#ifndef LOCAL
#pragma GCC optimize("O3")
#endif
#include <bits/stdc++.h>
using namespace std;
#define R22(r) template <class c> typename enable_if<sizeof(dud<c>(0)) r,muu&>::type operator<<(c g)
template <class c> struct rge {c b, e;};
template <class c> rge<c> range(c i, c j) {return rge<c>{i, j};}
template <class c> auto dud(c*r)->decltype(cerr << *r);
template <class c> char dud(...);
struct muu {
	#ifdef LOCAL
	stringstream a;
	~muu() {cerr << a.str() << endl;}
	R22(>=2) {a << boolalpha << g; return *this;}
	R22(==1) {return *this << range(begin(g), end(g));}
	template <class c > muu & operator<<( rge<c> u) {
		a << "[";
		for (c i = u.b; i != u.e; ++i)
			*this << ", " + 2 * (i == u.b) << *i;
		return *this << "]";
	}
	template <class c, class m > muu & operator<<( pair <m,c> r) {return *this << "(" << r.first << ", " << r.second << ")";}
	#else
	template <class c > muu & operator<<( const c&){return *this;}
	#endif
	muu & operator()(){return *this;}
};
#define imie(r) "[" #r ": " << (r) << "] "
#define debug (muu() << __FUNCTION__ << "#" << __LINE__ << ": ")
template<typename T, typename S> pair<T, S> operator+(pair<T,S> a, pair<T,S>b) {return {a.first+b.first, a.second+b.second};}
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pld = pair<ld, ld>;
using pii = pair<int, int>;