lines are parallel.

All input values are integers.

Inputs

Input is given from Standard Input in the following format:

N
A_1 B_1 C_1
:
A_N B_N C_N

Outputs

Print the x-coordinate and y-coordinate of the place of the exhibition that will be selected, in this order, with a space in between. The output will be judged as correct when the absolute or relative error is at most 10^{-9}.

Sample Input 1

3
1 1 1
2 -1 2
-1 2 2

Sample Output 1

1.000000000000000 1.000000000000000

There is a car at each place shown by a blue circle in the figure. The place to be selected is shown by a purple circle.

Sample Input 2

4
1 1 2
1 -1 0
3 -1 -2
1 -3 4

Sample Output 2

-1.000000000000000 -1.000000000000000

Sample Input 3

7
1 7 8
-2 4 9
3 -8 -5
9 2 -14
6 7 5
-8 -9 3
3 8 10

Sample Output 3

-1.722222222222222 1.325000000000000

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#pragma region preprocessor
#ifdef LOCAL
//*
    #define _GLIBCXX_DEBUG  // gcc
/*/
    #define _LIBCPP_DEBUG 0 // clang
//*/
    // #define __buffer_check__
#else
    #pragma GCC optimize("Ofast")
    // #define NDEBUG
#endif
#define __precision__ 15
#define __iostream_untie__ true
#include <bits/stdc++.h>
#include <ext/rope>

#ifdef LOCAL
    #include "dump.hpp"
    #define mesg(str) std::cerr << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]  " << str << "\n"
#else
    #define dump(...) ((void)0)
    #define mesg(str) ((void)0)
#endif
#pragma endregion

#pragma region std-overload
namespace std
{
    // hash
    template <class T> size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); }
    template <class T, class U> struct hash<pair<T, U>> { size_t operator()(pair<T, U> const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } };
    template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc<tuple_t, index - 1>::apply(seed, t), get<index>(t)); } };
    template <class tuple_t> struct tuple_hash_calc<tuple_t, 0> { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } };
    template <class... T> struct hash<tuple<T...>> { size_t operator()(tuple<T...> const &t) const { return tuple_hash_calc<tuple<T...>>::apply(0, t); } };
    // iostream
    template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }
    template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }
    template <class tuple_t, size_t index> struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis<tuple_t, index - 1>::apply(is, t); return is >> get<index>(t); } };
    template <class tuple_t> struct tupleis<tuple_t, SIZE_MAX> { static istream &apply(istream &is, tuple_t &t) { return is; } };
    template <class... T> istream &operator>>(istream &is, tuple<T...> &t) { return tupleis<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(is, t); }
    template <> istream &operator>>(istream &is, tuple<> &t) { return is; }
    template <class tuple_t, size_t index> struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };
    template <class tuple_t> struct tupleos<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };
    template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }
    template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; }
} // namespace std
#pragma endregion

#pragma region config
namespace config
{
    const auto start_time{std::chrono::system_clock::now()};
    int64_t elapsed()
    {
        using namespace std::chrono;
        const auto end_time{std::chrono::system_clock::now()};
        return duration_cast<milliseconds>(end_time - start_time).count();
    }
    __attribute__((constructor)) void setup()
    {
        using namespace std;
        if(__iostream_untie__) ios::sync_with_stdio(false), cin.tie(nullptr);
                cout << fixed << setprecision(__precision__);
        #ifdef DEBUG
                freopen("debug.out","w",stdout);
                freopen("debug.err","w",stderr);
                if(!freopen("debug.in","r",stdin))
                {
                    cerr << "error: \"./debug.in\" not found.\n";
                    exit(EXIT_FAILURE);
                }
        #endif
        #ifdef stderr_path
                freopen(stderr_path, "a", stderr);
        #endif
        #ifdef LOCAL
                cerr << fixed << setprecision(__precision__) << boolalpha << "\n----- stderr at LOCAL -----\n\n";
                atexit([]{ cerr << "\n----- Exec time : " << elapsed() << " ms -----\n\n"; });
        #endif
        #ifdef __buffer_check__
                atexit([]{ ofstream cnsl("CON"); char bufc; if(cin >> bufc) cnsl << "\n\033[1;35mwarning\033[0m: buffer not empty.\n\n"; });
        #endif
    }
} // namespace config
#pragma endregion

