結果
| 問題 | No.703 ゴミ拾い Easy |
| ユーザー |
 バイト
|
| 提出日時 | 2019-03-04 20:40:45 |
| 言語 | C++14 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
CE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 51,608 bytes |
| コンパイル時間 | 2,545 ms |
| コンパイル使用メモリ | 206,572 KB |
| 最終ジャッジ日時 | 2023-09-05 18:30:50 |
| 合計ジャッジ時間 | 5,571 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge11 |
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。（リジャッジ後のコンパイルエラーは公開されます）
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
コンパイルメッセージ
次のファイルから読み込み: /usr/local/gcc7/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/gthr.h:148,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/ext/atomicity.h:35,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/bits/ios_base.h:39,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/ios:42,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/istream:38,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/sstream:38,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/complex:45,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/ccomplex:39,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/stdc++.h:54,
次から読み込み: main.cpp:8:
/usr/local/gcc7/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/gthr-default.h:102:1: エラー: attribute value ‘tune=native’ was already specified in ‘target’ attribute
102 | __gthrw(pthread_once)
| ^~~~~~~
/usr/local/gcc7/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/gthr-default.h:102:1: エラー: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/local/gcc7/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/gthr-default.h:103:1: エラー: attribute value ‘tune=native’ was already specified in ‘target’ attribute
103 | __gthrw(pthread_getspecific)
| ^~~~~~~
/usr/local/gcc7/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/gthr-default.h:103:1: エラー: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/local/gcc7/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/gthr-default.h:104:1: エラー: attribute value ‘tune=native’ was already specified in ‘target’ attribute
104 | __gthrw(pthread_setspecific)
| ^~~~~~~
/usr/local/gcc7/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/gthr-default.h:104:1: エラー: attribute value ‘tune=native’ was already
ソースコード
//注意点
//Tは3つの値を持つ構造
//だがワイルドカードとしても使っている
//#pragma GCC optimize ("-O3")
#pragma GCC optimize ("O3")
#pragma GCC target ("tune=native")
#pragma GCC target ("avx")
#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
}
int operator[](int i) {
assert(i < 3);
return i == 0 ? f : i == 1 ? s : t;
}
};
//@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 F first
#define fi first
#define S second
#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 vvi(a, b, c) vec<vi> a(b,vi(c))
using vb = vector<bool>;
#define vvb(a, b, c) vec<vb> a(b,vb(c))
using vs = vector<string>;
#define vvs(a, b, c) vec<vs> a(b,vs(c))
using vl = vector<ll>;
#define vvl(a, b, c) vec<vl> a(b,vl(c))
using vd = vector<double>;
#define vvd(a, b, c) vec<vd> a(b,vd(c))
using vc=vector<char>;
#define vvc(a, b, c) vec<vc> a(b,vc(c))
using vp = vector<P>;
#define vvp(a, b, c) vec<vp> a(b,vp(c))
using vt = vector<T>;
#define vvt(a, b, c) vec<vt> a(b,vt(c))
#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 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 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) if (ve.size())for (int gi = 0, f = ve[gi].from, t = ve[gi].to, c = ve[gi].cost; gi < ve.size(); gi++,f = ve[gi].from, t = ve[gi].to, c = ve[gi].cost)
// ve[gi]が参照外を指すのを防ぐ
#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;((ve[gi].to==p?gi++:1),gi < 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) (a.size())
#define rs(a) (a.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
// 境界チェック付きvector
namespace std_vector_bounds_checking {
using namespace std;
template<class T, class A = std::allocator<T>> struct vector : std::vector<T, A> {
using std::vector<T, A>::vector;
typename std::vector<T>::reference operator[](typename std::vector<T>::size_type n) {
return this->at(n);
}
};
}
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:
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;
}
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 V, typename H> void resize(vector<V> &vec, const H head) { //再帰の終端。 可変長templateの長さが 0 になるとこっちが呼ばれる。
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;
}
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); }); };
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;;
}
};
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 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; }
//デバッグ
#define debug(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.F;
res[i].push_back(r);
for (auto &&v:p.S) {
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.F, a.S), C(b.F, b.S), C(c.F, c.S));
}
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]);
}
}
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() {
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 reverse(ll a) {
ll res = 0;
while (a) {
res *= 10;
res += a % 10;
a /= 10;
}
return res;
}
template<class T> void reverse(vector<T> &a) {
reverse(all(a));
}
ll ceil(ll a, ll b) {
if (b == 0) {
ole();
return -1;
} else return (a + b - 1) / b;
}
ll sqrt(ll a) {
if (a < 0)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.F);
return res;
}
template<class T, class U> vector<U> keys(map<T, U> a) {
vector<U> res;
for (auto &&k :a)res.pb(k.F);
return res;
}
template<class T, class U> vector<U> keys(umap<T, U> a) {
vector<U> res;
for (auto &&k :a)res.pb(k.F);
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.S);
return res;
}
template<class T, class U> vector<T> values(map<T, U> a) {
vector<T> res;
for (auto &&k :a)res.pb(k.S);
return res;
}
template<class T, class U> vector<T> values(umap<T, U> a) {
vector<T> res;
for (auto &&k :a)res.pb(k.S);
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.F += v[i].F;
res.S += v[i].S;
}
