結果
| 問題 | No.798 コレクション |
| ユーザー |
 バイト
|
| 提出日時 | 2019-03-15 22:49:43 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 40 ms / 2,000 ms |
| コード長 | 59,944 bytes |
| コンパイル時間 | 4,012 ms |
| コンパイル使用メモリ | 246,072 KB |
| 実行使用メモリ | 34,944 KB |
| 最終ジャッジ日時 | 2024-07-01 21:22:06 |
| 合計ジャッジ時間 | 5,009 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,816 KB |
| testcase_01 | AC | 2 ms
6,940 KB |
| testcase_02 | AC | 2 ms
6,940 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 2 ms
6,944 KB |
| testcase_05 | AC | 2 ms
6,940 KB |
| testcase_06 | AC | 2 ms
6,940 KB |
| testcase_07 | AC | 2 ms
6,944 KB |
| testcase_08 | AC | 2 ms
6,940 KB |
| testcase_09 | AC | 2 ms
6,944 KB |
| testcase_10 | AC | 2 ms
6,940 KB |
| testcase_11 | AC | 2 ms
6,940 KB |
| testcase_12 | AC | 2 ms
6,944 KB |
| testcase_13 | AC | 18 ms
17,280 KB |
| testcase_14 | AC | 29 ms
25,728 KB |
| testcase_15 | AC | 25 ms
22,528 KB |
| testcase_16 | AC | 13 ms
12,416 KB |
| testcase_17 | AC | 19 ms
17,920 KB |
| testcase_18 | AC | 38 ms
33,024 KB |
| testcase_19 | AC | 30 ms
27,008 KB |
| testcase_20 | AC | 13 ms
12,544 KB |
| testcase_21 | AC | 12 ms
11,520 KB |
| testcase_22 | AC | 25 ms
22,528 KB |
| testcase_23 | AC | 2 ms
6,944 KB |
| testcase_24 | AC | 40 ms
34,944 KB |
| testcase_25 | AC | 40 ms
34,944 KB |
ソースコード
//#pragma GCC optimize ("-O3")
#include <bits/stdc++.h>
using namespace std;
//@起動時
struct initon {
initon() {
cin.tie(0);
ios::sync_with_stdio(false);
cout.setf(ios::fixed);
cout.precision(16);
srand((unsigned) clock() + (unsigned) time(NULL));
};
} __initon;
//衝突対策
#define ws ___ws
//@必須構造
struct T {
int f, s, t;
T() { f = -1, s = -1, t = -1; }
T(int f, int s, int t) : f(f), s(s), t(t) {}
bool operator<(const T &r) const {
return f != r.f ? f < r.f : s != r.s ? s < r.s : t < r.t;
//return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 大きい順
}
bool operator>(const T &r) const {
return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t;
//return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 小さい順
}
bool operator==(const T &r) const {
return f == r.f && s == r.s && t == r.t;
}
bool operator!=(const T &r) const {
return f != r.f || s != r.s || t != r.t;
}
int operator[](int i) {
assert(i < 3);
return i == 0 ? f : i == 1 ? s : t;
}
};
struct F {
int a, b, c, d;
F() { a = -1, b = -1, c = -1, d = -1; }
F(int a, int b, int c, int d) : a(a), b(b), c(c), d(d) {}
bool operator<(const F &r) const {
return a != r.a ? a < r.a : b != r.b ? b < r.b : c != r.c ? c < r.c : d < r.d;
// return a != r.a ? a > r.a : b != r.b ? b > r.b : c != r.c ? c > r.c : d > r.d;
}
bool operator>(const F &r) const {
return a != r.a ? a > r.a : b != r.b ? b > r.b : c != r.c ? c > r.c : d > r.d;
// return a != r.a ? a < r.a : b != r.b ? b < r.b : c != r.c ? c < r.c : d < r.d;
}
bool operator==(const F &r) const {
return a == r.a && b == r.b && c == r.c && d == r.d;
}
bool operator!=(const F &r) const {
return a != r.a || b != r.b || c != r.c || d != r.d;
}
int operator[](int i) {
assert(i < 4);
return i == 0 ? a : i == 1 ? b : i == 2 ? c : d;
}
};
T mt(int a, int b, int c) {
return T(a, b, c);
}
//@マクロ省略系 型,構造
#define int long long
#define ll long long
#define double long double
#define ull unsigned long long
using dou = double;
using itn = int;
using str = string;
using bo= bool;
using P = pair<ll, ll>;
#define fi first
#define se second
#define vec vector
#define beg begin
#define rbeg rbegin
#define con continue
#define bre break
#define brk break
#define is ==
//マクロ省略系 コンテナ
using vi = vector<int>;
#define _overloadvvi(_1, _2, _3, _4, name, ...) name
#define vvi1(a) vec<vi> a
#define vvi2(a, b) vec<vi> a(b)
#define vvi3(a, b, c) vec<vi> a(b,vi(c))
#define vvi4(a, b, c, d) vec<vi> a(b,vi(c,d))
#define vvi(...) _overloadvvi(__VA_ARGS__,vvi4,vvi3,vvi2 ,vvi1)(__VA_ARGS__)
using vl = vector<ll>;
#define _overloadvvl(_1, _2, _3, _4, name, ...) name
#define vvl1(a) vec<vl> a
#define vvl2(a, b) vec<vl> a(b)
#define vvl3(a, b, c) vec<vl> a(b,vl(c))
#define vvl4(a, b, c, d) vec<vl> a(b,vl(c,d))
#define vvl(...) _overloadvvl(__VA_ARGS__,vvl4,vvl3,vvl2 ,vvl1)(__VA_ARGS__)
using vb = vector<bool>;
#define _overloadvvb(_1, _2, _3, _4, name, ...) name
#define vvb1(a) vec<vb> a
#define vvb2(a, b) vec<vb> a(b)
#define vvb3(a, b, c) vec<vb> a(b,vb(c))
#define vvb4(a, b, c, d) vec<vb> a(b,vb(c,d))
#define vvb(...) _overloadvvb(__VA_ARGS__,vvb4,vvb3,vvb2 ,vvb1)(__VA_ARGS__)
using vs = vector<string>;
#define _overloadvvs(_1, _2, _3, _4, name, ...) name
#define vvs1(a) vec<vs> a
#define vvs2(a, b) vec<vs> a(b)
#define vvs3(a, b, c) vec<vs> a(b,vs(c))
#define vvs4(a, b, c, d) vec<vs> a(b,vs(c,d))
#define vvs(...) _overloadvvs(__VA_ARGS__,vvs4,vvs3,vvs2 ,vvs1)(__VA_ARGS__)
using vd = vector<double>;
#define _overloadvvd(_1, _2, _3, _4, name, ...) name
#define vvd1(a) vec<vd> a
#define vvd2(a, b) vec<vd> a(b)
#define vvd3(a, b, c) vec<vd> a(b,vd(c))
#define vvd4(a, b, c, d) vec<vd> a(b,vd(c,d))
#define vvd(...) _overloadvvd(__VA_ARGS__,vvd4,vvd3,vvd2 ,vvd1)(__VA_ARGS__)
using vc=vector<char>;
#define _overloadvvc(_1, _2, _3, _4, name, ...) name
#define vvc1(a) vec<vc> a
#define vvc2(a, b) vec<vc> a(b)
#define vvc3(a, b, c) vec<vc> a(b,vc(c))
#define vvc4(a, b, c, d) vec<vc> a(b,vc(c,d))
#define vvc(...) _overloadvvc(__VA_ARGS__,vvc4,vvc3,vvc2 ,vvc1)(__VA_ARGS__)
using vp = vector<P>;
#define _overloadvvp(_1, _2, _3, _4, name, ...) name
#define vvp1(a) vec<vp> a
#define vvp2(a, b) vec<vp> a(b)
#define vvp3(a, b, c) vec<vp> a(b,vp(c))
#define vvp4(a, b, c, d) vec<vp> a(b,vp(c,d))
using vt = vector<T>;
#define _overloadvvt(_1, _2, _3, _4, name, ...) name
#define vvt1(a) vec<vt> a
#define vvt2(a, b) vec<vt> a(b)
#define vvt3(a, b, c) vec<vt> a(b,vt(c))
#define vvt4(a, b, c, d) vec<vt> a(b,vt(c,d))
#define v3i(a, b, c, d) vector<vector<vi>> a(b, vector<vi>(c, vi(d)))
#define v3d(a, b, c, d) vector<vector<vd>> a(b, vector<vd>(c, vd(d)))
#define v3m(a, b, c, d) vector<vector<vm>> a(b, vector<vm>(c, vm(d)))
#define _vvi vector<vi>
#define _vvl vector<vl>
#define _vvb vector<vb>
#define _vvs vector<vs>
#define _vvd vector<vd>
#define _vvc vector<vc>
#define _vvp vector<vp>
#define PQ priority_queue<ll, vector<ll>, greater<ll> >
#define tos to_string
using mapi = map<int, int>;
using mapd = map<dou, int>;
using mapc = map<char, int>;
using maps = map<str, int>;
using seti = set<int>;
using setd = set<dou>;
using setc = set<char>;
using sets = set<str>;
using qui = queue<int>;
#define bset bitset
#define uset unordered_set
#define mset multiset
#define umap unordered_map
#define umapi unordered_map<int,int>
