Submission #5913991
Source Code Expand
//#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
#ifdef _DEBUG
//区間削除は出来ない
template<class T> struct my_pbds_tree {
set<T> s;
auto begin() { return s.begin(); }
auto end() { return s.end(); }
auto rbegin() { return s.rbegin(); }
auto rend() { return s.rend(); }
auto empty() { return s.empty(); }
auto size() { return s.size(); }
void clear() { s.clear(); }
template<class U> void insert(U v) { s.insert(v); }
template<class U> void operator+=(U v) { insert(v); }
template<class F> auto erase(F v) { return s.erase(v); }
template<class U> auto find(U v) { return s.find(v); }
template<class U> auto lower_bound(U v) { return s.lower_bound(v); }
template<class U> auto upper_bound(U v) { return s.upper_bound(v); }
auto find_by_order(int k) {
auto it = s.begin();
for (int i = 0; i < k; i++)it++;
return it;
}
auto order_by_key(int v) { return s.lower_bound(v) - s.begin(); }
};
#define pbds(T) my_pbds_tree<T>
#else
#define unordered_map __gnu_pbds::gp_hash_table
//find_by_order(k) k番目のイテレーター
//order_of_key(k) k以上が前から何番目か
#define pbds(U) __gnu_pbds::tree<U, __gnu_pbds::null_type, less<U>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>
#endif
struct xorshift {
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template<class U, class L> void operator+=(__gnu_pbds::tree<U, __gnu_pbds::null_type, less<U>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update> &s, L v) { s.insert(v); }
//衝突対策
#define ws wszzzz
#define int long long
//@formatter:off
template<class A, class B, class C>struct T2 {A f;B s;C t;T2() { f = 0, s = 0, t = 0; }T2(A f, B s, C t) : f(f), s(s), t(t) {}bool operator<(const T2 &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 ?n s > r.s : t > r.t; 大きい順 */ } bool operator>(const T2 &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 T2 &r) const { return f == r.f && s == r.s && t == r.t; } bool operator!=(const T2 &r) const { return f != r.f || s != r.s || t != r.t; }};
template<class A, class B, class C, class D> struct F2 { A a; B b; C c; D d; F2() { a = 0, b = 0, c = 0, d = 0; } F2(A a, B b, C c, D d) : a(a), b(b), c(c), d(d) {} bool operator<(const F2 &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 F2 &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 F2 &r) const { return a == r.a && b == r.b && c == r.c && d == r.d; } bool operator!=(const F2 &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; }};
typedef T2<int, int, int> T;
typedef F2<int, int, int, int> F;
T mt(int a, int b, int c) {return T(a, b, c);}
//@マクロ省略系 型,構造
#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;
#define au auto
using P = pair<int, int>;
using pd =pair<dou, dou>;
#define fi first
#define se second
#define beg begin
#define rbeg rbegin
#define con continue
#define bre break
#define brk break
#define is ==
#define elf else if
#define wh while
#define maxq 1
#define minq -1
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
#define MALLOC(type, len) (type*)malloc((len) * sizeof(type))
#define lam(right) [&](int& p){return p right;}
//マクロ省略系 コンテナ
using vi = vector<int>;
using vb = vector<bool>;
using vs = vector<string>;
using vd = vector<double>;
using vc = vector<char>;
using vp = vector<P>;
using vt = vector<T>;
#define V vector
#define o_vvt(o1, o2, o3, o4, name, ...) name
#define vvt0(t) V<V<t>>
#define vvt1(t,a) V<V<t>>a
#define vvt2(t,a, b) V<V<t>>a(b)
#define vvt3(t,a, b, c) V<V<t>> a(b,V<t>(c))
#define vvt4(t,a, b, c, d) V<V<t>> a(b,V<t>(c,d))
#define vvi(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(int,__VA_ARGS__)
#define vvb(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(bool,__VA_ARGS__)
#define vvs(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(string,__VA_ARGS__)
#define vvd(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(double,__VA_ARGS__)
#define vvc(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(char,__VA_ARGS__)
#define vvp(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(P,__VA_ARGS__)
template<typename T> vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));}
#define vni(name, ...) auto name = make_v<int>(__VA_ARGS__)
#define vnb(name, ...) auto name = make_v<bool>(__VA_ARGS__)
#define vns(name, ...) auto name = make_v<string>(__VA_ARGS__)
#define vnd(name, ...) auto name = make_v<double>(__VA_ARGS__)
#define vnc(name, ...) auto name = make_v<char>(__VA_ARGS__)
#define vnp(name, ...) auto name = make_v<P>(__VA_ARGS__)
#define PQ priority_queue<int, vector<int>, greater<int> >
#define tos to_string
using mapi = map<int, int>;
using mapp = map<P, 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 useti unordered_set<int,int,xorshift>
#define mset multiset
#define umap unordered_map
#define umapi unordered_map<int,int,xorshift>
#define umapp unordered_map<P,int,xorshift>
#define mmap multimap
template<class T> struct pq { priority_queue<T, vector<T>, greater<T> > q;/*小さい順*/ T su = 0; void clear() {q = priority_queue<T, vector<T>, greater<T> >();su = 0;} void operator+=(T v) {su += v;q.push(v);} T sum() {return su;} T top() {return q.top();} void pop() {su -= q.top();q.pop();} T poll() {T ret = q.top();su -= ret;q.pop();return ret;} int size() {return q.size();}};
template<class T> struct pqg { priority_queue<T> q;/*大きい順*/ T su = 0; void clear() {q = priority_queue<T>();su = 0;} void operator+=(T v) {su += v;q.push(v);} T sum() {return su;} T top() {return q.top();} void pop() {su -= q.top();q.pop();} T poll() {T ret = q.top();su -= ret;q.pop();return ret;} int size() {return q.size();}};
#define pqi pq<int>
#define pqgi pqg<int>
//マクロ 繰り返し
#define o_rep(o1, o2, o3, o4, name, ...) name
# define rep1(n) for(int rep1i = 0,rep1lim=n; rep1i < rep1lim ; ++rep1i)
# define rep2(i, n) for(int i = 0,rep2lim=n; i < rep2lim ; ++i)
#define rep3(i, m, n) for(int i = m,rep3lim=n; i < rep3lim ; ++i)
#define rep4(i, m, n, ad) for(int i = m,rep4lim=n; i < rep4lim ; i+= ad)
#define rep(...) o_rep(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rer2(i, n) for(int i = n; i >= 0 ; i--)
#define rer3(i, m, n) for(int i = m,rer3lim=n; i >= rer3lim ; i--)
#define rer4(i, m, n, dec) for(int i = m,rer4lim=n; i >= rer4lim ; i-=dec)
#define rer(...) o_rep(__VA_ARGS__,rer4,rer3,rer2,)(__VA_ARGS__)
#define reps2(i, j, n) for(int i = 0,reps2lim=n; i < reps2lim ;++i)for(int j = 0; j < reps2lim ; ++j)
#define reps3(i, j, k, n) for(int i = 0,reps3lim=n; i < reps3lim ; ++i)for(int j = 0; j < reps3lim ; ++j)for(int k = 0; k < reps3lim ; ++k)
#define reps4(i, j, k, l, n) for(int i = 0,reps4lim=n; i < reps4lim ; ++i)for(int j = 0; j < reps4lim ; ++j)for(int k = 0; k < reps4lim ; ++k)for(int l = 0; l < reps4lim ; ++l)
#define o_reps(o1, o2, o3, o4, o5, name, ...) name
#define reps(...) o_reps(__VA_ARGS__,reps4,reps3,reps2,rep2,)(__VA_ARGS__)
#define repss(i, j, k, a, b, c) for(int i = 0; i < a ; ++i)for(int j = 0; j < b ; ++j)for(int k = 0; k < c ; ++k)
#define fora(a, b) for(auto&& a : b)
#define forg(gi, ve) for (int gi = 0,forglim = ve.size(), f, t, c; gi < forglim && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c, true); ++gi)
#define fort(gi, ve) for (int gi = 0, f, t, c; gi < ve.size() && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c, true); ++gi)if(t!=p)
#define form(st, l, r) for (auto &&it = st.lower_bound(l); it != st.end() && (*it).fi < r; ++it)
#define forit(st, l, r) for (auto &&it = st.lower_bound(l); it != st.end() && (*it) < r;)
//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 char infc = '{';
const string infs = "{";
const double eps = 1e-9;
const double PI = 3.1415926535897932384626433832795029L;
ll ma = numeric_limits<ll>::min();
ll mi = numeric_limits<ll>::max();
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 mp make_pair
#define pb pop_back
#define pf push_front
#define eb emplace_back
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
constexpr bool ev(int a) { return !(a & 1); }
constexpr bool od(int a) { return (a & 1); }
//@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);}};}
//stream まとめ
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<class T, class U> ostream &operator<<(ostream &os, pair<T, U> 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 T, typename U> ostream &operator<<(ostream &os, map<T, U> &m) { for (auto &&v:m) os << v; return os;}
template<typename W, typename H> void resize(vector<W> &vec, const H head) { vec.resize(head); }template<typename W, typename H, typename ... T> void resize(vector<W> &vec, const H &head, const T ... tail) {vec.resize(head);for (auto &v: vec)resize(v, tail...);}
template<typename T, typename F> bool all_of2(T &v, F f) { return f(v); }
template<typename T, typename F> bool all_of2(vector<T> &v, F f) { rep(i, sz(v)) { if (!all_of2(v[i], f))return false; } return true;}