#pragma region utility
// lambda wrapper for recursive method.
template <class lambda_type>
class fixed_point
{
    lambda_type func;
public:
    fixed_point(lambda_type &&f) : func(std::move(f)) {}
    template <class... Args> auto operator()(Args &&... args) const { return func(*this, std::forward<Args>(args)...); }
};
// read with std::cin.
template <class T = void>
struct read
{
    typename std::remove_const<T>::type value;
    template <class... types>
    read(types... args) : value(args...) { std::cin >> value; }
    operator T() const { return value; }
};
template <>
struct read<void>
{
    template <class T>
    operator T() const { T value; std::cin >> value; return value; }
};
// substitute y for x if x > y.
template <class T> inline bool chmin(T &x, const T &y) { return x > y ? x = y, true : false; }
// substitute y for x if x < y.
template <class T> inline bool chmax(T &x, const T &y) { return x < y ? x = y, true : false; }
// binary search on discrete range.
template <class iter_type, class pred_type>
iter_type binary(iter_type __ok, iter_type __ng, pred_type pred)
{
    assert(__ok != __ng);
    std::ptrdiff_t dist(__ng - __ok);
    while(std::abs(dist) > 1)
    {
        iter_type mid(__ok + dist / 2);
        if(pred(mid)) __ok = mid, dist -= dist / 2;
        else __ng = mid, dist /= 2;
    }
    return __ok;
}
// binary search on real numbers.
template <class pred_type>
long double binary(long double __ok, long double __ng, const long double eps, pred_type pred)
{
    assert(__ok != __ng);
    while(std::abs(__ok - __ng) > eps)
    {
        long double mid{(__ok + __ng) / 2};
        (pred(mid) ? __ok : __ng) = mid;
    }
    return __ok;
}
// trinary search on discrete range.
template <class iter_type, class comp_type>
iter_type trinary(iter_type __first, iter_type __last, comp_type comp)
{
    assert(__first < __last);
    std::ptrdiff_t dist(__last - __first);
    while(dist > 2)
    {
        iter_type __left(__first + dist / 3), __right(__first + dist * 2 / 3);
        if(comp(__left, __right)) __last = __right, dist = dist * 2 / 3;
        else __first = __left, dist -= dist / 3;
    }
    if(dist > 1 && comp(next(__first), __first)) ++__first;
    return __first;
}
// trinary search on real numbers.
template <class comp_type>
long double trinary(long double __first, long double __last, const long double eps, comp_type comp)
{
    assert(__first < __last);
    while(__last - __first > eps)
    {
        long double __left{(__first * 2 + __last) / 3}, __right{(__first + __last * 2) / 3};
        if(comp(__left, __right)) __last = __right;
        else __first = __left;
    }
    return __first;
}
// size of array.
template <class A, size_t N> size_t size(A (&array)[N]) { return N; }
// be careful that val is type-sensitive.
template <class T, class A, size_t N> void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); }
#pragma endregion

#pragma region alias
using namespace std;
using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t;
using p32 = pair<i32, i32>; using p64 = pair<i64, i64>;
template <class T, class Comp = less<T>> using heap = priority_queue<T, vector<T>, Comp>;
template <class T> using hashset = unordered_set<T>;
template <class Key, class Value> using hashmap = unordered_map<Key, Value>;
using namespace __gnu_cxx;
#pragma endregion

#pragma region library

#include <cassert>
#include <vector>

template <class monoid>
class segment_tree
{
    using size_type = typename std::vector<monoid>::size_type;

    class unique_queue
    {
        size_type *que, *begin, *end;
        bool *in;

    public:
        unique_queue() : que(), begin(), end(), in() {}
        unique_queue(size_type n) : que(new size_type[n]), begin(que), end(que), in(new bool[n]{}) {}
        ~unique_queue() { delete[] que; delete[] in; }

        void clear() { begin = end = que; }
        bool empty() const { return begin == end; }
        bool push(size_type index)
        {
            if(in[index]) return false;
            return in[*end++ = index] = true;
        }
        size_type pop() { return in[*begin] = false, *begin++; }
    }; // struct unique_queue

    size_type size_orig, height, size_ext;
    std::vector<monoid> data;
    unique_queue que;

    void recalc(const size_type node) { data[node] = data[node << 1] + data[node << 1 | 1]; }

    void rebuild()
    {
        while(!que.empty())
        {
            const size_type index = que.pop() >> 1;
            if(index && que.push(index)) recalc(index);
        }
        que.clear();
    }

    template <class pred_type>
    size_type left_search_subtree(size_type index, const pred_type pred, monoid mono) const
    {
        assert(index);
        while(index < size_ext)
        {
            const monoid tmp = data[(index <<= 1) | 1] + mono;
            if(pred(tmp)) mono = tmp;
            else ++index;
        }
        return ++index -= size_ext;
    }

    template <class pred_type>
    size_type right_search_subtree(size_type index, const pred_type pred, monoid mono) const
    {
        assert(index);
        while(index < size_ext)
        {
            const monoid tmp = mono + data[index <<= 1];
            if(pred(tmp)) ++index, mono = tmp;
        }
        return (index -= size_ext) < size_orig ? index : size_orig;
    }

