#include <bits/stdc++.h>
using namespace std;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
namespace debugger {
#ifdef EMOFUNC
    template <typename T>
    void __print_var(string_view name, const T & x) { std::cerr << name << " = " << x; }
    template <typename T>
    void __print_var(string_view name, const vector<T>& x) {
        std::cerr << name << " = ";
        bool is_first = true;
        for (auto & ele : x) std::cerr << (is_first ? (is_first = false, "[") : ", ") << ele;
        std::cerr << "]";
    }
    template <typename T>
    void __print_var(string_view name, const set<T>& x) {
        std::cerr << name << " = ";
        bool is_first = true;
        for (auto & ele : x) std::cerr << (is_first ? (is_first = false, "{") : ", ") << ele;
        std::cerr << "}";
    }
    template <typename K, typename V>
    void __print_var(string_view name, const map<K, V>& x) {
        std::cerr << name << " = ";
        bool is_first = true;
        for (auto & [k, v] : x) std::cerr << (is_first ? (is_first = false, "{") : ", ") << "(" << k << ": " << v << ")";
        std::cerr << "}";
    }
    template <typename T>
    void __log(string_view name, const T & x) {
        __print_var(name, x); std::cerr << std::endl;
    }
    template <typename T, typename... Ts>
    void __log(string_view name, const T & x, const Ts&... others) {
        size_t pos = name.find(',');
        __print_var(name.substr(0, pos), x); std::cerr << ", ";
        __log(name.substr(pos + 1), others...);
    }

#define LOG(args...)\
    { std::cerr << "line " << __LINE__ << ": " << __func__ << "(): ";\
    __log(#args, ##args); }
#else
#define LOG(...)
#endif
}
#define x first
#define y second
#define dbg(a)  cout<<#a<<" : "<<a<<endl;
#define IOS std::ios::sync_with_stdio(false);cin.tie(0),cout.tie(0);
#define rep(i , a , b) for (int i = a ; i <= b ; i ++ )
#define pre(i , a , b) for (int i = b ; i >= a ; i -- )
using namespace debugger;
typedef long long LL;
typedef pair<int , int> PII;
const int N = 100010;
const int inf = 0x3f3f3f3f;
const double eps = 1e-6;
const int MOD = 1e9 + 7;
int dx[] = {-1 , 0 , 1 , 0} , dy[] = {0 , 1 , 0 , -1};
int a[N];
inline void solve() {

}

int main() {
    //freopen("./input.txt" , "r" , stdin);
    solve();
    return 0;
}