template<typename T, typename F> bool any_of2(T &v, F f) { return f(v); }
template<typename T, typename F> bool any_of2(vector<T> &v, F f) { rep(i, sz(v)) { if (any_of2(v[i], f))return true; } return false;}
template<typename T, typename F> bool none_of2(T &v, F f) { return f(v); }
template<typename T, typename F> bool none_of2(vector<T> &v, F f) { rep(i, sz(v)) { if (none_of2(v[i], f))return false; } return true;}
template<typename T, typename F> bool find_if2(T &v, F f) { return f(v); }
template<typename T, typename F> int find_if2(vector<T> &v, F f) { rep(i, sz(v)) { if (find_if2(v[i], f))return i; } return sz(v);}
template<typename T, typename F> bool rfind_if2(T &v, F f) { return f(v); }
template<typename T, typename F> int rfind_if2(vector<T> &v, F f) { rer(i, sz(v) - 1) { if (rfind_if2(v[i], f))return i; } return -1;}
template<class T> bool contains(string &s, const T &v) { return s.find(v) != string::npos; }
template<typename T> bool contains(vector<T> &v, const T &val) { return std::find(v.begin(), v.end(), val) != v.end(); }
template<typename T, typename F> bool contains_if2(vector<T> &v, F f) { return find_if(v.begin(), v.end(), f) != v.end(); }
template<typename T, typename F> int count_if2(T &v, F f) { return f(v); }
template<typename T, typename F> int count_if2(vector<T> &vec, F f) { int ret = 0; fora(v, vec)ret += count_if2(v, f); return ret;}
template<typename T, typename F> void for_each2(T &v, F f) { f(v); }
template<typename T, typename F> void for_each2(vector<T> &vec, F f) { fora(v, vec)for_each2(v, f); }
template<typename W> int count_od(vector<W> &a) {return count_if2(a,[](int v){return v&1 ;});}
template<typename W> int count_ev(vector<W> &a) {return count_if2(a,[](int v){return !(v&1) ;});}
#define all_of(a,right) all_of2(a,lam(right))
#define any_of(a,right) any_of2(a,lam(right))
#define none_of(a,right) none_of2(a,lam(right))
#define find_if(a,right) find_if2(a,lam(right))
#define rfind_if(a,right) rfind_if2(a,lam(right))
#define contains_if(a,right) contains_if2(a,lam(right))
#define count_if(a, right) count_if2(a,lam(right))
#define for_each(a, right) do{fora(v,a){v right;}}while(0)
template<class T, class U> void replace(vector<T> &a, T key, U v) { replace(a.begin(), a.end(), key, v); }
void replace(str &a, char key, str v) { if (v == "")a.erase(remove(all(a), key), a.end()); }
void replace(str &a, char key, char v) { replace(all(a), key, v); }
//keyと同じかどうか01で置き換える
template<class T, class U> void replace(vector<T> &a, U k) { rep(i, sz(a)) a[i] = a[i] == k; }
template<class T, class U> void replace(vector<vector<T >> &a, U k) { rep(i, sz(a))rep(j, sz(a[0])) a[i][j] = a[i][j] == k; }
template<class T> void replace(T &a) { replace(a, '#'); }
void replace(str &a, str key, str v) {stringstream t;int kn = sz(key);std::string::size_type Pos(a.find(key));int l = 0;while (Pos != std::string::npos) {t << a.substr(l, Pos - l);t << v;l = Pos + kn;Pos = a.find(key, Pos + kn);}t << a.substr(l, sz(a) - l);a = t.str();}
template<class T> bool includes(vector<T> &a, vector<T> &b) {vi c = a;vi d = b;sort(all(c));sort(all(d));return includes(all(c), all(d));}
template<class T> bool is_permutation(vector<T> &a, vector<T> &b) { return is_permutation(all(a), all(b)); }
template<class T> bool next_permutation(vector<T> &a) { return next_permutation(all(a)); }
void iota(vector<int> &ve, int s, int n) {ve.resize(n);iota(all(ve), s);}
vi iota(int s, int len) {vi ve(len);iota(all(ve), s);return ve;}
template<class A, class B> auto vtop(vector<A> &a, vector<B> &b) { assert(sz(a) == sz(b)); /*stringを0で初期化できない */ vector<pair<A, B>> res; rep(i, sz(a))res.eb(a[i], b[i]);return res;}
template<class A, class B> void ptov(vector<pair<A, B>> &p, vector<A> &a, vector<B> &b) { a.resize(sz(p)), b.resize(sz(p)); rep(i, sz(p))a[i] = p[i].fi, b[i] = p[i].se;}
template<class A, class B, class C> auto vtot(vector<A> &a, vector<B> &b, vector<C> &c) { assert(sz(a) == sz(b) && sz(b) == sz(c)); vector<T2<A, B, C>> res; rep(i, sz(a))res.eb(a[i], b[i], c[i]); return res;}
template<class A, class B, class C, class D> auto vtof(vector<A> &a, vector<B> &b, vector<C> &c, vector<D> &d) { assert(sz(a) == sz(b) && sz(b) == sz(c) && sz(c) == sz(d)); vector<F2<A, B, C, D>> res; rep(i, sz(a))res.eb(a[i], b[i], c[i], d[i]); return res;}
enum pcomparator { fisi, fisd, fdsi, fdsd, sifi, sifd, sdfi, sdfd };
enum tcomparator { fisiti, fisitd, fisdti, fisdtd, fdsiti, fdsitd, fdsdti, fdsdtd, fitisi, fitisd, fitdsi, fitdsd, fdtisi, fdtisd, fdtdsi, fdtdsd, sifiti, sifitd, sifdti, sifdtd, sdfiti, sdfitd, sdfdti, sdfdtd, sitifi, sitifd, sitdfi, sitdfd, sdtifi, sdtifd, sdtdfi, sdfdfd, tifisi, tifisd, tifdsi, tifdsd, tdfisi, tdfisd, tdfdsi, tdfdsd, tisifi, tisifd, tisdfi, tisdfd, tdsifi, tdsifd, tdsdfi, tdsdfd};
template<class A, class B> void sort(vector<pair<A, B>> &a, pcomparator type) { typedef pair<A, B> U; if (type == fisi) sort(all(a), [&](U l, U r) { return l.fi != r.fi ? l.fi < r.fi : l.se < r.se; }); else if (type == fisd) sort(all(a), [&](U l, U r) { return l.fi != r.fi ? l.fi < r.fi : l.se > r.se; }); else if (type == fdsi) sort(all(a), [&](U l, U r) { return l.fi != r.fi ? l.fi > r.fi : l.se < r.se; }); else if (type == fdsd) sort(all(a), [&](U l, U r) { return l.fi != r.fi ? l.fi > r.fi : l.se > r.se; }); else if (type == sifi) sort(all(a), [&](U l, U r) { return l.se != r.se ? l.se < r.se : l.fi < r.fi; }); else if (type == sifd) sort(all(a), [&](U l, U r) { return l.se != r.se ? l.se < r.se : l.fi > r.fi; }); else if (type == sdfi) sort(all(a), [&](U l, U r) { return l.se != r.se ? l.se > r.se : l.fi < r.fi; }); else if (type == sdfd) sort(all(a), [&](U l, U r) { return l.se != r.se ? l.se > r.se : l.fi > r.fi; });};template<class U> void sort(vector<U> &a, pcomparator type) { if (type == fisi) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.s < r.s; }); else if (type == fisd) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.s > r.s; }); else if (type == fdsi) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.s < r.s; }); else if (type == fdsd) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.s > r.s; }); else if (type == sifi) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.f < r.f; }); else if (type == sifd) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.f > r.f; }); else if (type == sdfi) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.f < r.f; }); else if (type == sdfd) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.f > r.f; });};template<class A, class B, class C, class D> void sort(vector<F2<A, B, C, D> > &a, pcomparator type) { typedef F2<A, B, C, D> U; if (type == fisi) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.b < r.b; }); else if (type == fisd) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.b > r.b; }); else if (type == fdsi) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.b < r.b; }); else if (type == fdsd) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.b > r.b; }); else if (type == sifi) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.a < r.a; }); else if (type == sifd) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.a > r.a; }); else if (type == sdfi) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.a < r.a; }); else if (type == sdfd) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.a > r.a; });};template<class U> void sort(vector<U> &a, tcomparator type) { if (type == 0) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.s != r.s ? l.s < r.s : l.t < r.t; }); else if (type == 1) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.s != r.s ? l.s < r.s : l.t > r.t; }); else if (type == 2) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.s != r.s ? l.s > r.s : l.t < r.t; }); else if (type == 3) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.s != r.s ? l.s > r.s : l.t > r.t; }); else if (type == 4) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.s != r.s ? l.s < r.s : l.t < r.t; }); else if (type == 5) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.s != r.s ? l.s < r.s : l.t > r.t; }); else if (type == 6) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.s != r.s ? l.s > r.s : l.t < r.t; }); else if (type == 7) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.s != r.s ? l.s > r.s : l.t > r.t; }); else if (type == 8) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.t != r.t ? l.t < r.t : l.s < r.s; }); else if (type == 9) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.t != r.t ? l.t < r.t : l.s > r.s; }); else if (type == 10) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.t != r.t ? l.t > r.t : l.s < r.s; }); else if (type == 11) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f < r.f : l.t != r.t ? l.t > r.t : l.s > r.s; }); else if (type == 12) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.t != r.t ? l.t < r.t : l.s < r.s; }); else if (type == 13) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.t != r.t ? l.t < r.t : l.s > r.s; }); else if (type == 14) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.t != r.t ? l.t > r.t : l.s < r.s; }); else if (type == 15) sort(all(a), [&](U l, U r) { return l.f != r.f ? l.f > r.f : l.t != r.t ? l.t > r.t : l.s > r.s; }); else if (type == 16) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.f != r.f ? l.f < r.f : l.t < r.t; }); else if (type == 17) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.f != r.f ? l.f < r.f : l.t > r.t; }); else if (type == 18) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.f != r.f ? l.f > r.f : l.t < r.t; }); else if (type == 19) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.f != r.f ? l.f > r.f : l.t > r.t; }); else if (type == 20) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.f != r.f ? l.f < r.f : l.t < r.t; }); else if (type == 21) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.f != r.f ? l.f < r.f : l.t > r.t; }); else if (type == 22) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.f != r.f ? l.f > r.f : l.t < r.t; }); else if (type == 23) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.f != r.f ? l.f > r.f : l.t > r.t; }); else if (type == 24) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.t != r.t ? l.t < r.t : l.f < r.f; }); else if (type == 25) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.t != r.t ? l.t < r.t : l.f > r.f; }); else if (type == 26) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.t != r.t ? l.t > r.t : l.f < r.f; }); else if (type == 27) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s < r.s : l.t != r.t ? l.t > r.t : l.f > r.f; }); else if (type == 28) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.t != r.t ? l.t < r.t : l.f < r.f; }); else if (type == 29) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.t != r.t ? l.t < r.t : l.f > r.f; }); else if (type == 30) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.t != r.t ? l.t > r.t : l.f < r.f; }); else if (type == 31) sort(all(a), [&](U l, U r) { return l.s != r.s ? l.s > r.s : l.t != r.t ? l.t > r.t : l.f > r.f; }); else if (type == 32) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t < r.t : l.f != r.f ? l.f < r.f : l.s < r.s; }); else if (type == 33) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t < r.t : l.f != r.f ? l.f < r.f : l.s > r.s; }); else if (type == 34) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t < r.t : l.f != r.f ? l.f > r.f : l.s < r.s; }); else if (type == 35) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t < r.t : l.f != r.f ? l.f > r.f : l.s > r.s; }); else if (type == 36) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t > r.t : l.f != r.f ? l.f < r.f : l.s < r.s; }); else if (type == 37) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t > r.t : l.f != r.f ? l.f < r.f : l.s > r.s; }); else if (type == 38) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t > r.t : l.f != r.f ? l.f > r.f : l.s < r.s; }); else if (type == 39) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t > r.t : l.f != r.f ? l.f > r.f : l.s > r.s; }); else if (type == 40) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t < r.t : l.s != r.s ? l.s < r.s : l.f < r.f; }); else if (type == 41) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t < r.t : l.s != r.s ? l.s < r.s : l.f > r.f; }); else if (type == 42) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t < r.t : l.s != r.s ? l.s > r.s : l.f < r.f; }); else if (type == 43) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t < r.t : l.s != r.s ? l.s > r.s : l.f > r.f; }); else if (type == 44) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t > r.t : l.s != r.s ? l.s < r.s : l.f < r.f; }); else if (type == 45) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t > r.t : l.s != r.s ? l.s < r.s : l.f > r.f; }); else if (type == 46) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t > r.t : l.s != r.s ? l.s > r.s : l.f < r.f; }); else if (type == 47) sort(all(a), [&](U l, U r) { return l.t != r.t ? l.t > r.t : l.s != r.s ? l.s > r.s : l.f > r.f; });}template<class A, class B, class C, class D> void sort(vector<F2<A, B, C, D>> &a, tcomparator type) { typedef F2<A, B, C, D> U; if (type == 0) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.b != r.b ? l.b < r.b : l.c < r.c; }); else if (type == 1) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.b != r.b ? l.b < r.b : l.c > r.c; }); else if (type == 2) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.b != r.b ? l.b > r.b : l.c < r.c; }); else if (type == 3) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.b != r.b ? l.b > r.b : l.c > r.c; }); else if (type == 4) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.b != r.b ? l.b < r.b : l.c < r.c; }); else if (type == 5) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.b != r.b ? l.b < r.b : l.c > r.c; }); else if (type == 6) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.b != r.b ? l.b > r.b : l.c < r.c; }); else if (type == 7) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.b != r.b ? l.b > r.b : l.c > r.c; }); else if (type == 8) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.c != r.c ? l.c < r.c : l.b < r.b; }); else if (type == 9) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.c != r.c ? l.c < r.c : l.b > r.b; }); else if (type == 10) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.c != r.c ? l.c > r.c : l.b < r.b; }); else if (type == 11) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a < r.a : l.c != r.c ? l.c > r.c : l.b > r.b; }); else if (type == 12) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.c != r.c ? l.c < r.c : l.b < r.b; }); else if (type == 13) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.c != r.c ? l.c < r.c : l.b > r.b; }); else if (type == 14) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.c != r.c ? l.c > r.c : l.b < r.b; }); else if (type == 15) sort(all(a), [&](U l, U r) { return l.a != r.a ? l.a > r.a : l.c != r.c ? l.c > r.c : l.b > r.b; }); else if (type == 16) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.a != r.a ? l.a < r.a : l.c < r.c; }); else if (type == 17) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.a != r.a ? l.a < r.a : l.c > r.c; }); else if (type == 18) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.a != r.a ? l.a > r.a : l.c < r.c; }); else if (type == 19) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.a != r.a ? l.a > r.a : l.c > r.c; }); else if (type == 20) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.a != r.a ? l.a < r.a : l.c < r.c; }); else if (type == 21) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.a != r.a ? l.a < r.a : l.c > r.c; }); else if (type == 22) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.a != r.a ? l.a > r.a : l.c < r.c; }); else if (type == 23) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.a != r.a ? l.a > r.a : l.c > r.c; }); else if (type == 24) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.c != r.c ? l.c < r.c : l.a < r.a; }); else if (type == 25) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.c != r.c ? l.c < r.c : l.a > r.a; }); else if (type == 26) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.c != r.c ? l.c > r.c : l.a < r.a; }); else if (type == 27) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b < r.b : l.c != r.c ? l.c > r.c : l.a > r.a; }); else if (type == 28) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.c != r.c ? l.c < r.c : l.a < r.a; }); else if (type == 29) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.c != r.c ? l.c < r.c : l.a > r.a; }); else if (type == 30) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.c != r.c ? l.c > r.c : l.a < r.a; }); else if (type == 31) sort(all(a), [&](U l, U r) { return l.b != r.b ? l.b > r.b : l.c != r.c ? l.c > r.c : l.a > r.a; }); else if (type == 32) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c < r.c : l.a != r.a ? l.a < r.a : l.b < r.b; }); else if (type == 33) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c < r.c : l.a != r.a ? l.a < r.a : l.b > r.b; }); else if (type == 34) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c < r.c : l.a != r.a ? l.a > r.a : l.b < r.b; }); else if (type == 35) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c < r.c : l.a != r.a ? l.a > r.a : l.b > r.b; }); else if (type == 36) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c > r.c : l.a != r.a ? l.a < r.a : l.b < r.b; }); else if (type == 37) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c > r.c : l.a != r.a ? l.a < r.a : l.b > r.b; }); else if (type == 38) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c > r.c : l.a != r.a ? l.a > r.a : l.b < r.b; }); else if (type == 39) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c > r.c : l.a != r.a ? l.a > r.a : l.b > r.b; }); else if (type == 40) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c < r.c : l.b != r.b ? l.b < r.b : l.a < r.a; }); else if (type == 41) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c < r.c : l.b != r.b ? l.b < r.b : l.a > r.a; }); else if (type == 42) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c < r.c : l.b != r.b ? l.b > r.b : l.a < r.a; }); else if (type == 43) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c < r.c : l.b != r.b ? l.b > r.b : l.a > r.a; }); else if (type == 44) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c > r.c : l.b != r.b ? l.b < r.b : l.a < r.a; }); else if (type == 45) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c > r.c : l.b != r.b ? l.b < r.b : l.a > r.a; }); else if (type == 46) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c > r.c : l.b != r.b ? l.b > r.b : l.a < r.a; }); else if (type == 47) sort(all(a), [&](U l, U r) { return l.c != r.c ? l.c > r.c : l.b != r.b ? l.b > r.b : l.a > r.a; });}