#define umapp unordered_map<P,int>
#define mmap multimap
//マクロ 繰り返し
#define _overloadrep(_1, _2, _3, _4, name, ...) name
# define _rep(i, n) for(int i = 0,_lim=n; i < _lim ; i++)
#define repi(i, m, n) for(int i = m,_lim=n; i < _lim ; i++)
#define repadd(i, m, n, ad) for(int i = m,_lim=n; i < _lim ; i+= ad)
#define rep(...) _overloadrep(__VA_ARGS__,repadd,repi,_rep,)(__VA_ARGS__)
#define _rer(i, n) for(int i = n; i >= 0 ; i--)
#define reri(i, m, n) for(int i = m,_lim=n; i >= _lim ; i--)
#define rerdec(i, m, n, dec) for(int i = m,_lim=n; i >= _lim ; i-=dec)
#define rer(...) _overloadrep(__VA_ARGS__,rerdec,reri,_rer,)(__VA_ARGS__)
#define fora(a, b) for(auto&& a : b)
#define forg(gi, ve) for (int gi = 0, f, t, c; gi < ve.size() && (f = ve[gi].from, t = ve[gi].to, c = ve[gi].cost, true); gi++)
#define fort(gi, ve) for (int gi = 0, f, t, c;gi<ve.size()&& (gi+= (ve[gi].to==p))< ve.size() && (f = ve[gi].from,t=ve[gi].to, c = ve[gi].cost,true); gi++)
//マクロ 定数
#define k3 1010
#define k4 10101
#define k5 101010
#define k6 1010101
#define k7 10101010
const int inf = (int) 1e9 + 100;
const ll linf = (ll) 1e18 + 100;
const double eps = 1e-9;
const double PI = 3.1415926535897932384626433832795029L;
const int y4[] = {-1, 1, 0, 0};
const int x4[] = {0, 0, -1, 1};
const int y8[] = {0, 1, 0, -1, -1, 1, 1, -1};
const int x8[] = {1, 0, -1, 0, 1, -1, 1, -1};
//マクロ省略形 関数等
#define arsz(a) (sizeof(a)/sizeof(a[0]))
#define sz(a) ((int)(a).size())
#define rs resize
#define mp make_pair
#define pb push_back
#define pf push_front
#define eb emplace_back
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
//@拡張系 こう出来るべきというもの
//埋め込み 存在を意識せずに機能を増やされているもの
namespace std {
template<> class hash<std::pair<signed, signed>> {
public:
size_t operator()(const std::pair<signed, signed> &x) const {
return hash<ll>()(((ll) x.first << 32) + x.second);
}
};
template<> class hash<std::pair<ll, ll>> {
public:
//大きいllが渡されると、<<32でオーバーフローするがとりあえず問題ないと判断
size_t operator()(const std::pair<ll, ll> &x) const {
return hash<ll>()(((ll) x.first << 32) + x.second);
}
};
}
istream &operator>>(istream &iss, P &a) {
iss >> a.first >> a.second;
return iss;
}
template<typename T> istream &operator>>(istream &iss, vector<T> &vec) {
for (T &x: vec) iss >> x;
return iss;
}
ostream &operator<<(ostream &os, P p) {
os << p.fi << " " << p.se << endl;
return os;
}
ostream &operator<<(ostream &os, T p) {
os << p.f << " " << p.s << " " << p.t;
return os;
}
ostream &operator<<(ostream &os, F p) {
os << p.a << " " << p.b << " " << p.c << " " << p.d;
return os;
}
template<typename T> ostream &operator<<(ostream &os, vector <T> &vec) {
for (int i = 0; i < vec.size(); i++)os << vec[i] << (i + 1 == vec.size() ? "" : " ");
return os;
}
template<typename T> ostream &operator<<(ostream &os, vector <vector<T>> &vec) {
for (int i = 0; i < vec.size(); i++) {
for (int j = 0; j < vec[0].size(); j++) {
os << vec[i][j];
}
os << endl;
}
return os;
}
template<typename V, typename H> void resize(vector<V> &vec, const H head) { vec.resize(head); }
template<typename V, typename H, typename ... T> void resize(vector<V> &vec, const H &head, const T ... tail) {
vec.resize(head);
for (auto &v: vec) resize(v, tail...);
}
template<class T> T pop(set<T> &set) {
T res = *set.begin();
set.erase(set.find(res));
return res;
}
template<class T> T pop(mset<T> &set) {
T res = *set.begin();
set.erase(set.find(res));
return res;
}
template<class T> T popBack(set<T> &set) {
T res = *set.rbegin();
set.erase(set.find(res));
return res;
}
template<class T> T popBack(mset<T> &set) {
T res = *set.rbegin();
set.erase(set.find(res));
return res;
}
inline void sort(string &a) { sort(a.begin(), a.end()); }
template<class T> inline void sort(vector<T> &a) { sort(a.begin(), a.end()); };
template<class T> inline void sort(vector<T> &a, int len) { sort(a.begin(), a.begin() + len); };
template<class T, class F> inline void sort(vector<T> &a, F f) { sort(a.begin(), a.end(), [&](T l, T r) { return f(l) < f(r); }); };
enum ___pcomparator {
fisi, fisd, fdsi, fdsd, sifi, sifd, sdfi, sdfd
};
inline void sort(vector<P> &a, ___pcomparator type) {
switch (type) {
case fisi:
sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi < r.fi : l.se < r.se; });
break;
case fisd:
sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi < r.fi : l.se > r.se; });
break;
case fdsi:
sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi > r.fi : l.se < r.se; });
break;
case fdsd:
sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi > r.fi : l.se > r.se; });
break;
case sifi:
sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se < r.se : l.fi < r.fi; });
break;
case sifd:
sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se < r.se : l.fi > r.fi; });
break;
case sdfi:
sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se > r.se : l.fi < r.fi; });
break;
case sdfd:
sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se > r.se : l.fi > r.fi; });
break;
}
};
template<class T> inline void rsort(vector<T> &a) { sort(a.begin(), a.end(), greater<T>()); };
template<class T> inline void rsort(vector<T> &a, int len) { sort(a.begin(), a.begin() + len, greater<T>()); };
template<class U, class F> inline void rsort(vector<U> &a, F f) { sort(a.begin(), a.end(), [&](U l, U r) { return f(l) > f(r); }); };
template<class U> inline void sortp(vector<U> &a, vector<U> &b) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
sort(c);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;;
}
};
//F = T<T>
//例えばreturn p.fi + p.se;
template<class U, class F> inline void sortp(vector<U> &a, vector<U> &b, F f) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
sort(c, f);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;
}
};
template<class U, class F> inline void sortp(vector<U> &a, vector<U> &b, char type) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
sort(c, type);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;
}
};
template<class U, class F> inline void rsortp(vector<U> &a, vector<U> &b) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
rsort(c);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;
}
};
template<class U, class F> inline void rsortp(vector<U> &a, vector<U> &b, F f) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
rsort(c, f);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;
}
};
template<class U> inline void sortt(vector<U> &a, vector<U> &b, vector<U> &c) {
vt r;
int n = sz(a);
assert(n == sz(b));
assert(n == sz(c));
rep(i, n)r.eb(a[i], b[i], c[i]);
sort(r);
rep(i, n) {
a[i] = r[i].f;
b[i] = r[i].s;
c[i] = r[i].t;
}
};
