#line 1 "verify/verify-aoj-grl/aoj-grl-5-e.test.cpp"
#define PROBLEM \
"http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_E"
#line 2 "template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(vector<T> &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
} // namespace Nyaan
#line 58 "template/template.hpp"
// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
#line 61 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
#line 64 "template/template.hpp"
// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t t) {
if (t == 0) cerr << 0;
if (t < 0) cerr << '-', t = -t;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
void dump(__uint128_t t) {
if (t == 0) cerr << 0;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 5 "verify/verify-aoj-grl/aoj-grl-5-e.test.cpp"
//
#line 2 "segment-tree/lazy-segment-tree-utility.hpp"
template <typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E),
T (*ti)(), E (*ei)()>
struct LazySegmentTreeBase {
int n, log, s;
vector<T> val;
vector<E> laz;
explicit LazySegmentTreeBase() {}
explicit LazySegmentTreeBase(const vector<T>& vc) { init(vc); }
void init(const vector<T>& vc) {
n = 1, log = 0, s = vc.size();
while (n < s) n <<= 1, log++;
val.resize(2 * n, ti());
laz.resize(n, ei());
for (int i = 0; i < s; ++i) val[i + n] = vc[i];
for (int i = n - 1; i; --i) _update(i);
}
void update(int l, int r, const E& x) {
if (l == r) return;
l += n, r += n;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) _push(l >> i);
if (((r >> i) << i) != r) _push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) _apply(l++, x);
if (r & 1) _apply(--r, x);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) _update(l >> i);
if (((r >> i) << i) != r) _update((r - 1) >> i);
}
}
T query(int l, int r) {
if (l == r) return ti();
l += n, r += n;
T L = ti(), R = ti();
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) _push(l >> i);
if (((r >> i) << i) != r) _push((r - 1) >> i);
}
while (l < r) {
if (l & 1) L = f(L, val[l++]);
if (r & 1) R = f(val[--r], R);
l >>= 1;
r >>= 1;
}
return f(L, R);
}
void set_val(int k, const T& x) {
k += n;
for (int i = log; i >= 1; i--) {
if (((k >> i) << i) != k || (((k + 1) >> i) << i) != (k + 1))
_push(k >> i);
}
val[k] = x;
for (int i = 1; i <= log; i++) {
if (((k >> i) << i) != k || (((k + 1) >> i) << i) != (k + 1))
_update(k >> i);
}
}
void update_val(int k, const E& x) {
k += n;
for (int i = log; i >= 1; i--) {
if (((k >> i) << i) != k || (((k + 1) >> i) << i) != (k + 1))
_push(k >> i);
}
val[k] = g(val[k], x);
for (int i = 1; i <= log; i++) {
if (((k >> i) << i) != k || (((k + 1) >> i) << i) != (k + 1))
_update(k >> i);
}
}
T get_val(int k) {
k += n;
for (int i = log; i >= 1; i--) {
if (((k >> i) << i) != k || (((k + 1) >> i) << i) != (k + 1))
_push(k >> i);
}
return val[k];
}
template <class G>
int max_right(int l, G check) {
assert(0 <= l && l <= s);
assert(check(ei()));
if (l == n) return n;
l += n;
for (int i = log; i >= 1; i--) _push(l >> i);
T sm = ti();
do {
while (l % 2 == 0) l >>= 1;
if (!check(f(sm, val[l]))) {
while (l < n) {
_push(l);