void sort(string &a) { sort(all(a)); }
template<class T> void sort(vector<T> &a) { sort(all(a)); }
//P l, P rで f(P) の形で渡す
template<class U, class F> void sort(vector<U> &a, F f) { sort(all(a), [&](U l, U r) { return f(l) < f(r); }); };
template<class T> void rsort(vector<T> &a) { sort(all(a), greater<T>()); };
template<class U, class F> void rsort(vector<U> &a, F f) { sort(all(a), [&](U l, U r) { return f(l) > f(r); }); };
//F = T<T>
//例えばreturn p.fi + p.se;
template<class A, class B> void sortp(vector<A> &a, vector<B> &b) { auto c = vtop(a, b); sort(c); rep(i, sz(a)) a[i] = c[i].fi, b[i] = c[i].se;}template<class A, class B, class F> void sortp(vector<A> &a, vector<B> &b, F f) { auto c = vtop(a, b); sort(c, f); rep(i, sz(a)) a[i] = c[i].fi, b[i] = c[i].se;}template<class A, class B> void rsortp(vector<A> &a, vector<B> &b) { auto c = vtop(a, b); rsort(c); rep(i, sz(a))a[i] = c[i].first, b[i] = c[i].second;}template<class A, class B, class F> void rsortp(vector<A> &a, vector<B> &b, F f) { auto c = vtop(a, b); rsort(c, f); rep(i, sz(a))a[i] = c[i].first, b[i] = c[i].second;}
//@formatter:on
template<class A, class B, class C> void sortt(vector<A> &a, vector<B> &b, vector<C> &c) {
auto d = vtot(a, b, c);
sort(d);
rep(i, sz(a)) a[i] = d[i].f, b[i] = d[i].s, c[i] = d[i].t;
}
template<class A, class B, class C, class F> void sortt(vector<A> &a, vector<B> &b, vector<C> &c, F f) {
auto d = vtot(a, b, c);
sort(d, f);
rep(i, sz(a)) a[i] = d[i].f, b[i] = d[i].s, c[i] = d[i].t;
}
template<class A, class B, class C> void rsortt(vector<A> &a, vector<B> &b, vector<C> &c) {
auto d = vtot(a, b, c);
rsort(d);
rep(i, sz(a)) a[i] = d[i].f, b[i] = d[i].s, c[i] = d[i].t;
}
template<class A, class B, class C, class F> void rsortt(vector<A> &a, vector<B> &b, vector<C> &c, F f) {
auto d = vtot(a, b, c);
rsort(d, f);
rep(i, sz(a)) a[i] = d[i].f, b[i] = d[i].s, c[i] = d[i].t;
}
template<class A, class B, class C, class D> void sortf(vector<A> &a, vector<B> &b, vector<C> &c, vector<D> &d) {
auto e = vtof(a, b, c, d);
sort(e);
rep(i, sz(a)) a[i] = e[i].a, b[i] = e[i].b, c[i] = e[i].c, d[i] = e[i].d;
}
template<class A, class B, class C, class D> void rsortf(vector<A> &a, vector<B> &b, vector<C> &c, vector<D> &d) {
auto e = vtof(a, b, c, d);
rsort(e);
rep(i, sz(a)) a[i] = e[i].a, b[i] = e[i].b, c[i] = e[i].c, d[i] = e[i].d;
}
//@formatter:off
//sortindex 元のvectorはソートしない
template<class T> vi sorti(vector<T> &a) { auto b = a; vi ind = iota(0, sz(a)); sortp(b, ind); return ind;}/*indexの分で型が変わるためpcomparatorが必要*/template<class T> vi sorti(vector<T> &a, pcomparator f) { auto b = a; vi ind = iota(0, sz(a)); sortp(b, ind, f); return ind;}template<class T, class F> vi sorti(vector<T> &a, F f) { vi ind = iota(0, sz(a)); sort(all(ind), [&](int x, int y) { return f(a[x]) < f(a[y]); }); return ind;}template<class T> vi rsorti(vector<T> &a) { auto b = a; vi ind = iota(0, sz(a)); rsortp(b, ind); return ind;}template<class T, class F> vi rsorti(vector<T> &a, F f) { vi ind = iota(0, sz(a)); sort(all(ind), [&](int x, int y) { return f(a[x]) > f(a[y]); }); return ind;}template<class A, class B, class F> vi sortpi(vector<A> &a, vector<B> &b, F f) { auto c = vtop(a, b); vi ind = iota(0, sz(a)); sort(all(ind), [&](int x, int y) { return f(c[x]) < f(c[y]); }); return ind;}template<class A, class B> vi sortpi(vector<A> &a, vector<B> &b, pcomparator f) { vi ind = iota(0, sz(a)); auto c = a; auto d = b; sortt(c, d, ind, f); return ind;}template<class A, class B> vi sortpi(vector<A> &a, vector<B> &b) { return sortpi(a, b, fisi); };template<class A, class B, class F> vi rsortpi(vector<A> &a, vector<B> &b, F f) { auto c = vtop(a, b); vi ind = iota(0, sz(a)); sort(all(ind), [&](int x, int y) { return f(c[x]) > f(c[y]); }); return ind;}template<class A, class B> vi rsortpi(vector<A> &a, vector<B> &b) { return sortpi(a, b, fdsd); };template<class A, class B, class C, class F> vi sortti(vector<A> &a, vector<B> &b, vector<C> &c, F f) { auto d = vtot(a, b, c); vi ind = iota(0, sz(a)); sort(all(ind), [&](int x, int y) { return f(d[x]) < f(d[y]); }); return ind;}template<class A, class B, class C> vi sortti(vector<A> &a, vector<B> &b, vector<C> &c, pcomparator f) { vi ind = iota(0, sz(a)); auto d = vtof(a, b, c, ind); sort(d, f); rep(i, sz(a))ind[i] = d[i].d; return ind;}template<class A, class B, class C> vi sortti(vector<A> &a, vector<B> &b, vector<C> &c) { vi ind = iota(0, sz(a)); sort(all(ind), [&](int x, int y) { if (a[x] == a[y]) { if (b[x] == b[y])return c[x] < c[y]; else return b[x] < b[y]; } else { return a[x] < a[y]; } }); return ind;}template<class A, class B, class C, class F> vi rsortti(vector<A> &a, vector<B> &b, vector<C> &c, F f) { auto d = vtot(a, b, c); vi ind = iota(0, sz(a)); sort(all(ind), [&](int x, int y) { return f(d[x]) > f(d[y]); }); return ind;}template<class A, class B, class C> vi rsortti(vector<A> &a, vector<B> &b, vector<C> &c) { vi ind = iota(0, sz(a)); sort(all(ind), [&](int x, int y) { if (a[x] == a[y]) { if (b[x] == b[y])return c[x] > c[y]; else return b[x] > b[y]; } else { return a[x] > a[y]; } }); return ind;}
template<class T> void sort2(vector<vector<T >> &a) { for (int i = 0, n = a.size(); i < n; ++i)sort(a[i]); }
template<class T> 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 W, typename T>void fill(W &xx, const T vall) { xx = vall;}template<typename W, typename T>void fill(vector<W> &vecc, const T vall) { for (auto &&vx : vecc)fill(vx, vall);}
template<class T,class U>void fill(vector<T> &a,U val,vi& ind) {fora(v,ind)a[v]=val;}
template<typename A, size_t N> A sum(A (&a)[N]) { A res = 0; rep(i, N)res += a[i]; return res;}template<typename A, size_t N, size_t O> A sum(A (&a)[N][O]) { A res = 0; rep(i, N)rep(j, O)res += a[i][j]; return res;}template<typename A, size_t N, size_t O, size_t P> A sum(A (&a)[N][O][P]) { A res = 0; rep(i, N)rep(j, O)rep(k, P)res += a[i][j][k]; return res;}template<typename A, size_t N, size_t O, size_t P, size_t Q> A sum(A (&a)[N][O][P][Q]) { A res = 0; rep(i, N)rep(j, O)rep(k, P)rep(l, Q)res += a[i][j][k][l]; return res;}template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R> A sum(A (&a)[N][O][P][Q][R]) { A res = 0; rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)res += a[i][j][k][l][m]; return res;}template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, size_t S> A sum(A (&a)[N][O][P][Q][R][S]) { A res = 0; rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)rep(n, S)res += a[i][j][k][l][m][n]; return res;}
//@汎用便利関数 入力
int in() {int ret;cin >> ret;return ret;}
string sin() {string ret;cin >> ret;return ret;}
template<class T> void in(T &head) { cin >> head; }template<class T, class... U> void in(T &head, U &... tail) {cin >> head;in(tail...);}
#define o_din(o1, o2, o3, o4, name, ...) name
#define din1(a) int a;cin>>a
#define din2(a, b) int a,b;cin>>a>> b
#define din3(a, b, c) int a,b,c;cin>>a>>b>>c
#define din4(a, b, c, d) int a,b,c,d;cin>>a>>b>>c>>d
#define din(...) o_din(__VA_ARGS__,din4,din3,din2 ,din1)(__VA_ARGS__)
#define o_dind(o1, o2, o3, o4, name, ...) name
#define din1d(a) din1(a);a--
#define din2d(a, b) din2(a,b);a--,b--
#define din3d(a, b, c) din3(a,b,c);a--,b--,c--
#define din4d(a, b, c, d) din4(a,b,c,d);a--,b--,c--,d--
#define dind(...) o_dind(__VA_ARGS__,din4d,din3d,din2d ,din1d)(__VA_ARGS__)
#define o_out(o1, o2, o3, o4, name, ...) name
#define out1(a) cout<<a<<endl
#define out2(a, b) cout<<a<<" "<< b<<endl