template<class U, class F> inline void sortt(vector<U> &a, vector<U> &b, vector<U> &c, F f) {
vt r;
int n = sz(a);
assert(n == sz(b));
assert(n == sz(c));
rep(i, n)r.eb(a[i], b[i], c[i]);
sort(r, f);
rep(i, n) {
a[i] = r[i].f;
b[i] = r[i].s;
c[i] = r[i].t;
}
};
template<class U, class F> inline void rsortt(vector<U> &a, vector<U> &b, vector<U> &c, F f) {
vt r;
int n = sz(a);
assert(n == sz(b));
assert(n == sz(c));
rep(i, n)r.eb(a[i], b[i], c[i]);
rsort(r, f);
rep(i, n) {
a[i] = r[i].f;
b[i] = r[i].s;
c[i] = r[i].t;
}
};
template<class T> inline void sort2(vector<vector<T>> &a) { for (int i = 0, n = a.size(); i < n; i++)sort(a[i]); }
template<class T> inline void rsort2(vector<vector<T>> &a) { for (int i = 0, n = a.size(); i < n; i++)rsort(a[i]); }
template<typename A, size_t N, typename T> void fill(A (&a)[N], const T &v) { rep(i, N)a[i] = v; }
template<typename A, size_t N, size_t O, typename T> void fill(A (&a)[N][O], const T &v) { rep(i, N)rep(j, O)a[i][j] = v; }
template<typename A, size_t N, size_t O, size_t P, typename T> void fill(A (&a)[N][O][P], const T &v) { rep(i, N)rep(j, O)rep(k, P)a[i][j][k] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, typename T> void fill(A (&a)[N][O][P][Q], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)a[i][j][k][l] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, typename T> void fill(A (&a)[N][O][P][Q][R], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)a[i][j][k][l][m] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, size_t S, typename T> void fill(A (&a)[N][O][P][Q][R][S], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)rep(n, S)a[i][j][k][l][m][n] = v; }
template<typename V, typename T>
void fill(V &xx, const T vall) {
xx = vall;
}
template<typename V, typename T>
void fill(vector<V> &vecc, const T vall) {
for (auto &&vx: vecc) fill(vx, vall);
}
//@汎用便利関数 入力
template<typename T = int> T in() {
T x;
cin >> x;
return (x);
}
string sin() { return in<string>(); }
double din() { return in<double>(); }
ll lin() { return in<ll>(); }
#define na(a, n) a.resize(n); rep(i,n) cin >> a[i];
#define nao(a, n) a.resize(n+1); rep(i,n) cin >> a[i+1];
#define nad(a, n) a.resize(n); rep(i,n) cin >> a[i], a[i]--;
#define na2(a, b, n) a.resize(n),b.resize(n);rep(i, n)cin >> a[i] >> b[i];
#define na2d(a, b, n) a.resize(n),b.resize(n);rep(i, n)cin >> a[i] >> b[i],a[i]--,b[i]--;
#define na3(a, b, c, n) a.resize(n),b.resize(n),c.resize(n); rep(i, n)cin >> a[i] >> b[i] >> c[i];
#define na3d(a, b, c, n) a.resize(n),b.resize(n),c.resize(n); rep(i, n)cin >> a[i] >> b[i] >> c[i],a[i]--,b[i]--,c[i]--;
#define nt(a, h, w) resize(a,h,w);rep(hi,h)rep(wi,w) cin >> a[hi][wi];
#define ntd(a, h, w) rs(a,h,w);rep(hi,h)rep(wi,w) cin >> a[hi][wi], a[hi][wi]--;
#define ntp(a, h, w) fill(a,'#');rep(hi,1,h+1)rep(wi,1,w+1) cin >> a[hi][wi];
//汎用便利関数 出力
template<class T> void out(T x) { typeid(x) == typeid(double) ? cout << fixed << setprecision(10) << x << endl : cout << x << endl; }
template<class T> void out(vector<T> a) {
fora(v, a)cout << v << endl;
}
//デバッグ
#define sp << " " <<
#define debugName(VariableName) # VariableName
#define _deb1(x) cerr << debugName(x)<<" = "<<x << endl
#define _deb2(x, y) cerr << debugName(x)<<" = "<<x<<", "<< debugName(y)<<" = "<<y<< endl
#define _deb3(x, y, z) cerr << debugName(x)<<" = "<<x << ", " << debugName(y)<<" = "<<y <<", " debugName(z)<<" = "<<z <<endl
#define _deb4(x, y, z, a) cerr << debugName(x)<<" = "<<x <<", " << debugName(y)<<" = "<<y <<", " << debugName(z)<<" = "<<z <<", " << debugName(a)<<" = "<<a<<endl
#define _deb5(x, y, z, a, b) cerr << debugName(x)<<" = "<<x <<", " << debugName(y)<<" = "<<y <<", " << debugName(z)<<" = "<<z <<", " << debugName(a)<<" = "<<a<<", " << debugName(b)<<" = "<<b<<endl
#define _overloadebug(_1, _2, _3, _4, _5, name, ...) name
#define debug(...) _overloadebug(__VA_ARGS__,_deb5,_deb4,_deb3,_deb2,_deb1)(__VA_ARGS__)
#define deb(...) _overloadebug(__VA_ARGS__,_deb5,_deb4,_deb3,_deb2,_deb1)(__VA_ARGS__)
#define debugline(x) cerr << x << " " << "(L:" << __LINE__ << ")" << '\n'
//よく使うクラス、構造体
class UnionFind {
public:
vi par, rank, sizes;
int n, trees;
UnionFind(int n) : n(n), trees(n) {
par.resize(n), rank.resize(n), sizes.resize(n);
rep(i, n)par[i] = i, sizes[i] = 1;
}
int root(int x) {
if (par[x] == x)return x;
else return par[x] = root(par[x]);
}
int find(int x) { return root(x); }
void unite(int x, int y) {
x = root(x);
y = root(y);
if (x == y)return;
if (rank[x] < rank[y])swap(x, y);
trees--;
par[y] = x;
sizes[x] += sizes[y];
if (rank[x] == rank[y])rank[x]++;
}
bool same(int x, int y) { return root(x) == root(y); }
int size(int x) { return sizes[root(x)]; }
//順不同 umapなので
vec<vi> sets() {
vec<vi> res(trees);
umap<int, vi> map;
rep(i, n) map[root(i)].push_back(i);
int i = 0;
for (auto &&p:map) {
int r = p.fi;
res[i].push_back(r);
for (auto &&v:p.se) {
if (r == v)continue;
res[i].push_back(v);
}
i++;
}
return res;
}
};
//MOD関連
ll MOD = (int) 1e9 + 7;
class mint {
public:
int x;
mint() : x(0) {}
mint(signed y) : x(y >= 0 ? y % MOD : MOD - (-y) % MOD) {}
mint(int y) : x(y >= 0 ? y % MOD : MOD - (-y) % MOD) {}
static int _mpow(int v, ll a) {
ll x = v, n = a, res = 1;
while (n) {
if (n & 1)res = (res * x) % MOD;
x = (x * x) % MOD;
n >>= 1;
}
return res;
}
// Arithmetic Oprators
mint &operator+=(mint that) {
if ((x += that.x) >= MOD) x -= MOD;
return *this;
}
mint &operator-=(mint that) {
if ((x += MOD - that.x) >= MOD) x -= MOD;
return *this;
}
mint &operator*=(mint that) {
x = 1LL * x * that.x % MOD;
return *this;
}
mint &operator/=(const mint &that);
mint &operator^=(const mint &that) {
this->x = _mpow(x, that.x);
return *this;
}
mint &operator%=(mint that) {
x %= that.x;
return *this;
}
mint &operator+=(const int that) { return *this += mint(that); }
mint &operator-=(const int that) { return *this -= mint(that); }
mint &operator*=(const int that) { return *this *= mint(that); }
mint &operator/=(const int that);
mint &operator^=(const int that) {
this->x = _mpow(x, that);
return *this;
}
mint &operator%=(const int that) { return *this %= mint(that); }
mint &operator+=(const signed that) { return *this += mint(that); }
mint &operator-=(const signed that) { return *this -= mint(that); }
mint &operator*=(const signed that) { return *this *= mint(that); }
mint &operator/=(const signed that);
mint &operator^=(const signed that) {
this->x = _mpow(x, that);
return *this;
}
mint &operator%=(const signed that) { return *this %= mint(that); }
// Comparators
bool operator<(mint that) { return x < that.x; }
bool operator>(mint that) { return x > that.x; }