l = (2 * l);
if (check(f(sm, val[l]))) {
sm = f(sm, val[l]);
l++;
}
}
return l - n;
}
sm = f(sm, val[l]);
l++;
} while ((l & -l) != l);
return s;
}
template <class G>
int min_left(int r, G check) {
assert(0 <= r && r <= s);
assert(check(ei()));
if (r == 0) return 0;
r += n;
for (int i = log; i >= 1; i--) _push((r - 1) >> i);
T sm = ti();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!check(f(val[r], sm))) {
while (r < n) {
_push(r);
r = (2 * r + 1);
if (check(f(val[r], sm))) {
sm = f(val[r], sm);
r--;
}
}
return r + 1 - n;
}
sm = f(val[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
void _push(int i) {
if (laz[i] != ei()) {
val[2 * i + 0] = g(val[2 * i + 0], laz[i]);
val[2 * i + 1] = g(val[2 * i + 1], laz[i]);
if (2 * i < n) {
compose(laz[2 * i + 0], laz[i]);
compose(laz[2 * i + 1], laz[i]);
}
laz[i] = ei();
}
}
inline void _update(int i) { val[i] = f(val[2 * i + 0], val[2 * i + 1]); }
inline void _apply(int i, const E& x) {
if (x != ei()) {
val[i] = g(val[i], x);
if (i < n) compose(laz[i], x);
}
}
inline void compose(E& a, const E& b) { a = a == ei() ? b : h(a, b); }
};
namespace SegmentTreeUtil {
template <typename T>
struct Pair {
T first, second;
Pair() = default;
Pair(const T& f, const T& s) : first(f), second(s) {}
operator T() const { return first; }
friend ostream& operator<<(ostream& os, const Pair<T>& p) {
os << T(p.first);
return os;
}
};
template <typename T>
T Mx(T a, T b) {
return max(a, b);
}
template <typename T>
T Mn(T a, T b) {
return min(a, b);
}
template <typename T>
T Update(T, T b) {
return b;
}
template <typename T>
T Add(T a, T b) {
return a + b;
}
template <typename T>
Pair<T> Psum(Pair<T> a, Pair<T> b) {
return Pair<T>(a.first + b.first, a.second + b.second);
}
template <typename T>
Pair<T> Padd(Pair<T> a, T b) {
return Pair<T>(a.first + a.second * b, a.second);
}
template <typename T>
Pair<T> PUpdate(Pair<T> a, T b) {
return Pair<T>(a.second * b, a.second);
}
template <typename T>
Pair<T> Pid() {
return Pair<T>(0, 0);
}
template <typename T>
T Zero() {
return T(0);
}
template <typename T, T val>
T Const() {
return val;
}
template <typename T, T MINF>
struct AddMax_LazySegmentTree
: LazySegmentTreeBase<T, T, Mx<T>, Add<T>, Add<T>, Const<T, MINF>, Zero<T>> {
using base =
LazySegmentTreeBase<T, T, Mx<T>, Add<T>, Add<T>, Const<T, MINF>, Zero<T>>;
AddMax_LazySegmentTree(const vector<T>& v) : base(v) {}
};
template <typename T, T INF>
struct AddMin_LazySegmentTree
: LazySegmentTreeBase<T, T, Mn<T>, Add<T>, Add<T>, Const<T, INF>, Zero<T>> {
using base =
LazySegmentTreeBase<T, T, Mn<T>, Add<T>, Add<T>, Const<T, INF>, Zero<T>>;
AddMin_LazySegmentTree(const vector<T>& v) : base(v) {}
};
template <typename T>
struct AddSum_LazySegmentTree
: LazySegmentTreeBase<Pair<T>, T, Psum<T>, Padd<T>, Add<T>, Pid<T>, Zero<T>> {
using base =
LazySegmentTreeBase<Pair<T>, T, Psum<T>, Padd<T>, Add<T>, Pid<T>, Zero<T>>;
AddSum_LazySegmentTree(const vector<T>& v) {
vector<Pair<T>> w(v.size());
for (int i = 0; i < (int)v.size(); i++) w[i] = Pair<T>(v[i], 1);
base::init(w);
}
};
template <typename T, T MINF>