#define out3(a, b, c) cout<<a<<" "<<b<<" "<<c<<endl
#define out4(a, b, c, d) cout<<a<<" "<<b<<" "<<c<<" "<<d<<endl
#define out(...) o_out((__VA_ARGS__),out4,out3,out2,out1)((__VA_ARGS__))
template<class T> void outl(vector<T> &a) { fora(v, a)cout << v << endl; }
template<class T> void na(vector<T> &a, int n) {a.resize(n);rep(i, n)cin >> a[i];}
#define dna(a, n) vi a(n); rep(dnai,n) cin >> a[dnai];
template<class T> void nao(vector<T> &a, int n) { a.resize(n + 1); a[0] = 0; rep(i, n)cin >> a[i + 1];}
template<class T> void naod(vector<T> &a, int n) { a.resize(n + 1); a[0] = 0; rep(i, n)cin >> a[i + 1],a[i+1]--;}
template<class T> void nad(vector<T> &a, int n) { a.resize(n); rep(i, n)cin >> a[i], a[i]--;}
template<class T, class U> void na2(vector<T> &a, vector<U> &b, int n) { a.resize(n); b.resize(n); rep(i, n)cin >> a[i] >> b[i];}
#define dna2(a, b, n) vi a(n),b(n);rep(dna2i, n)cin >> a[dna2i] >> b[dna2i];
template<class T, class U> void nao2(vector<T> &a, vector<U> &b, int n) { a.resize(n + 1); b.resize(n + 1); a[0] = b[0] = 0; rep(i, n)cin >> a[i + 1] >> b[i + 1];}
#define dna2d(a, b, n) vi a(n),b(n);rep(dna2di, n){cin >> a[dna2di] >> b[dna2di];a[dna2di]--,b[dna2di]--;}
template<class T, class U> void na2d(vector<T> &a, vector<U> &b, int n) { a.resize(n); b.resize(n); rep(i, n)cin >> a[i] >> b[i], a[i]--, b[i]--;}
template<class T, class U, class W> void na3(vector<T> &a, vector<U> &b, vector<W> &c, int n) { a.resize(n); b.resize(n); c.resize(n); rep(i, n)cin >> a[i] >> b[i] >> c[i];}
#define dna3(a, b, c, n) vi a(n),b(n),c(n); rep(dna3i, n)cin >> a[dna3i] >> b[dna3i] >> c[dna3i];
template<class T, class U, class W> void na3d(vector<T> &a, vector<U> &b, vector<W> &c, int 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 dna3d(a, b, c, n) vi a(n),b(n),c(n); rep(dna3di, n){cin >> a[dna3di] >> b[dna3di] >> c[dna3di];a[dna3di]--,b[dna3di]--,c[dna3di]--;}
#define nt(a, h, w) resize(a,h,w);rep(nthi,h)rep(ntwi,w) cin >> a[nthi][ntwi];
#define ntd(a, h, w) resize(a,h,w);rep(ntdhi,h)rep(ntdwi,w) cin >> a[ntdhi][ntdwi], a[ntdhi][ntdwi]--;
#define ntp(a, h, w) resize(a,h+2,w+2);fill(a,'#');rep(ntphi,1,h+1)rep(ntpwi,1,w+1) cin >> a[ntphi][ntpwi];
//デバッグ
#define sp << " " <<
#define debugName(VariableName) # VariableName
#define deb1(x) debugName(x)<<" = "<<x
#define deb2(x, ...) deb1(x) <<", "<< deb1(__VA_ARGS__)
#define deb3(x, ...) deb1(x) <<", "<< deb2(__VA_ARGS__)
#define deb4(x, ...) deb1(x) <<", "<< deb3(__VA_ARGS__)
#define deb5(x, ...) deb1(x) <<", "<< deb4(__VA_ARGS__)
#define deb6(x, ...) deb1(x) <<", "<< deb5(__VA_ARGS__)
#define deb7(x, ...) deb1(x) <<", "<< deb6(__VA_ARGS__)
#define deb8(x, ...) deb1(x) <<", "<< deb7(__VA_ARGS__)
#define deb9(x, ...) deb1(x) <<", "<< deb8(__VA_ARGS__)
#define deb10(x, ...) deb1(x) <<", "<< deb9(__VA_ARGS__)
#define o_ebug(o1, o2, o3, o4, o5, o6, o7, o8, o9, o10, name, ...) name
#ifdef _DEBUG
#define deb(...) cerr<< o_ebug(__VA_ARGS__,deb10,deb9,deb8,deb7,deb6,deb5,deb4,deb3,deb2,deb1)(__VA_ARGS__) <<endl
#else
#define deb(...) ;
#endif
#define debugline(x) cerr << x << " " << "(L:" << __LINE__ << ")" << '\n'
//@formatter:on
//よく使うクラス、構造体
struct unionfind {
vector<int> par;
vector<int> siz;
vector<int> es;
int n, trees;
unionfind(int n) : n(n), trees(n) {
par.resize(n);
siz.resize(n);
es.resize(n);
for (int i = 0; i < n; i++) {
par[i] = i;
siz[i] = 1;
}
}
int root(int x) { if (par[x] == x) { return x; } else { return par[x] = root(par[x]); }}
void unite(int x, int y) {
x = root(x);
y = root(y);
es[x]++;
if (x == y) return;
if (siz[x] > siz[y]) swap(x, y);
trees--;
par[x] = y;
siz[y] += siz[x];
es[y] += es[x];
}
bool same(int x, int y) { return root(x) == root(y); }
int size(int x) { return siz[root(x)]; }
int esize(int x) { return es[root(x)]; }
//つながりを無向グラフと見なし、xが閉路に含まれるか判定
bool close(int x) { return esize(x) >= size(x); }
/*@formatter:off*/V<vi> sets() {vvi(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; }
};
using bint =__int128;
using u32 = unsigned;
using u64 = unsigned long long;
using u128 = __uint128_t;
std::ostream &operator<<(std::ostream &dest, __int128_t value) { std::ostream::sentry s(dest); if (s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest;}
//__int128 toi128(string &s) { __int128 ret = 0; for (int i = 0; i < s.length(); ++i) if ('0' <= s[i] && s[i] <= '9') ret = 10 * ret + s[i] - '0'; return ret;}
//エラー
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 re() { assert(0 == 1);exit(0); }
void tle() { while (inf)cout << inf << endl; }
//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;}
str ransu(int n) { str s; rep(i, n)s += (char) rand('A', 'Z'); return s;}
str ransl(int n) { str s; rep(i, n)s += (char) rand('a', 'z'); return s;}
//単調増加
vi ranvinc(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;}
//便利 汎用
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]); }}
vp run_length(vi &a) { vp ret; ret.eb(a[0], 1); rep(i, 1, sz(a)) { if (ret.back().fi == a[i]) { ret.back().se++; } else { ret.eb(a[i], 1); } } return ret;}
vector<pair<char, int>> run_length(string &a) { vector<pair<char, int>> ret; ret.eb(a[0], 1); rep(i, 1, sz(a)) { if (ret.back().fi == a[i]) { ret.back().se++; } else { ret.eb(a[i], 1); } } return ret;}
template<class F> int mgr(int ok, int ng, F f) {if (ok < ng)while (ng - ok > 1) { int mid = (ok + ng) / 2; if (f(mid))ok = mid; else ng = mid; } else while (ok - ng > 1) { int mid = (ok + ng) / 2; if (f(mid))ok = mid; else ng = mid; }return ok;}
//strを整数として比較
string smax(str &a, str b) { if (sz(a) < sz(b)) { return b; } else if (sz(a) > sz(b)) { return a; } else { rep(i, sz(a)) { if (a[i] < b[i]) { return b; } else if (a[i] > b[i])return a; } } return a;}
//strを整数として比較
string smin(str &a, str b) { if (sz(a) < sz(b)) { return a; } else if (sz(a) > sz(b)) { return b; } else { rep(i, sz(a)) { if (a[i] < b[i]) { return a; } else if (a[i] > b[i])return b; } } return a;}
template<typename W, typename T> int find(vector<W> &a,const T key) {rep(i, sz(a))if (a[i] == key)return i;return -1;}
template<typename W, typename T> P find(vector<vector<W >> &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 W, typename U> T find(vector<vector<vector<W >>> &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 W, typename T> int count2(W &a, const T k) { return a == k; }
template<typename W, typename T> int count2(vector<W> &a, const T k) {int ret = 0;fora(v, a)ret +=count(v, k);return ret;}
template<typename W, typename T> int count(vector<W> &a, const T k) {int ret = 0;fora(v, a)ret +=count2(v, k);return ret;}
int count(str& a, str k) {int ret = 0, len = k.length();auto pos = a.find(k);while (pos != string::npos)pos = a.find(k, pos + len), ++ret;return ret;}
vi count(str& a){ vi cou(26); char c='a'; if('A' <= a[0] && a[0]<='Z')c='A'; rep(i,sz(a))++cou[a[i]-c]; return cou;}
#define couif count_if
//algorythm
inline ll rev(ll a) {ll res = 0;while (a) {res *= 10;res += a % 10;a /= 10;}return res;}
template<class T> void rev(vector<T> &a) {reverse(all(a));}
template<class U> void rev(vector<vector<U>> &a) { vector<vector<U> > b(sz(a[0]), vector<U>(sz(a))); rep(h, sz(a)) rep(w, sz(a[0]))b[w][h] = a[h][w]; a = b;}
void inline rev(string &a) {reverse(all(a));}
constexpr int p10[] = {1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000ll, 100000000000ll, 1000000000000ll, 10000000000000ll, 100000000000000ll, 1000000000000000ll, 10000000000000000ll, 100000000000000000ll, 1000000000000000000ll};
int get(int a, int keta) { return (a / (int) pow(10, keta)) % 10; }
int keta(ll v) { if (v < p10[9]) { if (v < p10[4]) { if (v < p10[2]) { if (v < p10[1]) return 1; else return 2; } else { if (v < p10[3]) return 3; else return 4; }} else { if (v < p10[7]) { if (v < p10[5]) return 5; else if (v < p10[6])return 6; else return 7; } else { if (v < p10[8])return 8; else return 9; }}} else { if (v < p10[13]) { if (v < p10[11]) { if (v < p10[10]) return 10; else return 11; } else { if (v < p10[12]) return 12; else return 13; }} else { if (v < p10[15]) { if (v < p10[14]) return 14; else if (v < p10[15])return 15; else return 16; } else { if (v < p10[17])return 17; else return 18; }}}}
int dsum(int v) {int ret = 0;for (; v; v /= 10)ret += v % 10;return ret;}
struct sint {
int v;
sint(int v) : v(v) {}
operator int() { return v; }
//下からi番目
int operator[](int i) { return (v / p10[i]) % 10; }
int back(int i) { return operator[](i); }
//上からi番目
int top(int i) { int len = keta(v); return operator[](len - 1 - i); }
//先頭からi番目にセット
int settop(int i, int k) { int len = keta(v); return set(len - 1 - i, k); }
int set(int i, int k) { if (i < 0)return settop(abs(i) - 1, k); return v += p10[i] * (k - (v / p10[i]) % 10); }
int add(int i, int k = 1) { return v += p10[i] * k; }
int addtop(int i, int k = 1) { return v += p10[keta(v) - i - 1] * k; }