bool operator<=(mint that) { return x <= that.x; }
bool operator>=(mint that) { return x >= that.x; }
bool operator!=(mint that) { return x != that.x; }
bool operator==(mint that) { return x == that.x; }
bool operator!=(int that) { return x != that; }
bool operator==(int that) { return x == that; }
bool operator!=(signed that) { return x != that; }
bool operator==(signed that) { return x == that; }
// Utilities
unsigned getval() const { return x; }
operator int() { return x; }
mint operator+(mint that) const { return mint(*this) += that; }
mint operator-(mint that) const { return mint(*this) -= that; }
mint operator*(mint that) const { return mint(*this) *= that; }
mint operator%(mint that) const { return mint(*this) %= that; }
mint operator+(const int that) const { return mint(*this) += that; }
mint operator-(const int that) const { return mint(*this) -= that; }
mint operator*(const int that) const { return mint(*this) *= that; }
mint operator%(const int that) const { return mint(*this) %= that; }
mint operator=(const int that) { return *this = mint(that); }
mint operator+(const signed that) const { return mint(*this) += that; }
mint operator-(const signed that) const { return mint(*this) -= that; }
mint operator*(const signed that) const { return mint(*this) *= that; }
mint operator%(const signed that) const { return mint(*this) %= that; }
mint operator=(const signed that) { return *this = mint(that); }
mint operator++() {
x++;
return *this;
}
mint operator++(signed) {
auto ret = *this;
x++;
return ret;
}
friend void operator+=(ll &a, const mint &b) { a = mint(a % MOD + b.x); }
friend void operator-=(ll &a, const mint &b) { a = mint(a % MOD - b.x); }
friend void operator*=(ll &a, const mint &b) { a = mint(a % MOD * b.x); }
friend void operator/=(ll &a, const mint &b);
friend mint operator+(const ll a, const mint &b) { return mint(a % MOD + b.x); }
friend mint operator-(const ll a, const mint &b) { return mint(a % MOD - b.x); }
friend mint operator*(const ll a, const mint &b) { return mint(a % MOD * b.x); }
friend mint operator^(const ll a, const mint &b) { return _mpow(a, b.x); }
};
mint itom(int v) {
mint res;
res.x = v;
return res;
}
const int setModMax = 510000;
vector<mint> fac, finv, inv;
void setMod(int m = MOD) {
fac.resize(setModMax);
finv.resize(setModMax);
inv.resize(setModMax);
MOD = m;
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
inv[1] = 1;
for (int i = 2; i < setModMax; i++) {
fac[i] = fac[i - 1].x * i % MOD;
inv[i] = MOD - inv[MOD % i].x * (MOD / i) % MOD;
finv[i] = finv[i - 1].x * inv[i].x % MOD;
}
}
mint mpow(int v, ll a) {
return mint::_mpow(v, a);
}
mint com(ll n, ll r) {
if (n < r || n < 0 || r < 0)return 0;
if (fac.size() == 0)setMod();
return fac[n] * finv[r] * finv[n - r];
}
mint ncr(ll n, ll r) { return com(n, r); }
mint nhr(ll n, ll r) { return com(n + r - 1, r); }
//拡張ユークリッドの互除法
mint minv(ll a) {
if (fac[0] == 0)setMod();
if (a < setModMax) return inv[a];
a %= MOD;
ll b = MOD, x = 1, y = 0;
while (b) {
ll t = a / b;
a -= t * b;
swap(a, b);
x -= t * y;
swap(x, y);
}
return x;
}
mint &mint::operator/=(const mint &that) { return *this *= minv(that.x); }
mint &mint::operator/=(const ll a) { return *this *= minv(a); }
mint &mint::operator/=(const signed a) { return *this *= minv(a); }
void operator/=(ll &a, const mint &b) { a = (a * minv(b.x)).x; }
using vm=vector<mint>;
#define vvm(a, b, c) vec<vm> a(b,vm(c))
using PM = pair<mint, mint>;
vb isPrime;
vi primes;
void setPrime() {
isPrime.resize(4010101);
fill(isPrime, true);
int len = sizeof(isPrime) / sizeof(isPrime[0]);
isPrime[0] = isPrime[1] = false;
for (int i = 2; i <= sqrt(len) + 5; ++i) {
if (!isPrime[i])continue;
for (int j = 2; i * j < len; ++j) {
isPrime[i * j] = false;
}
}
rep(i, len)if (isPrime[i])primes.pb(i);
}
//幾何 Pをcomplexとして扱う
bool eq(double a, double b) { return fabs(a - b) < eps; }
using C =complex<double>;
C rot(C &a, dou th) {
return a * C(cos(th), sin(th));
}
dou inpro(C &a, C &b) {
return real(a * conj(b));
}
//90度回転させて内積が0なら平行
bool line(C a, C b, C c) {
C ab = b - a;
C ac = c - a;
//複素数の掛け算は回転
ab *= C(0, 1);
return eq(inpro(ab, ac), 0);
}
bool line(P a, P b, P c) {
return line(C(a.fi, a.se), C(b.fi, b.se), C(c.fi, c.se));
}
bool line(int xa, int ya, int xb, int yb, int xc, int yc) {
C a = C(xa, ya);
C b = C(xb, yb);
C c = C(xc, yc);
return line(a, b, c);
}
//便利関数
//テスト用
char ranc() {
return (char) ('a' + rand() % 26);
}
int rand(int min, int max) {
assert(min <= max);
if (min >= 0 && max >= 0) {
return rand() % (max + 1 - min) + min;
} else if (max < 0) {
return -rand(-max, -min);
} else {
//+
if (rand() % 2) {
return rand(0, max);
//-
} else {
return -rand(0, -min);
}
}
}
vi ranv(int n, int min, int max) {
vi v(n);
rep(i, n)v[i] = rand(min, max);
return v;
}
//単調増加
vi ranvi(int n, int min, int max) {
vi v(n);
bool bad = 1;
while (bad) {
bad = 0;
v.resize(n);
rep(i, n) {
if (i && min > max - v[i - 1]) {
bad = 1;
break;
}
if (i)v[i] = v[i - 1] + rand(min, max - v[i - 1]);
else v[i] = rand(min, max);
}
}
return v;
}
void ranvlr(int n, int min, int max, vi &l, vi &r) {
l.resize(n);
r.resize(n);
rep(i, n) {
l[i] = rand(min, max);
r[i] = l[i] + rand(0, max - l[i]);
}
}
//便利 汎用
template<typename V, typename T> int find(vector<V> &a, const T key) {
rep(i, sz(a))if (a[i] == key)return i;
return -1;
}
template<typename V, typename T> P find(vector<vector<V>> &a, const T key) {
rep(i, sz(a)) rep(j, sz(a[0]))if (a[i][j] == key)return mp(i, j);
return mp(-1, -1);
}
template<typename V, typename U> T find(vector<vector<vector<V>>> &a, const U key) {
rep(i, sz(a))rep(j, sz(a[0]))rep(k, sz(a[0][0]))if (a[i][j][k] == key)return mt(i, j, k);
return mt(-1, -1, -1);
}
template<typename V, typename T> int count(V &a, const T k) {
return a == k;
}
template<typename V, typename T> int count(vector<V> &a, const T k) {
int ret = 0;
fora(v, a)ret += count(v, k);
return ret;
}
int mod(int a, int m) {
return (a % m + m) % m;
}
int pow(int a) { return a * a; };
void iota(vector<int> &ve, int s, int n) {
ve.resize(n);
iota(all(ve), s);
}
vi iota(int s, int n) {
vi ve;
ve.resize(n);
iota(all(ve), s);
return ve;
}
void ole() {
#ifdef _DEBUG
debugline("ole");
exit(0);
#endif
string a = "a";
rep(i, 30)a += a;
rep(i, 1 << 17)cout << a << endl;
cout << "OLE 出力長制限超過" << endl;
exit(0);
}
void tle() { while (inf)cout << inf << endl; }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll gcd(vi b) {
ll res = b[0];
for (auto &&v :b)res = gcd(v, res);
return res;
}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
ll rev(ll a) {
ll res = 0;
while (a) {
res *= 10;