struct UpdateMax_LazySegmentTree
: LazySegmentTreeBase<T, T, Mx<T>, Update<T>, Update<T>, Const<T, MINF>,
Const<T, MINF>> {
using base = LazySegmentTreeBase<T, T, Mx<T>, Update<T>, Update<T>,
Const<T, MINF>, Const<T, MINF>>;
UpdateMax_LazySegmentTree(const vector<T>& v) : base(v) {}
};
template <typename T, T INF>
struct UpdateMin_LazySegmentTree
: LazySegmentTreeBase<T, T, Mn<T>, Update<T>, Update<T>, Const<T, INF>,
Const<T, INF>> {
using base = LazySegmentTreeBase<T, T, Mn<T>, Update<T>, Update<T>, Const<T, INF>,
Const<T, INF>>;
UpdateMin_LazySegmentTree(const vector<T>& v) : base(v) {}
};
template <typename T, T UNUSED_VALUE>
struct UpdateSum_LazySegmentTree
: LazySegmentTreeBase<Pair<T>, T, Psum<T>, PUpdate<T>, Update<T>, Pid<T>,
Const<T, UNUSED_VALUE>> {
using base = LazySegmentTreeBase<Pair<T>, T, Psum<T>, PUpdate<T>, Update<T>,
Pid<T>, Const<T, UNUSED_VALUE>>;
UpdateSum_LazySegmentTree(const vector<T>& v) {
vector<Pair<T>> w(v.size());
for (int i = 0; i < (int)v.size(); i++) w[i] = Pair<T>(v[i], 1);
base::init(w);
}
};
} // namespace SegmentTreeUtil
using SegmentTreeUtil::AddMax_LazySegmentTree;
using SegmentTreeUtil::AddMin_LazySegmentTree;
using SegmentTreeUtil::AddSum_LazySegmentTree;
using SegmentTreeUtil::UpdateMax_LazySegmentTree;
using SegmentTreeUtil::UpdateMin_LazySegmentTree;
using SegmentTreeUtil::UpdateSum_LazySegmentTree;
/**
* @brief 使用頻度の高い遅延セグメント木
* @docs docs/segment-tree/lazy-segment-tree-utility.md
*/
#line 2 "tree/heavy-light-decomposition.hpp"
#line 2 "graph/graph-template.hpp"
template <typename T>
struct edge {
int src, to;
T cost;
edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}
edge &operator=(const int &x) {
to = x;
return *this;
}
operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;
// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
bool is_1origin = true) {
UnweightedGraph g(N);
if (M == -1) M = N - 1;
for (int _ = 0; _ < M; _++) {
int x, y;
cin >> x >> y;
if (is_1origin) x--, y--;
g[x].push_back(y);
if (!is_directed) g[y].push_back(x);
}
return g;
}
// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
bool is_1origin = true) {
WeightedGraph<T> g(N);
if (M == -1) M = N - 1;
for (int _ = 0; _ < M; _++) {
int x, y;
cin >> x >> y;
T c;
cin >> c;
if (is_1origin) x--, y--;
g[x].emplace_back(x, y, c);
if (!is_directed) g[y].emplace_back(y, x, c);
}
return g;
}
// Input of Edges
template <typename T>
Edges<T> esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) {
Edges<T> es;
for (int _ = 0; _ < M; _++) {
int x, y;
cin >> x >> y;
T c;
if (is_weighted)
cin >> c;
else
c = 1;
if (is_1origin) x--, y--;
es.emplace_back(x, y, c);
}
return es;
}
// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
bool is_directed = false, bool is_1origin = true) {
vector<vector<T>> d(N, vector<T>(N, INF));
for (int _ = 0; _ < M; _++) {
int x, y;
cin >> x >> y;
T c;
if (is_weighted)
cin >> c;
else
c = 1;
if (is_1origin) x--, y--;
d[x][y] = c;
if (!is_directed) d[y][x] = c;
}
return d;
}
/**
* @brief グラフテンプレート
* @docs docs/graph/graph-template.md
*/
#line 4 "tree/heavy-light-decomposition.hpp"