int dec(int i, int k = 1) { return v -= p10[i] * k; }
int dectop(int i, int k = 1) { return v -= p10[keta(v) - i - 1] * k; }
#define op(t, o)template<class T>inline t operator o(T r){return v o r;}
op(int, +=);op(int, -=);op(int, *=);op(int, /=);op(int, %=);
op(int, +);op(int, -);op(int, *);op(int, /);op(int, %);
op(bool, ==);op(bool, !=);op(bool, <);op(bool, <=);op(bool, >);op(bool, >=);
#undef op
template<class T> inline int operator<<=(T r) { return v *= p10[r]; }
template<class T> inline int operator<<(T r) { return v * p10[r]; }
template<class T> inline int operator>>=(T r) { return v /= p10[r]; }
template<class T> inline int operator>>(T r) { return v / p10[r]; }
};
int mask10(int v) { return p10[v] - 1; }
//変換系
template<class T> auto keys(T a) {vector<decltype((a.begin())->fi)> res;for (auto &&k :a)res.push_back(k.fi);return res;}
template<class T> auto values(T a) {vector<decltype((a.begin())->se)> res;for (auto &&k :a)res.push_back(k.se);return res;}
template<class T, class U> inline bool chma(T &a, const U &b) { if (a < b) { a = b; return true; } return false;}
template<class U> inline bool chma(const U &b) { return chma(ma, b); }
template<class T, class U> inline bool chmi(T &a, const U &b) { if (b < a) { a = b; return true; } return false;}
template<class U> inline bool chmi(const U &b) { return chmi(mi, b); }
template<class T> inline T min(T a, signed b) { return a < b ? a : b; }
template<class T> inline T max(T a, signed b) { return a < b ? b : a; }
template<class T> inline T min(T a, T b, T c) { return a >= b ? b >= c ? c : b : a >= c ? c : a; }
template<class T> inline T max(T a, T b, T c) { return a <= b ? b <= c ? c : b : a <= c ? c : a; }
template<class T> inline T min(vector<T> a) { return *min_element(all(a)); }
template<class T> inline T mini(vector<T> a) { return min_element(all(a)) - a.begin(); }
template<class T> inline T min(vector<T> a, int n) { return *min_element(a.begin(), a.begin() + min(n, sz(a))); }
template<class T> inline T min(vector<T> a, int s, int n) { return *min_element(a.begin() + s, a.begin() + min(n, sz(a))); }
template<class T> inline T max(vector<T> a) { return *max_element(all(a)); }
template<class T> inline T maxi(vector<T> a) { return max_element(all(a)) - a.begin(); }
template<class T> inline T max(vector<T> a, int n) { return *max_element(a.begin(), a.begin() + min(n, sz(a))); }
template<class T> inline 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> inline 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> inline 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> inline 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> inline 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> inline 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> inline 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> inline 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> inline 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> inline 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> inline 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> inline 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> inline 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 s = 0, int t = inf) { T ret = 0; rep(i, s, min(sz(v), t))ret += v[i]; return ret;}
template<class T> T sum(vector<vector<T> > &v) {T ret = 0;rep(i, sz(v))ret += sum(v[i]);return ret;}
template<class T> T sum(vector<vector<vector<T> > > &v) {T ret = 0;rep(i, sz(v))ret += sum(v[i]);return ret;}
template<class T> T sum(vector<vector<vector<vector<T> > > > &v) {T ret = 0;rep(i, sz(v))ret += sum(v[i]);return ret;}
template<class T> T sum(vector<vector<vector<vector<vector<T> > > > > &v) {T ret = 0;rep(i, sz(v))ret += sum(v[i]);return ret;}
template<class T> auto sum(priority_queue<T, vector<T>, greater<T> > &r) {auto q = r;T ret = 0;while (sz(q)) {ret += q.top();q.pop();}return ret;}
template<class T> auto sum(priority_queue<T> &r) { auto q = r; T ret = 0; while (sz(q)) { ret += q.top(); q.pop(); } return ret;}
//template<class T, class U, class... W> inline auto sumn(vector<T> &v, U head, W... tail) { auto ret = sum(v[0], tail...); rep(i, 1, min(sz(v), head))ret += sum(v[i], tail...); return ret;}
void clear(PQ &q) { q=PQ(); }
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; return a;}
//imoは0-indexed
//ruiは1-indexed
template<class T> vector<T> imo(vector<T> &v) { vector<T> ret = v; rep(i, sz(ret) - 1)ret[i + 1] += ret[i]; return ret;}
//kと同じものの数
template<class T, class U> vi imocou(vector<T> &a, U k) { vector<T> ret = a; rep(i, sz(ret) - 1)ret[i + 1] = ret[i] + (a[i] == k); return ret;}
template<class T> vector<T> imox(vector<T> &v) { vector<T> ret = v; rep(i, sz(ret) - 1)ret[i + 1] ^= ret[i]; return ret;}
//漸化的に最小を持つ
template<class T> vector<T> imi(vector<T> &v) { vector<T> ret = v; rep(i, sz(ret) - 1)chmi(ret[i + 1], ret[i]); return ret;}
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]; } T back() { return rui.back(); } int size() { return rui.size(); }};
template<class T> struct rruic { const T *rrui; rruic(T *ru) : rrui(ru) {} inline T operator()(int l, int r) { assert(l >= r); return rrui[r] - rrui[l]; } inline T operator[](int i) { return rrui[i]; }};
template<class T> vector<T> ruiv(vector<T> &a) { vector<T> ret(a.size() + 1); rep(i, a.size())ret[i + 1] = ret[i] + a[i]; return ret;}
template<class T> ruiC<T> ruic(vector<T> &a) { vector<T> ret = ruiv(a); return ruiC<T>(ret);}
vector<int> ruiv(string &a) { if (sz(a) == 0)return vi(1); int dec = ('0' <= a[0] && a[0] <= '9') ? '0' : 0; vector<int> ret(a.size() + 1); rep(i, a.size())ret[i + 1] = ret[i] + a[i] - dec; return ret;}
ruiC<int> ruic(string &a) { vector<int> ret = ruiv(a); return ruiC<int>(ret);}
//kと同じものの数
template<class T, class U> vi ruiv(T &a, U k) { vi ret(a.size() + 1); rep(i, a.size())ret[i + 1] = ret[i] + (a[i] == k); return ret;}
template<class T, class U> ruiC<int> ruic(T &a, U k) { vi ret = ruiv(a, k); return ruiC<int>(ret);}
//xor
template<class T> vector<T> ruix(vector<T> &a) { vector<T> ret(a.size() + 1); rep(i, a.size())ret[i + 1] = ret[i] ^ a[i]; return ret;}
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;}
//漸化的に最小を1indexで持つ
template<class T> vector<T> ruimi(vector<T> &a) { int n = sz(a); vector<T> ret(n + 1); rep(i, 1, n) { ret[i] = a[i - 1]; chmi(ret[i + 1], ret[i]); } return ret;}
//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, 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 U> void dec(string &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); }
bool ins(int h, int w, int H, int W) { return h >= 0 && w >= 0 && h < H && w < W; }
bool ins(int l, int v, int r) { return l <= v && v < r; }
template<class T>bool ins(vector<T>& a,int i,int j=0){return ins(0,i,sz(a)) &&ins(0,j,sz(a));}
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())chmi(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())chma(res, *max_element(all(a[i])));return res;}
constexpr 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;}
ll bit(int n) { return (1LL << (n)); }
ll bit(int n, int sinsuu) { return (ll) pow(sinsuu, n); }
int mask(int n) { return (1ll << n) - 1; }
#define bcou __builtin_popcountll
//最下位ビット
int lbit(int n) {return n & -n;}
//最上位ビット
int hbit(int n) {n |= (n >> 1);n |= (n >> 2);n |= (n >> 4);n |= (n >> 8);n |= (n >> 16);n |= (n >> 32);return n - (n >> 1);}
int hbitk(int n) {int k = 0;rer(i, 5) {int a = k + (1ll << i);int b = 1ll << a;if (b <= n)k += 1ll << i;}return k;}
//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
vi bitCombList(int n, int r) {vi res;int m = 0;while (nextComb(m, n, r)) {res.push_back(m);}return res;}
char itoal(int i) { return 'a' + i;}
char itoaL(int i) { return 'A' + i;}
int altoi(char c) { if ('A' <= c && c <= 'Z')return c - 'A'; return c - 'a';}
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.push_back(i % 10); i /= 10; } rev(res); return res;}
vi stov(string &a) { int n = sz(a); vi ret(n); rep(i, n) { ret[i] = a[i] - '0'; } return ret;}
//基準を満たさないものは0になる
vi stov(string &a,char one) { int n=sz(a); vi ret (n); rep(i,n)ret[i]=a[i]==one; return ret;}
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() );
//[i] := i番として圧縮されたものを返す
vi 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(); } int blen = sz(b); vi ret(blen); rep(i, blen) { ret[i] = b[i]; } return ret;}
vi compress(vi &a, umap<int, int> &map) { 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) { int v = a[i]; a[i] = lower_bound(all(b), a[i]) - b.begin(); map[v] = a[i]; } int blen = sz(b); vi ret(blen); rep(i, blen) { ret[i] = b[i]; } return ret;}