res += a % 10;
a /= 10;
}
return res;
}
template<class T> vector<T> rev(vector<T> &a) {
vector<T> ret = a;
reverse(all(ret));
return ret;
}
ll ceil(ll a, ll b) {
if (b == 0) {
debugline("ceil");
deb(a, b);
ole();
return -1;
} else return (a + b - 1) / b;
}
ll sqrt(ll a) {
if (a < 0) {
debugline("sqrt");
deb(a);
ole();
}
ll res = (ll) std::sqrt(a);
while (res * res < a)res++;
return res;
}
double log(double e, double x) { return log(x) / log(e); }
ll sig(ll t) { return (1 + t) * t / 2; }
ll sig(ll s, ll t) { return (s + t) * (t - s + 1) / 2; }
vi divisors(int v) {
vi res;
for (int i = 1; i <= sqrt(v); ++i) {
if (v % i == 0) {
res.pb(i);
if (i != v / i)res.pb(v / i);
}
}
return res;
}
vi factorization(int v) {
int tv = v;
vi res;
if (isPrime.size() == 0)setPrime();
for (auto &&p :primes) {
if (v % p == 0)res.push_back(p);
while (v % p == 0) {
v /= p;
}
if (v == 1 || p * p > tv)break;
}
if (v > 1)res.pb(v);
return res;
}
unordered_map<int, int> factorizationMap(int v) {
int tv = v;
unordered_map<int, int> res;
if (isPrime.size() == 0)setPrime();
for (auto &&p :primes) {
while (v % p == 0) {
res[p]++;
v /= p;
}
if (v == 1 || p * p > tv)break;
}
if (v > 1)res[v]++;
return res;
}
int get(int a, int keta) { return (a / (int) pow(10, keta)) % 10; }
int keta(int v) {
int cou = 0;
while (v) { cou++, v %= 10; }
return cou;
}
template<class T> void imo(vector<T> &v) {
int n = v.size();
rep(i, n - 1)v[i + 1] += v[i];
}
//変換系
template<class T, class U> vector<T> keys(vector<pair<T, U>> a) {
vector<T> res;
for (auto &&k :a)res.pb(k.fi);
return res;
}
template<class T, class U> vector<U> keys(map<T, U> a) {
vector<U> res;
for (auto &&k :a)res.pb(k.fi);
return res;
}
template<class T, class U> vector<U> keys(umap<T, U> a) {
vector<U> res;
for (auto &&k :a)res.pb(k.fi);
return res;
}
template<class T, class U> vector<U> values(vector<pair<T, U>> a) {
vector<U> res;
for (auto &&k :a)res.pb(k.se);
return res;
}
template<class T, class U> vector<T> values(map<T, U> a) {
vector<T> res;
for (auto &&k :a)res.pb(k.se);
return res;
}
template<class T, class U> vector<T> values(umap<T, U> a) {
vector<T> res;
for (auto &&k :a)res.pb(k.se);
return res;
}
vi list(int a) {
vi res;
while (a) {
res.insert(res.begin(), a % 10);
a /= 10;
}
return res;
}
template<class T, class U> bool chmax(T &a, const U &b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template<class T, class U> bool chmin(T &a, const U &b) {
if (b < a) {
a = b;
return true;
}
return false;
}
template<class T> T min(T a, signed b) {
return a < b ? a : b;
}
template<class T> T max(T a, signed b) {
return a < b ? b : a;
}
template<class T> T min(T a, T b, T c) {
return a >= b ? b >= c ? c : b : a >= c ? c : a;
}
template<class T> T max(T a, T b, T c) {
return a <= b ? b <= c ? c : b : a <= c ? c : a;
}
template<class T> T min(vector<T> a) {
return *min_element(all(a));
}
template<class T> T min(vector<T> a, int n) {
return *min_element(a.begin(), a.begin() + min(n, sz(a)));
}
template<class T> T min(vector<T> a, int s, int n) {
return *min_element(a.begin() + s, a.begin() + min(n, sz(a)));
}
template<class T> T max(vector<T> a) {
return *max_element(all(a));
}
template<class T> T max(vector<T> a, int n) {
return *max_element(a.begin(), a.begin() + min(n, sz(a)));
}
template<class T> T max(vector<T> a, int s, int n) {
return *max_element(a.begin() + s, a.begin() + min(n, sz(a)));
}
template<typename A, size_t N> A max(A (&a)[N]) {
A res = a[0];
rep(i, N)res = max(res, a[i]);
return res;
}
template<typename A, size_t N, size_t O> A max(A (&a)[N][O]) {
A res = max(a[0]);
rep(i, N)res = max(res, max(a[i]));
return res;
}
template<typename A, size_t N, size_t O, size_t P> A max(A (&a)[N][O][P]) {
A res = max(a[0]);
rep(i, N)res = max(res, max(a[i]));
return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q> A max(A (&a)[N][O][P][Q], const T &v) {
A res = max(a[0]);
rep(i, N)res = max(res, max(a[i]));
return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R> A max(A (&a)[N][O][P][Q][R]) {
A res = max(a[0]);
rep(i, N)res = max(res, max(a[i]));
return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, size_t S> A max(A (&a)[N][O][P][Q][R][S]) {
A res = max(a[0]);
rep(i, N)res = max(res, max(a[i]));
return res;
}
template<typename A, size_t N> A min(A (&a)[N]) {
A res = a[0];
rep(i, N)res = min(res, a[i]);
return res;
}
template<typename A, size_t N, size_t O> A min(A (&a)[N][O]) {
A res = min(a[0]);
rep(i, N)res = min(res, max(a[i]));
return res;
}
template<typename A, size_t N, size_t O, size_t P> A min(A (&a)[N][O][P]) {
A res = min(a[0]);
rep(i, N)res = min(res, min(a[i]));
return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q> A min(A (&a)[N][O][P][Q], const T &v) {
A res = min(a[0]);
rep(i, N)res = min(res, min(a[i]));
return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R> A min(A (&a)[N][O][P][Q][R]) {
A res = min(a[0]);
rep(i, N)res = min(res, min(a[i]));
return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, size_t S> A min(A (&a)[N][O][P][Q][R][S]) {
A res = min(a[0]);
rep(i, N)res = min(res, min(a[i]));
return res;
}
template<class T> T sum(vector<T> v, int len = -1) {
if (len == -1)len = v.size();
T res = 0;
chmin(len, v.size());
rep(i, len)res += v[i];
return res;
}
template<class T> T sum(vector<vector<T>> &v, int h = -1, int w = -1) {
if (h == -1)h = v.size();
if (w == -1)w = v[0].size();
T res = 0;
chmin(h, v.size());
chmin(w, v[0].size());
rep(i, h)rep(j, w)res += v[i][j];
return res;
}
P sump(vp &v, int len = -1) {
if (len == -1)len = v.size();
P res = {0, 0};
chmin(len, v.size());
rep(i, len) {
res.fi += v[i].fi;
res.se += v[i].se;
}
return res;
}
///要素が0の時、返り値は0か1か
template<class T> T mul(vector<T> &v, int len = -1) {
if (len == -1)len = v.size();
T res = 1;
chmin(len, v.size());
rep(i, len)res *= v[i];
return res;
}
void clear(PQ &q) { while (q.size())q.pop(); }
template<class T> void clear(queue<T> &q) { while (q.size())q.pop(); }
template<class T> T *negarr(int size) {
T *body = (T *) malloc((size * 2 + 1) * sizeof(T));
return body + size;
}
template<class T> T *negarr2(int h, int w) {
double **dummy1 = new double *[2 * h + 1];
double *dummy2 = new double[(2 * h + 1) * (2 * w + 1)];
dummy1[0] = dummy2 + w;
for (int i = 1; i <= 2 * h + 1; i++) {
dummy1[i] = dummy1[i - 1] + 2 * w + 1;
}
double **a = dummy1 + h;
}
template<class T> struct ruic {
const vector<T> rui;
ruic(vector<T> &ru) : rui(ru) {}
T operator()(int l, int r) {
assert(l <= r);
return rui[r] - rui[l];
}
T operator[](int i) {
return rui[i];
}
};
template<class T> struct rruic {
const T *rrui;