public:
    segment_tree(const size_type n = 0) : size_orig{n}, height(n > 1 ? 32 - __builtin_clz(n - 1) : 0), size_ext{1u << height}, data(size_ext << 1), que(size_ext << 1) {}

    segment_tree(const size_type n, const monoid &init) : segment_tree(n)
    {
        std::fill(std::next(std::begin(data), size_ext), std::end(data), init);
        for(size_type i{size_ext}; --i; ) recalc(i);
    }

    template <class iter_type, class value_type = typename std::iterator_traits<iter_type>::value_type>
    segment_tree(iter_type first, iter_type last)
        : size_orig(std::distance(first, last)), height(size_orig > 1 ? 32 - __builtin_clz(size_orig - 1) : 0), size_ext{1u << height}, data(size_ext << 1), que(size_ext << 1)
    {
        static_assert(std::is_constructible<monoid, value_type>::value, "monoid(iter_type::value_type) is not constructible.");
        for(auto iter{std::next(std::begin(data), size_ext)}; iter != std::end(data) && first != last; ++iter, ++first) *iter = monoid{*first};
        for(size_type i{size_ext}; --i; ) recalc(i);
    }

    template <class container_type, typename = typename container_type::value_type>
    segment_tree(const container_type &cont) : segment_tree(std::begin(cont), std::end(cont)) {}

    size_type size() const { return size_orig; }
    size_type capacity() const { return size_ext; }

    // reference to the element at the index.
    typename decltype(data)::reference operator[](size_type index)
    {
        assert(index < size_orig);
        que.push(index |= size_ext);
        return data[index];
    }

    // const reference to the element at the index.
    typename decltype(data)::const_reference operator[](size_type index) const
    {
        assert(index < size_orig);
        return data[index |= size_orig];
    }

    monoid fold(size_type first, size_type last)
    {
        assert(last <= size_orig);
        rebuild();
        monoid leftval{}, rightval{};
        first += size_ext, last += size_ext;
        while(first < last)
        {
            if(first & 1) leftval = leftval + data[first++];
            if(last & 1) rightval = data[--last] + rightval;
            first >>= 1, last >>= 1;
        }
        return leftval + rightval;
    }

    monoid fold() { return fold(0, size_orig); }

    template <class pred_type>
    size_type left_search(size_type right, const pred_type pred)
    {
        assert(right <= size_orig);
        rebuild();
        right += size_ext;
        monoid mono{};
        for(size_type left{size_ext}; left != right; left >>= 1, right >>= 1)
        {
            if((left & 1) != (right & 1))
            {
                const monoid tmp = data[--right] + mono;
                if(!pred(tmp)) return left_search_subtree(right, pred, mono);
                mono = tmp;
            }
        }
        return 0;
    }

    template <class pred_type>
    size_type right_search(size_type left, const pred_type pred)
    {
        assert(left <= size_orig);
        rebuild();
        left += size_ext;
        monoid mono{};
        for(size_type right{size_ext << 1}; left != right; left >>= 1, right >>= 1)
        {
            if((left & 1) != (right & 1))
            {
                const monoid tmp = mono + data[left];
                if(!pred(tmp)) return right_search_subtree(left, pred, mono);
                mono = tmp;
                ++left;
            }
        }
        return size_orig;
    }
}; // class segment_tree

#pragma endregion

struct solver; template <class> void main_(); int main() { main_<solver>(); }
template <class solver> void main_()
{
    unsigned t = 1;
#ifdef LOCAL
    t = 1;
#endif
    // t = -1; // infinite loop
    // cin >> t; // case number given

    while(t--) solver();
}

struct solver
{
    i64 n;

    double calc(vector<pair<double,double>> lines)
    {
        sort(begin(lines), end(lines));
        auto ok=[&](const double k)
        {
            vector<double> val;
            for(auto [x,y]: lines) val.emplace_back(x*k+y);
            sort(begin(val), end(val));
            segment_tree<int> seg(n);
            i64 cnt=0;
            for(auto [x,y]: lines)
            {
                double now=x*k+y;
                int ival=lower_bound(begin(val), end(val), now)-begin(val);
                cnt+=seg.fold(0,ival);
                seg[ival]++;
            }
            return cnt*2>=n*(n-1)/2;
        };
        return binary(1e6,-1e6,1e-9,ok);
    }

    solver() : n(read())
    {
        vector<pair<double,double>> lx,ly;
        for(int i=0; i<n; ++i)
        {
            int a=read(),b=read(),c=read();
            lx.emplace_back(double(-a)/b,double(c)/b);
            ly.emplace_back(double(-b)/a,double(c)/a);
        }
        cout<<calc(lx)<<" "<<calc(ly)<<endl;
    }
};