vi compress(vi &a, vi &r) { vi b; int len = a.size(); fora(v, a)b.push_back(v); fora(v, r)b.push_back(v); sort(b); unique(b); for (int i = 0; i < len; ++i) a[i] = lower_bound(all(b), a[i]) - b.begin(); for (int i = 0; i < sz(r); ++i) r[i] = lower_bound(all(b), r[i]) - b.begin(); int blen = sz(b); vi ret(blen); rep(i, blen) { ret[i] = b[i]; } return ret;}
vi compress(vi &a, vi &r, vi &s) { vi b; int len = a.size(); fora(v, a)b.push_back(v); fora(v, r)b.push_back(v); fora(v, s)b.push_back(v); sort(b); unique(b); for (int i = 0; i < len; ++i) a[i] = lower_bound(all(b), a[i]) - b.begin(); for (int i = 0; i < sz(r); ++i) r[i] = lower_bound(all(b), r[i]) - b.begin(); for (int i = 0; i < sz(s); ++i) r[i] = lower_bound(all(b), s[i]) - b.begin(); int blen = sz(b); vi ret(blen); rep(i, blen) { ret[i] = b[i]; } return ret;}
vi compress(V<vi> &a) { vi b; fora(vv, a)fora(v, vv)b.push_back(v); sort(b); unique(b); fora(vv, a)fora(v, vv)v = lower_bound(all(b), v) - b.begin(); int blen = sz(b); vi ret(blen); rep(i, blen) { ret[i] = b[i]; } return ret;}
vi compress(vector<vector<vi >> &a) { vi b; fora(vvv, a)fora(vv, vvv)fora(v, vv)b.push_back(v); sort(b); unique(b); fora(vvv, a)fora(vv, vvv)fora(v, vv)v = lower_bound(all(b), v) - b.begin(); int blen = sz(b); vi ret(blen); rep(i, blen) { ret[i] = b[i]; } return ret;}
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))
template<class T> void fin(T s) { cout << s << endl, exit(0); }
//便利 数学 math
int mod(int a, int m) { return (a % m + m) % m; }
int pow(int a) { return a * a; };
ll fact(int v) { return v <= 1 ? 1 : v * fact(v - 1); }
ll comi(int n, int r) { assert(n < 100); static vvi(pas, 100, 100); if (pas[0][0])return pas[n][r]; pas[0][0] = 1; rep(i, 1, 100) { pas[i][0] = 1; rep(j, 1, i + 1)pas[i][j] = pas[i - 1][j - 1] + pas[i - 1][j]; } return pas[n][r];}
double comd(int n, int r) { static vd fac; if (sz(fac) < n + 1) { if (sz(fac) == 0)fac.push_back(1); rep(i, sz(fac) - 1, n) { fac.push_back(fac.back() * (i + 1)); } } if (n < r || n <= 0)return 0; return fac[n] / fac[n - r] / fac[r];}
int gcd(int a, int b) { while (b) a %= b, swap(a, b); return abs(a);}
int gcd(vi b) { ll res = b[0]; rep(i, 1, sz(b))res = gcd(b[i], res); return res;}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
ll lcm(vi a) { int res = a[0]; rep(i, 1, sz(a))res = lcm(a[i], res); return res;}
ll ceil(ll a, ll b) { if (b == 0) { debugline("ceil"); deb(a, b); ole(); return -1; } else if (a < 0) { return 0; } else {return (a + b - 1) / b;}}
int lower_remi__bx_a(int kei, int rem, int x) { if (rem >= x) return 0; return (x - rem + kei - 1) / kei;}
int lower_remv__bx_a(int kei, int rem, int x) { if (rem >= x) return rem; return (x - rem + kei - 1) / kei * kei + rem;}
int upper_remi__bx_a(int kei, int rem, int x) { if (rem > x) return 0; return (x - rem + kei) / kei;}
int upper_remv__bx_a(int kei, int rem, int x) { if (rem > x) return rem; return (x - rem + kei) / kei * kei + rem;}
//v * v >= aとなる最小のvを返す
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; }
//幾何 Pをcomplexとして扱う
template<class T, class U> bool eq(T a, U b) { return fabs(a - b) < eps; }
dou atan2(pd a) { return atan2(a.se, a.fi); }
dou angle(pd f, pd t) { return atan2(t.se - f.se, t.fi - f.fi); }
dou distance(pd a, pd b) { return hypot(a.fi - b.fi, a.se - b.se); }
//bを中心とするabcのtheta aからcにかけて時計回り
dou angle(pd a, pd b, pd c) { dou ax = a.fi - b.fi; dou ay = a.se - b.se; dou cx = c.fi - b.fi; dou cy = c.se - b.se; double ret = atan2(cy, cx) - atan2(ay, ax); if (ret < 0) ret += 2 * PI; return ret;}
dou dot(pd a, pd b) { return a.fi * b.fi + a.se + b.se; }
dou cro(pd a, pd b) { return a.fi * b.se - a.se + b.fi; }
//機能拡張
template<class T, class U> void operator+=(queue<T> &a, U v) { a.push(v); }
template<class T, class U> void operator+=(deque<T> &a, U v) { a.push_back(v); }
template<class T> priority_queue<T, vector<T>, greater<T> > &operator+=(priority_queue<T, vector<T>, greater<T> > &a, vector<T> &v) { fora(d, v)a.push(d); return a;}
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> set<T> &operator+=(set<T> &a, vector<T> v) { fora(d, v)a.insert(d); 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.push_back(v); return a;}
template<class T, class U> vector<T> operator+(const vector <T> &a, U v) {vector<T> ret = a;ret += v;return ret;}
template<class T, class U> vector<T> operator+(U v, const vector <T> &a) {vector<T> ret = a;ret.insert(ret.begin(), v);return ret;}
template<class T> vector<T> operator+(vector<T> a, vector <T> b) {vector<T> ret;ret = a;fora(v, b)ret += v;return ret;}
template<class T> vector<T> &operator+=(vector<T> &a, vector <T> &b) {fora(v, b)a += v;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);exit(0);}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(sz(a));rep(i, sz(a))res[i] = a[i] - b[i];return res;}
template<class T,class U> vector<T> operator*(vector<T> &a, U b) {vector<T> ret;fora(v,a)ret+=v*b;return ret;}
template<class T,class U> vector<T> operator/(vector<T> &a, U b) {vector<T> ret;fora(v,a)ret+=v/b;return ret;}
template<class T,class U> vector<T> operator*=(vector<T> &a, U b) {fora(v,a)v*=b;return a;}
template<class T,class U> vector<T> operator/=(vector<T> &a, U b) {fora(v,a)v/=b;return a;}
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<class T, class U> void erase(map<T, U> &m, int okl, int ngr) {m.erase(m.lower_bound(okl), m.lower_bound(ngr));}
template<class T> void erase(set<T> &m, int okl, int ngr) {m.erase(m.lower_bound(okl), m.lower_bound(ngr));}
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, typename U> void insert(vector<T> &v, unsigned int i,U t) {v.insert(v.begin()+ i, t);}
template<typename T, typename U> void push_front(vector<T> &v, U t) {v.insert(v.begin(), t);}
template<typename T, typename U> void insert(vector<T> &v, unsigned int i,vector<T> 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);}
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) { vector<string> res; int kn = sz(deli); std::string::size_type Pos(a.find(deli)); int l = 0; while (Pos != std::string::npos) { if (Pos - l)res.push_back(a.substr(l, Pos - l)); l = Pos + kn; Pos = a.find(deli, Pos + kn); } if (sz(a) - l)res.push_back(a.substr(l, sz(a) - l)); 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);}
void POSSIBLE(bool a) {if (a)cout << "POSSIBLE" << endl; else cout << "IMPOSSIBLE" << endl; exit(0);}
//@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));
};
} initonv;
//@formatter:on
//gra mint pr
int n, m, k, d, H, W, x, y, z, q;
int cou;
vi t, a, b, c;
//vvi (s, 0, 0);
vvc (ba, 0, 0);
vp p;
str s;
//@formatter:off
template<typename T> T minv(T a, T m);
template<typename T> T minv(T a);
template<typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type; constexpr Modular() : value() {} template<typename U> Modular(const U &x) { value = normalize(x); } template<typename U> static Type normalize(const U &x) { Type v; if (-mod() <= x && x < mod()) v = static_cast<Type>(x); else v = static_cast<Type>(x % mod()); if (v < 0) v += mod(); return v; } const Type &operator()() const { return value; } template<typename U>explicit operator U() const { return static_cast<U>(value); } constexpr static Type mod() { return T::value; } Modular &operator+=(const Modular &other) { if ((value += other.value) >= mod()) value -= mod(); return *this; } Modular &operator-=(const Modular &other) { if ((value -= other.value) < 0) value += mod(); return *this; } template<typename U> Modular &operator+=(const U &other) { return *this += Modular(other); } template<typename U> Modular &operator-=(const U &other) { return *this -= Modular(other); } Modular &operator++() { return *this += 1; } Modular &operator--() { return *this -= 1; } Modular operator++(signed) { Modular result(*this); *this += 1; return result; } Modular operator--(signed) { Modular result(*this); *this -= 1; return result; } Modular operator-() const { return Modular(-value); }
template<typename U = T>typename enable_if<is_same<typename Modular<U>::Type, signed>::value, Modular>::type &operator*=(const Modular &rhs) {
#ifdef _WIN32
uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;asm("divl %4; \n\t": "=a" (d), "=d" (m): "d" (xh), "a" (xl), "r" (mod()));value = m;
#else
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
return *this;
}
template<typename U = T> typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type &operator*=(const Modular &rhs) { int64_t q = static_cast<int64_t>(static_cast<double>(value) * rhs.value / mod()); value = normalize(value * rhs.value - q * mod()); return *this; } template<typename U = T> typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type &operator*=(const Modular &rhs) { value = normalize(value * rhs.value); return *this; } Modular &operator/=(const Modular &other) { return *this *= Modular(minv(other.value)); } template<typename U> friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs); template<typename U> friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs); template<typename U> friend std::istream &operator>>(std::istream &stream, Modular<U> &number); operator int() { return value; }private: Type value;