rruic(T *ru) : rrui(ru) {}
//n-1から-1へ
T operator()(int l, int r) {
assert(l >= r);
return rrui[r] - rrui[l];
}
T operator[](int i) {
return rrui[i];
}
};
//template<class T> vector<T> ruiv(vector<T> &a)
template<class T> ruic<T> ruiv(vector<T> &a) {
vector<T> res(a.size() + 1);
rep(i, a.size())res[i + 1] = res[i] + a[i];
return ruic<T>(res);
}
template<class T> vector<T> ruim(vector<T> &a) {
vector<T> res(a.size() + 1, 1);
rep(i, a.size())res[i + 1] = res[i] * a[i];
return res;
}
//template<class T> T *rrui(vector<T> &a) {
//右から左にかけての半開区間 (-1 n-1]
template<class T> rruic<T> rrui(vector<T> &a) {
int len = a.size();
T *body = (T *) malloc((len + 1) * sizeof(T));
T *res = body + 1;
rer(i, len - 1)res[i - 1] = res[i] + a[i];
return rruic<T>(res);
}
//掛け算
template<class T> T *rruim(vector<T> &a) {
int len = a.size();
T *body = (T *) malloc((len + 1) * sizeof(T));
T *res = body + 1;
res[len - 1] = 1;
rer(i, len - 1)res[i - 1] = res[i] * a[i];
return res;
}
template<class T, class U> void inc(T &a, U v = 1) { a += v; }
template<class T, class U> void inc(vector<T> &a, U v = 1) { for (auto &u :a)inc(u, v); }
template<class T> void inc(vector<T> &a) { for (auto &u :a)inc(u, 1); }
template<class T, class U> void dec(T &a, U v = 1) { a -= v; }
template<class T, class U> void dec(vector<T> &a, U v = 1) { for (auto &u :a)dec(u, v); }
template<class T> void dec(vector<T> &a) { for (auto &u :a)dec(u, 1); }
inline bool inside(int h, int w, int H, int W) { return h >= 0 && w >= 0 && h < H && w < W; }
ll u(ll a) { return a < 0 ? 0 : a; }
template<class T> vector<T> u(const vector<T> &a) {
vector<T> ret = a;
fora(v, ret)v = u(v);
return ret;
}
#define MIN(a) numeric_limits<a>::min()
#define MAX(a) numeric_limits<a>::max()
ll goldd(ll left, ll right, function<ll(ll)> calc) {
double GRATIO = 1.6180339887498948482045868343656;
ll lm = left + (ll) ((right - left) / (GRATIO + 1.0));
ll rm = lm + (ll) ((right - lm) / (GRATIO + 1.0));
ll fl = calc(lm);
ll fr = calc(rm);
while (right - left > 10) {
if (fl < fr) {
right = rm;
rm = lm;
fr = fl;
lm = left + (ll) ((right - left) / (GRATIO + 1.0));
fl = calc(lm);
} else {
left = lm;
lm = rm;
fl = fr;
rm = lm + (ll) ((right - lm) / (GRATIO + 1.0));
fr = calc(rm);
}
}
ll minScore = MAX(ll);
ll resIndex = left;
for (ll i = left; i < right + 1; i++) {
ll score = calc(i);
if (minScore > score) {
minScore = score;
resIndex = i;
}
}
return resIndex;
}
ll goldt(ll left, ll right, function<ll(ll)> calc) {
double GRATIO = 1.6180339887498948482045868343656;
ll lm = left + (ll) ((right - left) / (GRATIO + 1.0));
ll rm = lm + (ll) ((right - lm) / (GRATIO + 1.0));
ll fl = calc(lm);
ll fr = calc(rm);
while (right - left > 10) {
if (fl > fr) {
right = rm;
rm = lm;
fr = fl;
lm = left + (ll) ((right - left) / (GRATIO + 1.0));
fl = calc(lm);
} else {
left = lm;
lm = rm;
fl = fr;
rm = lm + (ll) ((right - lm) / (GRATIO + 1.0));
fr = calc(rm);
}
}
if (left > right) {
ll l = left;
left = right;
right = l;
}
ll maxScore = MIN(ll);
ll resIndex = left;
for (ll i = left; i < right + 1; i++) {
ll score = calc(i);
if (maxScore < score) {
maxScore = score;
resIndex = i;
}
}
return resIndex;
}
template<class T> T min(vector<vector<T>> &a) {
T res = MAX(T);
rep(i, a.size())chmin(res, *min_element(all(a[i])));
return res;
}
template<class T> T max(vector<vector<T>> &a) {
T res = MIN(T);
rep(i, a.size())chmax(res, *max_element(all(a[i])));
return res;
}
bool bget(ll m, int keta) { return (m >> keta) & 1; }
int bget(ll m, int keta, int sinsuu) {
m /= (ll) pow(sinsuu, keta);
return m % sinsuu;
}
inline ll bit(int n) { return (1LL << (n)); }
inline ll bit(int n, int sinsuu) { return (ll) pow(sinsuu, n); }
int bcou(ll m) { return __builtin_popcount(m & 0xFFFFFFFF) + __builtin_popcount(m >> 32); }
//初期化は0を渡す
ll nextComb(ll &mask, int n, int r) {
if (!mask)return mask = (1LL << r) - 1;
ll x = mask & -mask; //最下位の1
ll y = mask + x; //連続した下の1を繰り上がらせる
ll res = ((mask & ~y) / x >> 1) | y;
if (bget(res, n))return mask = 0;
else return mask = res;
}
//n桁以下でビットがr個立っているもののvectorを返す
vl bitCombList(int n, int r) {
vl res;
int m = 0;
while (nextComb(m, n, r)) {
res.pb(m);
}
return res;
}
//大文字小文字を区別する
int altoiaZ(char c) {
if ('A' <= c && c <= 'Z')return c - 'A';
return c - 'a' + 26;
}
char itoalaZ(int i) {
if (i < 26)return 'A' + i;
return 'a' + i - 26;
}
//aもAも0を返す 基本小文字
int altoi(char c) {
if ('A' <= c && c <= 'Z')return c - 'A';
return c - 'a';
}
char itoal(int i) {
return 'a' + i;
}
int ctoi(char c) { return c - '0'; }
char itoc(int i) { return i + '0'; }
int vtoi(vi &v) {
int res = 0;
if (sz(v) > 18) {
debugline("vtoi");
deb(sz(v));
ole();
}
rep(i, sz(v)) {
res *= 10;
res += v[i];
}
return res;
}
vi itov(int i) {
vi res;
while (i) {
res.pb(i % 10);
i /= 10;
}
rev(res);
return res;
}
vector<vector<int>> ctoi(vector<vector<char>> s, char c) {
int n = sz(s), m = sz(s[0]);
vector<vector<int>> res(n, vector<int>(m));
rep(i, n)rep(j, m)res[i][j] = s[i][j] == c;
return res;
}
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
void compress(vi &a) {
vi b;
int len = a.size();
for (int i = 0; i < len; ++i) {
b.push_back(a[i]);
}
sort(b);
UNIQUE(b);
for (int i = 0; i < len; ++i) {
a[i] = lower_bound(all(b), a[i]) - b.begin();
}
}
void compress(int a[], int len) {
vi b;
for (int i = 0; i < len; ++i) {
b.push_back(a[i]);
}
sort(b);
UNIQUE(b);
for (int i = 0; i < len; ++i) {
a[i] = lower_bound(all(b), a[i]) - b.begin();
}
}
//要素が見つからなかったときに困る
#define binarySearch(a, v) (binary_search(all(a),v))
#define lowerIndex(a, v) (lower_bound(all(a),v)-a.begin())
#define lowerBound(a, v) (*lower_bound(all(a),v))
#define upperIndex(a, v) (upper_bound(all(a),v)-a.begin())
#define upperBound(a, v) (*upper_bound(all(a),v))
#define ans(a) cout<<a<<endl;continue;
#define poll(a) q.front();q.pop()
#define dpoll(a) q.front();q.pop_front()
#define pollLast(a) q.back();q.pop_back()
#define pollBack(a) q.back();q.pop_back()
template<class T> inline void fin(T s) { cout << s << endl, exit(0); }
template<class T> struct edge {
int from, to;
T cost;
int id;
int type;
edge(int f, int t, T c = 1, int id = -1, int ty = -1) : from(f), to(t), cost(c), id(id), type(ty) {}
bool operator<(const edge &b) const { return cost < b.cost; }
bool operator>(const edge &b) const { return cost > b.cost; }
};
template<typename T> class graph {
protected:
vector<bool> _used;
public :
vector<vector<edge<T>>> g;
vector<edge<T>> edges;
int n;
graph(int n) : n(n) { g.resize(n), _used.resize(n); }
void clear() { g.clear(), edges.clear(); }
void resize(int n) {
this->n = n;
g.resize(n);
_used.resize(n);
}
