結果
| 問題 |
No.3217 Shiki no Shiki
|
| ユーザー |
 miscalc
|
| 提出日時 | 2025-08-01 21:24:06 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 59,198 bytes |
| コンパイル時間 | 5,100 ms |
| コンパイル使用メモリ | 329,772 KB |
| 実行使用メモリ | 11,744 KB |
| 最終ジャッジ日時 | 2025-08-01 21:24:14 |
| 合計ジャッジ時間 | 8,006 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 2 WA * 11 RE * 10 |
ソースコード
#define SINGLE_TESTCASE
// #define MULTI_TESTCASE
// #define AOJ_TESTCASE
#ifndef LOCAL
#define FAST_IO
// #define FAST_CIO
// #define INTERACTIVE
#endif
#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11
/**
* @brief テンプレート（型）
* @docs docs/template/template_types.md
*/
#include <bits/stdc++.h>
using namespace std;
#ifndef EPS
#define EPS 1e-11
#endif
using ld = decltype(EPS);
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
using tllll = tuple<ll, ll, ll, ll>;
#define vc vector
template <class T>
using vvc = vc<vc<T>>;
template <class T>
using vvvc = vc<vc<vc<T>>>;
using vb = vc<bool>;
using vl = vc<ll>;
using vpll = vc<pll>;
using vtlll = vc<tlll>;
using vtllll = vc<tllll>;
using vstr = vc<string>;
using vvb = vvc<bool>;
using vvl = vvc<ll>;
template <class T>
using pql = priority_queue<T, vc<T>, greater<T>>;
template <class T>
using pqg = priority_queue<T>;
#ifdef __SIZEOF_INT128__
using i128 = __int128_t;
using u128 = __uint128_t;
i128 stoi128(const string &s)
{
i128 res = 0;
if (s.front() == '-')
{
for (int i = 1; i < (int)s.size(); i++)
res = 10 * res + s[i] - '0';
res = -res;
}
else
{
for (auto &&c : s)
res = 10 * res + c - '0';
}
return res;
}
string i128tos(i128 x)
{
if (x == 0) return "0";
string sign = "", res = "";
if (x < 0)
x = -x, sign = "-";
while (x > 0)
{
res += '0' + x % 10;
x /= 10;
}
reverse(res.begin(), res.end());
return sign + res;
}
istream &operator>>(istream &is, i128 &a)
{
string s;
is >> s;
a = stoi128(s);
return is;
}
ostream &operator<<(ostream &os, const i128 &a)
{
os << i128tos(a);
return os;
}
#endif
#define cauto const auto
/**
* @brief テンプレート（rep）
* @docs docs/template/template_rep.md
*/
// https://trap.jp/post/1224/
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(i, n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)
#define rep2(i, l, r) for (ll i = ll(l), rrrrr = ll(r); i < rrrrr; i++)
#define rep3(i, l, r, d) for (ll i = ll(l), rrrrr = ll(r), ddddd = ll(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi1(i, n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i, l, r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi3(i, l, r, d) for (int i = int(l), rrrrr = int(r), ddddd = int(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)
#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
#define fem(...) for (auto &__VA_ARGS__)
#ifndef INF
#define INF 4'000'000'000'000'000'037LL
#endif
#ifndef EPS
#define EPS 1e-11
#endif
/**
* @brief テンプレート（演算）
* @docs docs/template/template_math.md
*/
template <class T, class U>
inline bool chmin(T &a, U b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, U b) { return a < b ? a = b, true : false; }
template <class T = ll, class U, class V>
inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); }
template <class T = ll, class U, class V>
inline constexpr T divceil(U a, V b) { return T(a) / T(b) + (T(a) % T(b) && (T(a) ^ T(b)) >= 0); }
template <class T = ll, class U, class V>
inline constexpr T divround(U a, V b) { return divfloor<T>(2 * T(a) + T(b), 2 * T(b)); }
template <class T = ll, class U, class V>
inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor<T>(a, b); }
template <class T = ll, class U, class V>
constexpr T ipow(U a, V b)
{
assert(b >= 0);
if (b == 0)
return 1;
if (a == 0 || a == 1)
return a;
if (a < 0 && a == -1)
return b & 1 ? -1 : 1;
T res = 1, tmp = a;
while (true)
{
if (b & 1)
res *= tmp;
b >>= 1;
if (b == 0)
break;
tmp *= tmp;
}
return res;
}
template <class T = ll, class A, class B, class M>
T mul_limited(A a, B b, M m)
{
assert(a >= 0 && b >= 0 && m >= 0);
if (b == 0)
return 0;
return T(a) > T(m) / T(b) ? T(m) : T(a) * T(b);
}
template <class T = ll, class A, class B>
T mul_limited(A a, B b) { return mul_limited<T>(a, b, INF); }
template <class T = ll, class A, class B, class M>
T pow_limited(A a, B b, M m)
{
assert(a >= 0 && b >= 0 && m >= 0);
if (a <= 1 || b == 0)
return min(ipow<T>(a, b), T(m));
T res = 1, tmp = a;
while (true)
{
if (b & 1)
{
if (res > T(m) / tmp)
return m;
