base_form.cpp

#define FNAME ""

#include <bits/stdc++.h>

using namespace std;

#define tcT template <class T
#define tcTU tcT, class U

tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
tcT > using PR = pair<T, T>;

template<typename... T>
void see(T&... args) { ((cin >> args), ...);}
template<typename... T>
void put(T&&... args) { ((cout << args << " "), ...);}
template<typename... T>
void putl(T&&... args) { ((cout << args << " "), ...); cout<<'\n';}

#define el '\n'
#define sp ' '

#define int long long

//pair
#define st first
#define nd second
#define mp(a,b) make_pair(a,b)

// vector , data structure
#define bg(x) begin(x)
#define eb(x) emplace_back(x);
#define pb(x) push_back(x);
#define pf(x) push_front(x);
#define ph(x) push(x);
#define PB pop_back();
#define PF pop_front();
#define all(a) bg(a),end(a)
#define rall(a) a.rbegin(),a.rend()
#define sz(a) (int) a.size()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define mty empty()
#define ms(a,val) memset(a,val,sizeof(a))

#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T> &a, const T &b) { return (int)(lb(all(a), b) - bg(a)); }
tcT > int upb(V<T> &a, const T &b) { return (int)(ub(all(a), b) - bg(a)); }
// loops
#define fu(i,a,b) for(int i=a;i<=b;++i)
#define fd(i,a,b) for(int i=a;i>=b;--i)
#define f0u(i,b)  for(int i=0;i<b;++i)
#define f0d(i,b)  for(int i=(b)-1;i>=0;--i)
#define FU(i,a,b,x) for (int i=a;i<=b;i+=x)
#define FD(i,a,b,x) for (int i=a;i>=b;i-=x)
#define trav(a, x) for (auto &a : x)
#define fos(it,s) for(set<int> :: iterator it=s.begin(); it!=s.end();++it)

#define seea(a,x,y) fu(i,x,y) {cin>>a[i];}
#define seev(v,n) for(int i=0;i<n;i++){int x; cin>>x; v.push_back(x);}
#define sees(s,n) for(int i=0;i<n;i++){int x; cin>>x; s.insert(x);}

//# pragma GCC target("avx")
//# pragma GCC target("avx2")
//# pragma GCC target("fma")
//# pragma GCC optimize("Os")
//# pragma GCC optimize("Ofast")
//# pragma GCC optimization ("03")
//# pragma GCC optimization ("unroll-loops")

//datatypes
//using ll  = long long;
using str = string;
using db  = double;
using ldb = long double;
using ull = unsigned long long;
// pair , vector
using pii  = pair<int,int>;
using pd   = pair<db,db>;
using mii  = map<int,int>;
using vpi  = vector<pii>;
using vpd  = vector<pd>;
using vi   = vector<int>;
using vd   = vector<db>;
using vs   = vector<str>;
using vvi  = vector<vi>;
using vvd  = vector<vd>;

const int MOD=1e9+7;
const int N=2e5+5;
const ldb PI = acos((ldb)-1);
const int dx[4] = {1, 0, -1, 0},
          dy[4] = {0, 1, 0, -1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
template <class T> using pql = priority_queue<T, vector<T>, less<T>>;

tcT> long long add(T &a, const T b) { a+=b; return a>=MOD?a-MOD:a; } 

//math
tcT>inline T gcd(T a,T b) { while (b != 0) swap(b, a %= b); return a; }
tcT>inline T lcm(T a,T b) { return a / gcd(a, b) * b; }
tcT>inline tuple<T,T,T> extgcd(T a,T b) {
    if(a==0)return mt(b,0,1);
    T g,x,y;
	tie(g,x,y)=extgcd(b%a,a);
    return mt(g,y-(b/a)*x,x);
}
//bitwise
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int ctz(int x) { return __builtin_ctzll(x); }
constexpr int clz(int x) { return __builtin_clzll(x); }
constexpr int ffs(int x) { return __builtin_ffsll(x); }
constexpr int bits(int x) {  // assert(x >= 0); 
	return x == 0 ? 0 : 31 - __builtin_clz(x);
}  // floor(log2(x))
constexpr int pow2(int x) { return 1ll << (x); }
constexpr int msk2(int x) { return pow2(x) - 1; }

bool is_power2(int n){
    //return pct(n)==1;
    return n > 0 && (!(n & (n - 1)));
}

int cdiv(int a, int b) {
	return a / b + ((a ^ b) > 0 && a % b);
}  // divide a by b rounded up
int fdiv(int a, int b) {
	return a / b - ((a ^ b) < 0 && a % b);
}  // divide a by b rounded down

tcT > bool ckmin(T &a, const T &b) {
	return b < a ? a = b, 1 : 0;
}  // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }

tcTU > T fstTrue(T lo, T hi, U f) {
	hi++;
	assert(lo <= hi);  // assuming f is increasing
	while (lo < hi) {  // find first index such that f is true
		T mid = lo + ((hi - lo) >> 1);
		f(mid) ? hi = mid : lo = mid + 1;
	}
	return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
	lo--;
	assert(lo <= hi);  // assuming f is decreasing
	while (lo < hi) {  // find first index such that f is true
		T mid = lo + ((hi - lo + 1) >> 1);
		f(mid) ? lo = mid : hi = mid - 1;
	}
	return lo;
}
tcT > void remDup(vector<T> &v) {  // sort and remove duplicates
	sort(all(v));
	v.erase(unique(all(v)), end(v));
}
tcTU > void erase(T &t, const U &u) {  // don't erase
	auto it = t.find(u);
	assert(it != end(t));
	t.erase(it);
}  // element that doesn't exist from (multi)set

// INPUT
#define tcTUU tcT, class... U
tcT > void re(complex<T> &c);
tcTU > void re(pair<T, U> &p);
tcT > void re(V<T> &v);
tcT, size_t SZ > void re(AR<T, SZ> &a);

tcT > void re(T &x) { cin >> x; }
void re(db &d) {
	str t;
	re(t);
	d = stod(t);
}
void re(ldb &d) {
	str t;
	re(t);
	d = stold(t);
}
tcTUU > void re(T &t, U &...u) {
	re(t);
	re(u...);
}

tcT > void re(complex<T> &c) {
	T a, b;
	re(a, b);
	c = {a, b};
}
tcTU > void re(pair<T, U> &p) { re(p.f, p.s); }
tcT > void re(V<T> &x) { trav(a, x) re(a); }
tcT, size_t SZ > void re(AR<T, SZ> &x) { trav(a, x) re(a); }
tcT > void rv(int n, V<T> &x) {
	x.rsz(n);
	re(x);
}


// TO_STRING
#define ts to_string
str ts(char c) { return str(1, c); }
str ts(const char *s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
	return b ? "true" : "false";
#else
	return ts((int)b);
#endif
}
tcT > str ts(complex<T> c) {
	stringstream ss;
	ss << c;
	return ss.str();
}
str ts(V<bool> v) {
	str res = "{";
	fu(i,0, sz(v)) res += char('0' + v[i]);
	res += "}";
	return res;
}
template <size_t SZ> str ts(bitset<SZ> b) {
	str res = "";
	fu(i,0, SZ) res += char('0' + b[i]);
	return res;
}
tcTU > str ts(pair<T, U> p);
tcT > str ts(T v) {  // containers with begin(), end()
#ifdef LOCAL
	bool fst = 1;
	str res = "{";
	for (const auto &x : v) {
		if (!fst) res += ", ";
		fst = 0;
		res += ts(x);
	}
	res += "}";
	return res;
#else
	bool fst = 1;
	str res = "";
	for (const auto &x : v) {
		if (!fst) res += " ";
		fst = 0;
		res += ts(x);
	}
	return res;

#endif
}
tcTU > str ts(pair<T, U> p) {
#ifdef LOCAL
	return "(" + ts(p.f) + ", " + ts(p.s) + ")";
#else
	return ts(p.f) + " " + ts(p.s);
#endif
}

// OUTPUT
tcT > void pr(T x) { cout << ts(x); }
tcTUU > void pr(const T &t, const U &...u) {
	pr(t);
	pr(u...);
}
void ps() { pr("\n"); }  // print w/ spaces
tcTUU > void ps(const T &t, const U &...u) {
	pr(t);
	if (sizeof...(u)) pr(" ");
	ps(u...);
}

// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU > void DBG(const T &t, const U &...u) {
	cerr << ts(t);
	if (sizeof...(u)) cerr << ", ";
	DBG(u...);
}
#ifdef LOCAL  // compile with -DLOCAL, chk -> fake assert
#define dbg(...)                                                               \
	cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [",         \
	    DBG(__VA_ARGS__)
#define chk(...)                                                               \
	if (!(__VA_ARGS__))                                                        \
		cerr << "Line(" << __LINE__ << ") -> function(" << __FUNCTION__        \
		     << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")"                    \
		     << "\n",                                                          \
		    exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif


void setPrec(signed x) { cout << fixed << setprecision(x); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
// FILE I/O
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s) {
	unsyncIO(); //FAST
	//setPrec(2);
	// cin.exceptions(cin.failbit);
	// ex. try to read letter into int
	if (sz(s)>0) setIn(s + ".INP"), setOut(s + ".OUT");
}

signed main(signed argc, char *argv[]) {
    setIO(FNAME);
    return 0;
}