int size() { return g.size(); }
vector<edge<T> > &operator[](int i) { return g[i]; }
virtual void add(int from, int to, T cost, int id, int ty) = 0;
virtual bool used(edge<T> &e) = 0;
virtual bool used(int id) = 0;
virtual void del(edge<T> &e) = 0;
virtual void del(int id) = 0;
};
template<class T> vector<T> dijkstra(const graph<T> &g, int s);
template<typename T =ll> class digraph : public graph<T> {
public:
using graph<T>::g;
using graph<T>::n;
using graph<T>::edges;
using graph<T>::_used;
digraph(int n) : graph<T>(n) {}
void add(int f, int t, T cost = 1, int id = -1, int ty = -1) {
if (!(0 <= f && f < n && 0 <= t && t < n)) {
debugline("digraph add");
deb(f, t, cost, id, ty);
ole();
}
if (id == -1)id = edges.size();
g[f].emplace_back(f, t, cost, id, ty);
edges.emplace_back(f, t, cost, id, ty);
}
bool used(edge<T> &e) { return _used[e.id]; }
bool used(int id) { return _used[id]; }
void del(edge<T> &e) { _used[e.id] = _used[e.id ^ 1] = 1; }
void del(int id) { _used[id] = _used[id ^ 1] = 1; }
};
template<class T=int> class undigraph : public graph<T> {
public:
using graph<T>::g;
using graph<T>::n;
using graph<T>::edges;
using graph<T>::_used;
undigraph(int n) : graph<T>(n) {
}
void add(int f, int t, T cost = 1, int id = -1, int ty = -1) {
if (!(0 <= f && f < n && 0 <= t && t < n)) {
debugline("undigraph add");
deb(f, t, cost, id, ty);
ole();
}
if (id == -1)id = edges.size();
g[f].emplace_back(f, t, cost, id, ty);
g[t].emplace_back(t, f, cost, id + 1, ty);
edges.emplace_back(f, t, cost, id, ty);
edges.emplace_back(t, f, cost, id + 1, ty);
}
void add(edge<T> &e) {
int f = e.from, t = e.to, ty = e.type;
T cost = e.cost;
add(f, t, cost, ty);
}
bool used(edge<T> &e) { return _used[e.id]; }
bool used(int id) { return _used[id]; }
void del(edge<T> &e) { _used[e.id] = _used[e.id ^ 1] = 1; }
void del(int id) { _used[id] = _used[id ^ 1] = 1; }
};
template<class T=int> class tree : public undigraph<T> {
public:
using undigraph<T>::g;
using undigraph<T>::n;
using undigraph<T>::edges;
using undigraph<T>::_used;
vi dep;
vi disv;
private:
bool never = 1;
int root = -1;
vector<vector<int>> par;
bool costallone;
void dfs(int v, int p, int d) {
dep[v] = d;
par[0][v] = p;
int lim = (*this)[v].size();
for (int i = 0; i < lim; i++) {
int t = g[v][i].to;
if (t == p)con;
dfs(t, v, d + 1);
}
}
void built() {
never = 0;
n = g.size();
par.assign(30, vi(n));
dep.resize(n);
costallone = 1;
fora(e, edges)if (e.cost != 1)costallone = 0;
dfs(root, -1, 0);
rep(k, par.size() - 1) {
rep(i, n) {
if (par[k][i] == -1)par[k + 1][i] = -1;
else par[k + 1][i] = par[k][par[k][i]];
}
}
if (costallone)disv = dep;
else disv = dijkstra(*this, root);
}
int _lca(int u, int v) {
if (dep[u] > dep[v])swap(u, v);
rep(k, par.size()) {
if ((dep[u] - dep[v]) >> k & 1) {
v = par[k][v];
}
}
if (u == v)return u;
rer(k, par.size() - 1) {
if (par[k][u] != par[k][v]) {
u = par[k][u];
v = par[k][v];
}
}
return par[0][u];
}
int _dis(int u, int v) {
int p = _lca(u, v);
return disv[u] + disv[v] - disv[p] * 2;
}
public:
tree(int n, int root = 0) : undigraph<T>(n), root(root) {}
bool leaf(int v) {
return sz(g[v]) == 1 && v != root;
}
int dis(int u, int v) {
if (never) {
built();
}
return _dis(u, v);
}
int lca(int u, int v) {
if (never) {
built();
}
return _lca(u, v);
}
};
//辺によりメモリを大量消費
// よってedgesを消している
//頂点10^6でメモリを190MB(制限の8割)使う
//軽量化のため、辺を持たないbig gridクラスがあってもいいかもしれない
//
template<class T=int> class grid_k6 : public undigraph<T> {
public:
using undigraph<T>::g;
using undigraph<T>::n;
using undigraph<T>::edges;
using undigraph<T>::_used;
int H, W;
int eid = 0;
void add(int f, int t, T cost = 1, int id = -1, int ty = -1) {
if (!(0 <= f && f < n && 0 <= t && t < n)) {
debugline("grid_k6 add");
deb(f, t, cost, id, ty);
ole();
}
g[f].emplace_back(f, t, cost, eid++, ty);
g[t].emplace_back(t, f, cost, eid++, ty);
}
int getid(int h, int w) {
if (!inside(h, w, H, W))return -1;
return W * h + w;
}
P get2(int id) {
return mp(id / W, id % W);
}
P operator()(int id) {
return get2(id);
}
int operator()(int h, int w) {
return getid(h, w);
}
grid_k6(int H, int W) : H(H), W(W), undigraph<T>(H * W) {
rep(h, H) {
rep(w, W) {
int f = getid(h, w);
if (w + 1 < W) add(f, getid(h, w + 1));
if (h + 1 < H)add(f, getid(h + 1, w));
}
}
}
grid_k6(_vvc ba, char wall = '#') : H(sz(ba)), W(sz(ba[0])), undigraph<T>(sz(ba) * sz(ba[0])) {
rep(h, H) {
rep(w, W) {
if (ba[h][w] == wall)con;
int f = getid(h, w);
if (w + 1 < W && ba[h][w + 1] != wall) {
add(f, getid(h, w + 1));
}
if (h + 1 < H && ba[h + 1][w] != wall) {
add(f, getid(h + 1, w));
}
}
}
}
void add(int fh, int fw, int th, int tw) {
add(getid(fh, fw), getid(th, tw));
}
};
template<class T> bool nibu(const graph<T> &g) {
if (g.edges.size() == 0)return true;
UnionFind uf(g.n * 2);
for (auto &&e :g.edges)uf.unite(e.from, e.to + g.n), uf.unite(e.from + g.n, e.to);
rep(i, g.n)if (uf.same(i, i + g.n))return 0;
return 1;
}
//二部グラフを色分けした際の頂点数を返す
template<class T> vp nibug(graph<T> &g) {
vp cg;
if (!nibu(g)) {
debugline("nibu");
ole();
}
int _n = g.size();
vb _was(_n);
queue<P> q;
rep(i, _n) {
if (_was[i])continue;
q.push(mp(i, 1));
_was[i] = 1;
int red = 0;
int coun = 0;
while (q.size()) {
int now = q.front().fi;
int col = q.front().se;
red += col;
coun++;
q.pop();
forg(gi, g[now]) {
if (_was[t])continue;
q.push(mp(t, col ^ 1));
_was[t] = 1;
}
}
cg.push_back(mp(red, coun - red));
}
return cg;
}
template<class T> vector<T> dijkstra(const graph<T> &g, int s, int cant_arrive = -1) {
if (!(0 <= s && s < g.n)) {
debugline("dijkstra");
deb(s, g.n);
ole();
}
T initValue = MAX(T);
vector<T> dis(g.n, initValue);
priority_queue<pair<T, int>, vector<pair<T, int>>, greater<pair<T, int>>> q;
dis[s] = 0;
q.emplace(0, s);
while (q.size()) {
T nowc = q.top().fi;
int i = q.top().se;
q.pop();
if (dis[i] != nowc)continue;
for (auto &&e : g.g[i]) {
int to = e.to;
T cost = nowc + e.cost;
if (dis[to] > cost) {
dis[to] = cost;
q.emplace(dis[to], to);
}
}
}
//基本、たどり着かないなら-1
if (cant_arrive == -1)for (auto &&d :dis) if (d == initValue)d = -1;
return dis;
}
template<class T> vector<vector<T>> warshall(const graph<T> &g, int cant_arrive = -1) {
int n = g.n;
vector<vector<T> > dis(n, vector<T>(n, linf));
fora(e, g.edges) chmin(dis[e.from][e.to], e.cost);
rep(i, n)dis[i][i] = 0;
rep(k, n)rep(i, n)rep(j, n)chmin(dis[i][j], dis[i][k] + dis[k][j]);
//基本、たどり着かないなら-1
if (cant_arrive == -1)rep(i, n)rep(j, n) if (dis[i][j] == linf)dis[i][j] = -1;
return dis;
}
//機能拡張
vp vtop(vi &a, vi &b) {
vp res(sz(a));
rep(i, sz(a))res[i] = mp(a[i], b[i]);
return res;
}
void ptov(vp &p, vi &a, vi &b) {
a.resize(sz(p));
b.resize(sz(p));
