Template

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#include <bits/stdc++.h>
using namespace std;
 
namespace Config
{
    bool USACO = false;
    const string USACO_IO = "shell";
 
    bool TEST_CASES = false;

    inline constexpr bool STDERR_ON_SERVER = false;
}
 
#ifdef LOCAL
const int INF = INT32_MAX - 10;
#endif // LOCAL
 
#ifndef LOCAL
const long long INF = LLONG_MAX - 10;
#define int long long
#endif // LOCAL
 
struct Coordinate
{
    int x, y;
 
    static void sortByX(vector<Coordinate*>& vec)
    {
        sort(vec.begin(), vec.end(), [](Coordinate* a, Coordinate* b) {
            return a->x < b->x;
        });
    }
 
    static void sortByY(vector<Coordinate*>& vec)
    {
        sort(vec.begin(), vec.end(), [](Coordinate* a, Coordinate* b) {
            return a->y < b->y;
        });
    }
};
 
struct Rect
{
    int x1, y1, x2, y2;
 
    friend ostream& operator<<(ostream& os, const Rect& rect)
    {
        return os << rect.x1 << ' ' << rect.y1 << ' ' << rect.x2 << ' ' << rect.y2;
    }
 
    friend istream& operator>>(istream& is, Rect& rect)
    {
        return is >> rect.x1 >> rect.y1 >> rect.x2 >> rect.y2;
    }
};
 
void cartesianPrint(int* arr, int rows, int cols) {
    for (int y = rows - 1; y >= 0; --y) {
        cerr << setw(3) << y << " | ";
        for (int x = 0; x < cols; ++x) {
            cerr << setw(3) << setfill(' ') << arr[y * cols + x] << ' ';
        }
        cerr << '\n';
    } cerr << "    ";
 
    for (int x = 0; x < cols; ++x) {
        cerr << "----";
    } cerr << '\n'; cerr << "     ";
    for (int x = 0; x < cols; ++x) {
        cerr << setw(3) << x << ' ';
    }
    cerr << '\n';
}
 
long long max(signed x, long long y) { return max((long long) x, y); }
long long max(long long y, signed x) { return max((long long) x, y); }
 
const vector<pair<int, int>> dirs = {
    {1, 0}, {0, 1}, {-1, 0}, {0, -1},
    {1, 1}, {-1, 1}, {-1, -1}, {1, -1}
};
const int MOD = 1000000007;

struct NullDebug {
    template <class T>
    constexpr NullDebug& operator<<(T&&) noexcept { return *this; }
    constexpr NullDebug& operator<<(std::ostream& (*)(std::ostream&)) noexcept { return *this; }
    constexpr NullDebug& operator<<(std::ios_base& (*)(std::ios_base&)) noexcept { return *this; }
};
class RealDebug {
public:
    RealDebug()
#if defined(LOCAL)
        : out(std::cout)
#else
        : out(std::cerr)
#endif
    {}

    template <class T>
    RealDebug& operator<<(const T& v) {
        if (at_line_start) { out << "\tdebug: "; at_line_start = false; }
        out << v;
        return *this;
    }

    RealDebug& operator<<(std::ostream& (*manip)(std::ostream&)) {
        // avoid endl flush
        if (manip == static_cast<std::ostream& (*)(std::ostream&)>(std::endl)) {
            out << '\n';
            at_line_start = true;
        } else {
            if (at_line_start) { out << "\tdebug: "; at_line_start = false; }
            out << manip;
        }
        return *this;
    }

    RealDebug& operator<<(std::ios_base& (*manip)(std::ios_base&)) {
        if (at_line_start) { out << "\tdebug: "; at_line_start = false; }
        out << manip;
        return *this;
    }

private:
    std::ostream& out;
    bool at_line_start = true;
};
#if Config::STDERR_ON_SERVER
inline RealDebug debug;
#else
inline NullDebug debug;
#endif

signed main(signed argc, char** args)
{
    void solve();
 
    #ifdef LOCAL
        cout << "Code running w/ test cases locally" << endl;
        cout << "Is USACO mode on? " << (Config::USACO ? "True" : "False");
        if (Config::USACO) cout << "\twill read from " << Config::USACO_IO << ".in";
        cout << endl;
        cout << "Multi-test-cases on? " << (Config::TEST_CASES ? "True" : "False") << "\n\n";
        
        // freopen("shell.txt", "r", stdin)
        // note: freopen deleted for using designated competitive programming editor
    #endif // LOCAL
 
    #ifndef LOCAL
        if (Config::USACO)
        {
            freopen((Config::USACO_IO + ".in").c_str(), "r", stdin);
            freopen((Config::USACO_IO + ".out").c_str(), "w", stdout);
        }

        if (Config::STDERR_ON_SERVER == false)
            cerr << "stderr on server is off" << endl;
 
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout.tie(nullptr);
    #endif // LOCAL
 
    if (Config::TEST_CASES)
    {
        int test_cases_numbers_main; cin >> test_cases_numbers_main;
        for (int test_case_main = 0; test_case_main < test_cases_numbers_main; test_case_main++)
            solve();
    }
    else
        solve();
 
    return 0;
}

constexpr int N1E5 = 100005;
constexpr int N1E6 = 1000006;
constexpr int N1E9 = 1000000009;
/*------------------------------------------------------------------------*/
 

 
void solve()
{
    
}