};
template<typename T> bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value == rhs.value; }template<typename T, typename U> bool operator==(const Modular<T> &lhs, U rhs) { return lhs == Modular<T>(rhs); }template<typename T, typename U> bool operator==(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) == rhs; }template<typename T> bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) { return !(lhs == rhs); }template<typename T, typename U> bool operator!=(const Modular<T> &lhs, U rhs) { return !(lhs == rhs); }template<typename T, typename U> bool operator!=(U lhs, const Modular<T> &rhs) { return !(lhs == rhs); }template<typename T> bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value < rhs.value; }template<typename T> Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }template<typename T, typename U> Modular<T> operator+(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) += rhs; }template<typename T, typename U> Modular<T> operator+(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }template<typename T> Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }template<typename T, typename U> Modular<T> operator-(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) -= rhs; }template<typename T, typename U> Modular<T> operator-(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }template<typename T> Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }template<typename T, typename U> Modular<T> operator*(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) *= rhs; }template<typename T, typename U> Modular<T> operator*(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }template<typename T> Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }template<typename T, typename U> Modular<T> operator/(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) /= rhs; }template<typename T, typename U> Modular<T> operator/(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }
constexpr signed MOD =
998244353;
//1e9 + 7;//MOD
using mint = Modular<std::integral_constant<decay<decltype(MOD)>::type, MOD>>;
constexpr int mint_len = 1400001;
vi fac, finv, inv;
vi p2;
mint com(int n, int r) { if (r < 0 || r > n) return 0; return mint(finv[r] * fac[n] % MOD * finv[n - r]);}
mint pom(int n, int r) {/* if (!sz(fac)) com(0, -1);*/ if (r < 0 || r > n) return 0; return mint(fac[n] * finv[n - 1]);}
mint npr(int n, int r) {/* if (!sz(fac)) com(0, -1);*/ if (r < 0 || r > n) return 0; return mint(fac[n] * finv[n - r]);}
int nprin(int n, int r) {/* if (!sz(fac)) com(0, -1);*/ if (r < 0 || r > n) return 0; return fac[n] * finv[n - r] % MOD;}
int icom(int n, int r) { const int NUM_ = 1400001; static ll fac[NUM_ + 1], finv[NUM_ + 1], inv[NUM_ + 1]; if (fac[0] == 0) { inv[1] = fac[0] = finv[0] = 1; for (int i = 2; i <= NUM_; ++i) inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD; for (int i = 1; i <= NUM_; ++i) fac[i] = fac[i - 1] * i % MOD, finv[i] = finv[i - 1] * inv[i] % MOD; } if (r < 0 || r > n) return 0; return ((finv[r] * fac[n] % MOD) * finv[n - r]) % MOD;}
#define ncr com
#define ncri icom
//n個の場所にr個の物を置く
mint nhr(int n, int r) { return com(n + r - 1, r); }
mint hom(int n, int r) { return com(n + r - 1, r); }
int nhri(int n, int r) { return icom(n + r - 1, r); }
template<typename T> T minv(T a, T m) { T u = 0, v = 1; while (a != 0) { T t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return u;}
template<typename T> T minv(T a) { if (a < mint_len)return inv[a]; T u = 0, v = 1; T m = MOD; while (a != 0) { T t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return u;}
template<typename T, typename U> Modular<T> mpow(const Modular<T> &a, const U &b) { assert(b >= 0); int x = a(), res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= MOD; (x *= x) %= MOD; p >>= 1; } return res;}
template<typename T, typename U, typename V> mint mpow(const T a, const U b, const V m = MOD) { assert(b >= 0); int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= m; (x *= x) %= m; p >>= 1; } return res;}
template<typename T, typename U> mint mpow(const T a, const U b) { assert(b >= 0); int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= MOD; (x *= x) %= MOD; p >>= 1; } return res;}
template<typename T, typename U, typename V> int mpowi(const T &a, const U &b, const V &m = MOD) { assert(b >= 0); int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= m; (x *= x) %= m; p >>= 1; } return res;}
template<typename T> string to_string(const Modular<T> &number) { return to_string(number());}
template<typename T> std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) { return stream << number();}
template<typename T> std::istream &operator>>(std::istream &stream, Modular<T> &number) { typename common_type<typename Modular<T>::Type, int64_t>::type x; stream >> x; number.value = Modular<T>::normalize(x); return stream;}
using PM = pair<mint, mint>;
using vm = vector<mint>;
using mapm = map<int, mint>;
using umapm = umap<int, mint>;
#define vvm(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(mint,__VA_ARGS__)
#define vnm(name, ...) auto name = make_v<mint>(__VA_ARGS__)
struct setmod{
setmod() {
// p2.resize(mint_len);p[0] = 1; for (int i = 1; i < mint_len; ++i) p2[i] = p2[i - 1] * 2 % MOD;
fac.resize(mint_len); finv.resize(mint_len); inv.resize(mint_len); inv[1] = fac[0] = finv[0] = 1; for (int i = 2; i < mint_len; ++i) inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD; for (int i = 1; i < mint_len; ++i) fac[i] = fac[i - 1] * i % MOD, finv[i] = finv[i - 1] * inv[i] % MOD;
}
}setmodv;
//@formatter:on
//vnm(dp, 303, 303 * 303, 2);//2つめに入れたか
//mint dp[303][303 * 303][2];
mint dp[303][303 * 303][2];
void solve() {
int lim=303*303;
// int lim = 6;
in(n);
na(a, n);
dp[0][0][0] = 1;
rep(i, n) {
rep(s, lim) {
rep(b, 2) {
if (dp[i][s][b] == 0)con;
mint r = dp[i][s][b];
// int r = dp[i][s][b];
//自分
dp[i + 1][s + a[i]][b] += r;
//2
dp[i + 1][s][1] += r;
//3
dp[i + 1][s][b] += r;
// deb(i, s, b);
// deb(dp[i + 1][s + a[i]], dp[i + 1][s][1], dp[i + 1][s][b]);
}
}
}
mint res;
int su = sum(a);
rep(s, lim) {
if (s * 2 >= su) {
res += dp[n][s][0] * 3;
res += dp[n][s][1] * 3;
}
}
if (su % 2 == 0) {
res -= dp[n][su / 2][0] * 3;
}
cout << mpow(3,n)-res << endl;
}
int my(int n, vi &a) {
return 0;
}
int sister(int n, vi &a) {
int ret = 0;
return ret;
}
signed main() {
solve();
#define arg n,a
#ifdef _DEBUG
bool bad = 0;
for (int i = 0, ok = 1; i < k5 && ok; ++i) {
int n = rand(1, 8);
vi a = ranv(n, 1, 10);
int myres = my(arg);
int res = sister(arg);
ok = myres == res;
if (!ok) {
out(arg);
cerr << "正解 : " << res << endl;
cerr << "自分 : " << myres << endl;
bad = 1;
break;
}
}
if (!bad) {
// cout << "完璧 : solveを書き直そう" << endl;
// cout << " : そして、solve()を呼び出すのだ" << endl;
// cout << " : cin>>n; na(a,n);も忘れるな" << endl;
}
#endif
return 0;
};
Submission Info
| Submission Time |
|
| Task |
D - Three Colors |
| User |
baito |
| Language |
C++14 (GCC 5.4.1) |
| Score |
600 |
| Code Size |
90070 Byte |
| Status |
AC |
| Exec Time |
353 ms |
| Memory |
250240 KB |
Judge Result
| Set Name |
Sample |
All |
| Score / Max Score |
0 / 0 |
600 / 600 |
| Status |
|
|
| Set Name |
Test Cases |
| Sample |
s1.txt, s2.txt, s3.txt |
| All |
01.txt, 02.txt, 03.txt, 04.txt, 05.txt, 06.txt, 07.txt, 08.txt, 09.txt, 10.txt, 11.txt, 12.txt, 13.txt, 14.txt, 15.txt, 16.txt, 17.txt, 18.txt, 19.txt, 20.txt, 21.txt, 22.txt, 23.txt, 24.txt, s1.txt, s2.txt, s3.txt |
| Case Name |
Status |
Exec Time |
Memory |
| 01.txt |
AC |
262 ms |
248192 KB |
| 02.txt |
AC |
265 ms |
248192 KB |
| 03.txt |
AC |
269 ms |
248192 KB |
| 04.txt |
AC |
267 ms |
250240 KB |
| 05.txt |
AC |
158 ms |
248192 KB |
| 06.txt |
AC |
158 ms |
248192 KB |
| 07.txt |
AC |
157 ms |
248192 KB |
| 08.txt |
AC |
159 ms |
250240 KB |
| 09.txt |
AC |
155 ms |
248192 KB |
| 10.txt |
AC |
155 ms |
248192 KB |
| 11.txt |
AC |
350 ms |
248192 KB |
| 12.txt |
AC |
353 ms |
250240 KB |
| 13.txt |
AC |
155 ms |
248192 KB |
| 14.txt |
AC |
155 ms |
248192 KB |
| 15.txt |
AC |
155 ms |
248192 KB |
| 16.txt |
AC |
156 ms |
250240 KB |
| 17.txt |
AC |
155 ms |
248192 KB |
| 18.txt |
AC |
155 ms |
248192 KB |
| 19.txt |
AC |
154 ms |
248192 KB |
| 20.txt |
AC |
155 ms |
250240 KB |
| 21.txt |
AC |
51 ms |
37248 KB |
| 22.txt |
AC |
51 ms |
37248 KB |
| 23.txt |
AC |
52 ms |
37248 KB |
| 24.txt |
AC |
52 ms |
37248 KB |
| s1.txt |
AC |
52 ms |
37248 KB |
| s2.txt |
AC |
53 ms |
39296 KB |
| s3.txt |
AC |
57 ms |
49536 KB |