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> vector<T> ruiv(vector<T> &a) {
vector<T> res(a.size() + 1);
rep(i, a.size())res[i + 1] = res[i] + a[i];
return 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;
}
//右から左にかけての半開区間 (-1 n-1]
template<class T> 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 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> void plus(vector<T> &a, T v = 1) { for (auto &&u :a)u += v; }
template<class T> void minu(vector<T> &a, T v = 1) { for (auto &&u :a)u -= v; }
template<class T> void minus(vector<T> &a, T v = 1) { for (auto &&u :a)u -= v; }
inline bool inside(int y, int x, int H, int W) { return y >= 0 && x >= 0 && y < H && x < W; }
ll u(ll a) { return a < 0 ? 0 : a; }
#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)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;
}
reverse(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, root = -1;
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(); }
bool isleaf(int v) {
assert(root != -1);
return g[v].size() == 1 && g[v][0].from != root;
}
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=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))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<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))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> 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))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().F;
int col = q.front().S;
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) {
if (!(0 <= s && 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().F;
int i = q.top().S;
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);
}
}
}
//たどり着かないなら-1
for (auto &&d :dis) if (d == initValue)d = -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].F, b[i] = p[i].S;
}
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))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))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);
}
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;
#define chtMin 0
#define chtMax 1
class ConvexHullDynamic {
typedef long long coef_t;
typedef long long coord_t;
typedef long long val_t;
/*
* Line 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
* and 'xLeft' which is intersection with previous line in hull(first line has -INF)
*/
private:
struct Line {
coef_t a, b;
double xLeft;
enum Type {
line, maxQuery, minQuery
} type;
coord_t val;
explicit Line(coef_t aa = 0, coef_t bb = 0) : a(aa), b(bb), xLeft(-INFINITY), type(Type::line), val(0) {}
val_t valueAt(coord_t x) const { return a * x + b; }
friend bool areParallel(const Line &l1, const Line &l2) { return l1.a == l2.a; }
friend double intersectX(const Line &l1, const Line &l2) { return areParallel(l1, l2) ? INFINITY : 1.0 * (l2.b - l1.b) / (l1.a - l2.a); }
bool operator<(const Line &l2) const {
if (l2.type == line)
return this->a < l2.a;
if (l2.type == maxQuery)
return this->xLeft < l2.val;
if (l2.type == minQuery)
return this->xLeft > l2.val;
}
};
bool isMax; //whether or not saved envelope is top(search of max value)
public:
std::set<Line> hull; //envelope itself
private:
/*
* INFO: Check position in hull by iterator
* COMPLEXITY: O(1)
*/
bool hasPrev(std::set<Line>::iterator it) { return it != hull.begin(); }
bool hasNext(std::set<Line>::iterator it) { return it != hull.end() && std::next(it) != hull.end(); }
/*
* INFO: Check whether line l2 is irrelevant
* NOTE: Following positioning in hull must be true
* l1 is next left to l2
* l2 is right between l1 and l3
* l3 is next right to l2
* COMPLEXITY: O(1)
*/
bool irrelevant(const Line &l1, const Line &l2, const Line &l3) { return intersectX(l1, l3) <= intersectX(l1, l2); }
bool irrelevant(std::set<Line>::iterator it) {
return hasPrev(it) && hasNext(it)
&& (isMax && irrelevant(*std::prev(it), *it, *std::next(it))
|| !isMax && irrelevant(*std::next(it), *it, *std::prev(it)));
}
/*
* INFO: Updates 'xValue' of line pointed by iterator 'it'
* COMPLEXITY: O(1)
*/
std::set<Line>::iterator updateLeftBorder(std::set<Line>::iterator it) {
if (isMax && !hasPrev(it) || !isMax && !hasNext(it))
return it;
double val = intersectX(*it, isMax ? *std::prev(it) : *std::next(it));
Line buf(*it);
it = hull.erase(it);
buf.xLeft = val;
it = hull.insert(it, buf);
return it;
}
public:
explicit ConvexHullDynamic(signed isMax) : isMax(isMax) {}
/*
* INFO: Adding line to the envelope
* Line is of type 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
* COMPLEXITY: Adding N lines(N calls of function) takes O(N*log N) time
*/
void addLine(coef_t a, coef_t b) {
//find the place where line will be inserted in set
Line l3 = Line(a, b);
auto it = hull.lower_bound(l3);
//if parallel line is already in set, one of them becomes irrelevant
if (it != hull.end() && areParallel(*it, l3)) {
if (isMax && it->b < b || !isMax && it->b > b)
it = hull.erase(it);
else
return;
}
//try to insert
it = hull.insert(it, l3);
if (irrelevant(it)) {
hull.erase(it);
return;
}
//remove lines which became irrelevant after inserting line
while (hasPrev(it) && irrelevant(std::prev(it))) hull.erase(std::prev(it));
while (hasNext(it) && irrelevant(std::next(it))) hull.erase(std::next(it));
//refresh 'xLine'
it = updateLeftBorder(it);
if (hasPrev(it))
updateLeftBorder(std::prev(it));
if (hasNext(it))
updateLeftBorder(std::next(it));
}
val_t getBest(coord_t x) const {
Line q;
q.val = x;
q.type = isMax ? Line::Type::maxQuery : Line::Type::minQuery;
auto bestLine = hull.lower_bound(q);
if (isMax) --bestLine;
return bestLine->valueAt(x);
}
};
void solve() {
cin >> n;
nao(a, n);
vi vx, vy;
nao(vx, n);
nao(vy, n);
vi dp(n + 1);
ConvexHullDynamic cht(chtMin);
rep(i, 1, n + 1) {
cht.addLine(-2 * vx[i], dp[i - 1] + pow(vx[i]) + pow(vy[i]));
dp[i] = cht.getBest(a[i]) + pow(a[i]);
}
cout << dp[n] << endl;
}
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;
}
}
// if (!bad)cout << "お兄ちゃんすごい！天才！！" << endl;
#endif
return 0;
};