#include <bits/stdc++.h>
namespace __DEBUG_UTIL__
{
    using namespace std;
    template <typename T>
    concept is_iterable = requires(T &&x) { begin(x); } &&
                          !is_same_v<remove_cvref_t<T>, string>;
    void print(const char *x) { cerr << x; }
    void print(char x) { cerr << "\'" << x << "\'"; }
    void print(bool x) { cerr << (x ? "T" : "F"); }
    void print(string x) { cerr << "\"" << x << "\""; }
    void print(vector<bool> &v)
    { /* Overloaded this because stl optimizes vector<bool> by using
         _Bit_reference instead of bool to conserve space. */
        int f = 0;
        cerr << '{';
        for (auto &&i : v)
            cerr << (f++ ? "," : "") << (i ? "T" : "F");
        cerr << "}";
    }
    template <typename T>
    void print(T &&x)
    {
        if constexpr (is_iterable<T>)
            if (size(x) && is_iterable<decltype(*(begin(x)))>)
            { /* Iterable inside Iterable */
                int f = 0;
                cerr << "\n~~~~~\n";
                for (auto &&i : x)
                {
                    cerr << setw(2) << left << f++, print(i), cerr << "\n";
                }
                cerr << "~~~~~\n";
            }
            else
            { /* Normal Iterable */
                int f = 0;
                cerr << "{";
                for (auto &&i : x)
                    cerr << (f++ ? "," : ""), print(i);
                cerr << "}";
            }
        else if constexpr (requires { x.pop(); }) /* Stacks, Priority Queues, Queues */
        {
            auto temp = x;
            int f = 0;
            cerr << "{";
            if constexpr (requires { x.top(); })
                while (!temp.empty())
                    cerr << (f++ ? "," : ""), print(temp.top()), temp.pop();
            else
                while (!temp.empty())
                    cerr << (f++ ? "," : ""), print(temp.front()), temp.pop();
            cerr << "}";
        }
        else if constexpr (requires { x.first; x.second; }) /* Pair */
        {
            cerr << '(', print(x.first), cerr << ',', print(x.second), cerr << ')';
        }
        else if constexpr (requires { get<0>(x); }) /* Tuple */
        {
            int f = 0;
            cerr << '(', apply([&f](auto... args)
                               { ((cerr << (f++ ? "," : ""), print(args)), ...); },
                               x);
            cerr << ')';
        }
        else
            cerr << x;
    }
    template <typename T, typename... V>
    void printer(const char *names, T &&head, V &&...tail)
    {
        int i = 0;
        for (size_t bracket = 0; names[i] != '\0' and (names[i] != ',' or bracket != 0); i++)
            if (names[i] == '(' or names[i] == '<' or names[i] == '{')
                bracket++;
            else if (names[i] == ')' or names[i] == '>' or names[i] == '}')
                bracket--;
        cerr.write(names, i) << " = ";
        print(head);
        if constexpr (sizeof...(tail))
            cerr << " ||", printer(names + i + 1, tail...);
        else
            cerr << "]\n";
    }
    template <typename T, typename... V>
    void printerArr(const char *names, T arr[], size_t N, V... tail)
    {
        size_t i = 0;
        for (; names[i] and names[i] != ','; i++)
            cerr << names[i];
        for (i++; names[i] and names[i] != ','; i++)
            ;
        cerr << " = {";
        for (size_t ind = 0; ind < N; ind++)
            cerr << (ind ? "," : ""), print(arr[ind]);
        cerr << "}";
        if constexpr (sizeof...(tail))
            cerr << " ||", printerArr(names + i + 1, tail...);
        else
            cerr << "]\n";
    }

}
#ifdef ONLINE_JUDGE
#define dbg(...)
#define dbgArr(...)
#else
#define dbg(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printer(#__VA_ARGS__, __VA_ARGS__)
#define dbgArr(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printerArr(#__VA_ARGS__, __VA_ARGS__)
#endif