rep(i, sz(p))a[i] = p[i].fi, b[i] = p[i].se;
}
template<typename _CharT, typename _Traits, typename _Alloc>
basic_string<_CharT, _Traits, _Alloc>
operator+(const basic_string<_CharT, _Traits, _Alloc> &__lhs, const int __rv) {
basic_string<_CharT, _Traits, _Alloc> __str(__lhs);
__str.append(to_string(__rv));
return __str;
}
template<typename _CharT, typename _Traits, typename _Alloc>
void operator+=(basic_string<_CharT, _Traits, _Alloc> &__lhs, const int __rv) {
__lhs += to_string(__rv);
}
template<typename _CharT, typename _Traits, typename _Alloc>
basic_string<_CharT, _Traits, _Alloc>
operator+(const basic_string<_CharT, _Traits, _Alloc> &__lhs, const signed __rv) {
basic_string<_CharT, _Traits, _Alloc> __str(__lhs);
__str.append(to_string(__rv));
return __str;
}
template<typename _CharT, typename _Traits, typename _Alloc>
void operator+=(basic_string<_CharT, _Traits, _Alloc> &__lhs, const signed __rv) {
__lhs += to_string(__rv);
}
template<class T, class U> void operator+=(queue<T> &a, U v) {
a.push(v);
}
template<class T, class U>
priority_queue<T, vector<T>, greater<T> > &operator+=(priority_queue<T, vector<T>, greater<T> > &a, U v) {
a.push(v);
return a;
}
template<class T, class U> priority_queue<T> &operator+=(priority_queue<T> &a, U v) {
a.push(v);
return a;
}
template<class T, class U> set<T> &operator+=(set<T> &a, U v) {
a.insert(v);
return a;
}
template<class T, class U> set<T, greater<T>> &operator+=(set<T, greater<T>> &a, U v) {
a.insert(v);
return a;
}
template<class T, class U> vector<T> &operator+=(vector<T> &a, U v) {
a.pb(v);
return a;
}
template<class T> vector<T> &operator+=(vector<T> &a, vector <T> &b) {
a.pb(b);
return a;
}
template<class T, class U> vector<T> &operator+=(vector<T> &a, initializer_list<U> v) {
for (auto &&va :v)a.pb(va);
return a;
}
template<class T> vector<T> &operator-=(vector<T> &a, vector <T> &b) {
if (sz(a) != sz(b)) {
debugline("vector<T> operator-=");
deb(a);
deb(b);
ole();
}
rep(i, sz(a))a[i] -= b[i];
return a;
}
template<class T> vector<T> &operator-(vector<T> &a, vector <T> &b) {
if (sz(a) != sz(b)) {
debugline("vector<T> operator-");
deb(a);
deb(b);
ole();
}
vector<T> res;
rep(i, sz(a))res[i] = a[i] - b[i];
return res;
}
template<typename T> void remove(vector<T> &v, unsigned int i) { v.erase(v.begin() + i); }
template<typename T> void remove(vector<T> &v, unsigned int s, unsigned int e) {
v.erase(v.begin() + s, v.begin() + e);
}
template<typename T> void removen(vector<T> &v, unsigned int s, unsigned int n) {
v.erase(v.begin() + s, v.begin() + s + n);
}
template<typename T> void erase(vector<T> &v, unsigned int i) { v.erase(v.begin() + i); }
template<typename T> void erase(vector<T> &v, unsigned int s, unsigned int e) {
v.erase(v.begin() + s, v.begin() + e);
}
template<typename T> void erasen(vector<T> &v, unsigned int s, unsigned int n) {
v.erase(v.begin() + s, v.begin() + s + n);
}
template<typename T> void insert(vector<T> &v, unsigned int i, T t) { v.insert(v.begin() + i, t); }
template<typename T> void insert(vector<T> &v, unsigned int i, vector<T> list) {
for (auto &&va :list)v.insert(v.begin() + i++, va);
}
template<typename T, typename U> void insert(vector<T> &v, initializer_list<U> list) {
for (auto &&va :list)v.pb(va);
}
template<typename T, typename U> void insert(vector<T> &v, unsigned int i, initializer_list<U> list) {
for (auto &&va :list)v.insert(v.begin() + i++, va);
}
template<typename T> void insert(set<T> &v, vector<T> list) {
for (auto &&va :list)v.insert(va);
}
template<typename T> void insert(set<T> &v, initializer_list<T> list) {
for (auto &&va :list)v.insert(va);
}
ll ma = numeric_limits<ll>::min();
ll mi = numeric_limits<ll>::max();
//閉路がなければtrue
bool topo(vi &res, digraph<int> &g) {
int n = g.g.size();
vi nyu(n);
rep(i, n)for (auto &&e :g[i])nyu[e.to]++;
queue<int> st;
rep(i, n)if (nyu[i] == 0)st.push(i);
while (st.size()) {
int v = st.front();
st.pop();
res.pb(v);
fora(e, g[v]) if (--nyu[e.to] == 0)st.push(e.to);
}
return res.size() == n;
}
//辞書順最小トポロジカルソート
bool topos(vi &res, digraph<int> &g) {
int n = g.g.size();
vi nyu(n);
rep(i, n)for (auto &&e :g[i])nyu[e.to]++;
//小さい順
priority_queue<int, vector<int>, greater<int> > q;
rep(i, n)if (nyu[i] == 0)q.push(i);
while (q.size()) {
int i = q.top();
q.pop();
res.pb(i);
fora(e, g[i])if (--nyu[e.to] == 0)q.push(e.to);
}
return res.size() == n;
}
vector<string> split(const string a, const char deli) {
string b = a + deli;
int l = 0, r = 0, n = b.size();
vector<string> res;
rep(i, n) {
if (b[i] == deli) {
r = i;
if (l < r)res.push_back(b.substr(l, r - l));
l = i + 1;
}
}
return res;
}
vector<string> split(const string a, const string deli) {
string b = a + deli;
int l = 0, r = 0, n = b.size(), dn = deli.size();
vector<string> res;
rep(i, n) {
if (i + dn <= n && b.substr(i, i + dn) == deli) {
r = i;
if (l < r)res.push_back(b.substr(l, r - l));
i += dn - 1;
l = i + 1;
}
}
return res;
}
void yn(bool a) {
if (a)cout << "yes" << endl;
else cout << "no" << endl;
}
void Yn(bool a) {
if (a)cout << "Yes" << endl;
else cout << "No" << endl;
}
void YN(bool a) {
if (a)cout << "YES" << endl;
else cout << "NO" << endl;
}
void fyn(bool a) {
if (a)cout << "yes" << endl;
else cout << "no" << endl;
exit(0);
}
void fYn(bool a) {
if (a)cout << "Yes" << endl;
else cout << "No" << endl;
exit(0);
}
void fYN(bool a) {
if (a)cout << "YES" << endl;
else cout << "NO" << endl;
exit(0);
}
void Possible(bool a) {
if (a)cout << "Possible" << endl;
else cout << "Impossible" << endl;
exit(0);
}
int n, m, k, d, H, W, x, y, z, q;
int cou;
vi a, b, c;
vvi (s, 0, 0);
vvc (ba, 0, 0);
vp p;
void solve() {
cin >> n;
na2(a, b, n);
sortp(a, b, sdfi);
vvi(dp, n + 2, n + 2, linf);
a.insert(a.begin(), 0);
b.insert(b.begin(), 0);
dp[0][0] = 0;//1 index で0日目
vi rumi(n + 1);
//もらう
rep(i, 1, n + 1) {
rumi = dp[i - 1];
rep(j, 1, n + 1)chmin(rumi[j], rumi[j - 1]);
rep(j, 1, n + 1) {
int pre = rumi[j - 1];
if (pre == linf)con;
chmin(dp[i][j], pre + a[j] + b[j] * (i - 1));
}
}
int eat = 0;
rep(i, 1, n + 1) {
eat++;
if (i % 2 == 0)eat++;
if (eat >= n)fin(min(dp[i]));
}
}
int my(int n, vi a) {
return 0;
}
int sister(int n, vi a) {
return 0;
}
signed main() {
solve();
#define _arg n,a
//cin>>n;
//na(a,n);
//my(_arg);
//cout << my(_arg) << endl;
#ifdef _DEBUG
bool bad = 0;
for (int i = 0, ok = 1; i < k5 && ok; i++) {
int n = rand(1, 3);
vi a = ranv(m, 1, 10);
int myres = my(_arg);
int res = sister(_arg);
ok = myres == res;
if (!ok) {
cout << n << endl;
cout << a << endl;
cout << "正解 : " << res << endl;
cout << "出力 : " << myres << endl;
bad = 1;
break;
}
}
#endif
return 0;
};