template <typename G>
struct HeavyLightDecomposition {
private:
void dfs_sz(int cur) {
size[cur] = 1;
for (auto& dst : g[cur]) {
if (dst == par[cur]) {
if (g[cur].size() >= 2 && int(dst) == int(g[cur][0]))
swap(g[cur][0], g[cur][1]);
else
continue;
}
depth[dst] = depth[cur] + 1;
par[dst] = cur;
dfs_sz(dst);
size[cur] += size[dst];
if (size[dst] > size[g[cur][0]]) {
swap(dst, g[cur][0]);
}
}
}
void dfs_hld(int cur) {
down[cur] = id++;
for (auto dst : g[cur]) {
if (dst == par[cur]) continue;
nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst));
dfs_hld(dst);
}
up[cur] = id;
}
// [u, v)
vector<pair<int, int>> ascend(int u, int v) const {
vector<pair<int, int>> res;
while (nxt[u] != nxt[v]) {
res.emplace_back(down[u], down[nxt[u]]);
u = par[nxt[u]];
}
if (u != v) res.emplace_back(down[u], down[v] + 1);
return res;
}
// (u, v]
vector<pair<int, int>> descend(int u, int v) const {
if (u == v) return {};
if (nxt[u] == nxt[v]) return {{down[u] + 1, down[v]}};
auto res = descend(u, par[nxt[v]]);
res.emplace_back(down[nxt[v]], down[v]);
return res;
}
public:
G& g;
int id;
vector<int> size, depth, down, up, nxt, par;
HeavyLightDecomposition(G& _g, int root = 0)
: g(_g),
id(0),
size(g.size(), 0),
depth(g.size(), 0),
down(g.size(), -1),
up(g.size(), -1),
nxt(g.size(), root),
par(g.size(), root) {
dfs_sz(root);
dfs_hld(root);
}
void build(int root) {
dfs_sz(root);
dfs_hld(root);
}
pair<int, int> idx(int i) const { return make_pair(down[i], up[i]); }
template <typename F>
void path_query(int u, int v, bool vertex, const F& f) {
int l = lca(u, v);
for (auto&& [a, b] : ascend(u, l)) {
int s = a + 1, t = b;
s > t ? f(t, s) : f(s, t);
}
if (vertex) f(down[l], down[l] + 1);
for (auto&& [a, b] : descend(l, v)) {
int s = a, t = b + 1;
s > t ? f(t, s) : f(s, t);
}
}
template <typename F>
void path_noncommutative_query(int u, int v, bool vertex, const F& f) {
int l = lca(u, v);
for (auto&& [a, b] : ascend(u, l)) f(a + 1, b);
if (vertex) f(down[l], down[l] + 1);
for (auto&& [a, b] : descend(l, v)) f(a, b + 1);
}
template <typename F>
void subtree_query(int u, bool vertex, const F& f) {
f(down[u] + int(!vertex), up[u]);
}
int lca(int a, int b) {
while (nxt[a] != nxt[b]) {
if (down[a] < down[b]) swap(a, b);
a = par[nxt[a]];
}
return depth[a] < depth[b] ? a : b;
}
int dist(int a, int b) { return depth[a] + depth[b] - depth[lca(a, b)] * 2; }
};
/**
* @brief Heavy Light Decomposition(重軽分解)
* @docs docs/tree/heavy-light-decomposition.md
*/
#line 8 "verify/verify-aoj-grl/aoj-grl-5-e.test.cpp"
using namespace Nyaan;
void Nyaan::solve() {
ini(N);
vvi g(N);
rep(i, N) {
ini(n);
g[i].resize(n);
in(g[i]);
}
HeavyLightDecomposition<vvi> hld(g);
AddSum_LazySegmentTree<ll> seg(vl(N, 0));
ll W = 0;
auto add = [&](int u, int v) { seg.update(u, v, W); };
ll ans = 0;
auto query = [&](int u, int v) { ans += seg.query(u, v); };
ini(Q);
rep(_, Q) {
ini(c);
if (c == 0) {
inl(v, w);
W = w;
hld.path_query(0, v, false, add);
} else {
ini(v);
ans = 0;
hld.path_query(0, v, false, query);
out(ans);
}
}
}
verify/verify-aoj-grl/aoj-grl-5-e.test.cpp