res *= tmp;
}
b >>= 1;
if (b == 0)
break;
if (tmp > T(m) / tmp)
return m;
tmp *= tmp;
}
return res;
}
template <class T = ll, class A, class B>
T pow_limited(A a, B b) { return pow_limited<T>(a, b, INF); }
template <class T = ll, class A, class K>
constexpr T iroot(A a, K k)
{
assert(a >= 0 && k >= 1);
if (a <= 1 || k == 1)
return a;
if (k == 2)
{
if constexpr (sizeof(T) > sizeof(ull))
{
if ((u128)a < ((u128)1 << 120))
return sqrtl(a);
}
else
return sqrtl(a);
}
auto isok = [&](T x) -> bool
{
if (x == 0)
return true;
T res = 1, k2 = k;
while (true)
{
if (k2 & 1)
{
if (res > T(a) / x)
return false;
res *= x;
}
k2 >>= 1;
if (k2 == 0)
break;
if (x > T(a) / x)
return false;
x *= x;
}
return res <= T(a);
};
T x = pow(a, 1.0 / k);
bool up = true;
while (!isok(x))
up = false, x--;
if (up)
{
while (x < numeric_limits<T>::max() && isok(x + 1))
x++;
}
return x;
}
template <class T = ll, class A, class K>
constexpr T iroot_ceil(A a, K k)
{
T x = iroot<T>(a, k);
return ipow<T>(x, k) == a ? x : x + 1;
}
// https://misawa.github.io/others/avoid_errors/techniques_to_avoid_errors.html
template <class D = decltype(EPS), class A>
int SGN(A a, D eps = EPS) { return int(a > eps) - int(a < -eps); }
// 位取り記数法と同じ順番（下位桁が後ろ）
// 0 に対しては {0} が返る
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base)
{
assert(val >= 0);
assert(base >= 2);
if (val == 0)
return {0};
vc<T> a;
while (val > 0)
{
a.emplace_back(val % base);
val /= base;
}
reverse(a.begin(), a.end());
return a;
}
// 位取り記数法と同じ順番（下位桁が後ろ）
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base, int n)
{
assert(val >= 0);
assert(base >= 2);
assert(n >= 0);
vc<T> a(n);
repi(i, n)
{
a[i] = val % base;
val /= base;
}
reverse(a.begin(), a.end());
return a;
}
template <const bool use_upper = true, class U>
string base_repr_str(U val, int base)
{
assert(val >= 0);
assert(2 <= base && base <= 36);
auto a = base_repr(val, base);
string s = "";
for (cauto &ai : a)
s += (ai < 10 ? '0' + ai : (use_upper ? 'A' : 'a') + (ai - 10));
return s;
}
template <const bool use_upper = true, class U>
string base_repr_str(U val, int base, int n)
{
assert(val >= 0);
assert(2 <= base && base <= 36);
assert(n >= 0);
auto a = base_repr(val, base, n);
string s = "";
for (cauto &ai : a)
s += (ai < 10 ? '0' + ai : (use_upper ? 'A' : 'a') + (ai - 10));
return s;
}
/**
* @brief テンプレート（vector）
* @docs docs/template/template_vector.md
*/
#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back
#define LMD(x, fx) ([&](auto x) { return fx; })
template <class F>
auto gen_vec(int n, const F &f)
{
vc<decltype(f(0))> res(n);
repi(i, n) res[i] = f(i);
return res;
}
#define GEN_VEC(n, i, fi) (gen_vec(n, LMD(i, fi)))
// https://qiita.com/Chippppp/items/13150f5e0ea99f444d97#%E5%A4%9A%E6%AC%A1%E5%85%83vector%E7%94%9F%E6%88%90%E9%96%A2%E6%95%B0
template <class T, size_t d, size_t i = 0, class V>
auto dvec(const V (&sz)[d], const T &init)
{
if constexpr (i < d)
return vc(sz[i], dvec<T, d, i + 1>(sz, init));
else
return init;
}
template <class T = ll>
T ctol(const char &c, const string &s)
{
repi(i, SZ<int>(s)) if (s[i] == c) return i;
return -1;
}
template <class T = ll>
vc<T> stov(const string &s, char first)
{
return gen_vec(SZ<int>(s), [&](int i) -> T
{ return s[i] - first; });
}
template <class T = ll>
vc<T> stov(const string &s, const string &t)
{
return gen_vec(SZ<int>(s), [&](int i) -> T
{ return ctol(s[i], t); });
}
template <class T>
string vtos(const vc<T> &v, char first)
{
string res = "";
fe(vi : v) res += vi + first;
return res;
}
template <class T>
string vtos(const vc<T> &v, const string &t)
{
string res = "";
fe(vi : v) res += t[vi];
return res;
}
template <class T>
vc<T> concat(const vvc<T> &vs)
{
vc<T> res;
for (cauto &v : vs)
res.insert(res.end(), ALL(v));
return res;
}
template <class T>
vc<T> concat(const vc<T> &v) { return v; }
template <class T, class... Ts>
vc<T> concat(vc<T> v, const vc<Ts> &...vs)
{
(v.insert(v.end(), ALL(vs)), ...);
return v;
}
template <class T, class I>
T vecget(const vc<T> &v, I i, const T &dflt_negative = -INF, const T &dflt_positive = INF)
{
if (i < 0)
return dflt_negative;
if (i >= SZ<int>(v))
return dflt_positive;
return v[i];
}
#ifndef INF
#define INF 4'000'000'000'000'000'037LL
#endif
/**
* @brief テンプレート（アルゴリズム）
* @docs docs/template/template_algo.md
*/
template <class V>
auto SUM(const V &v)
{
typename V::value_type s{};
fec(vi : v) s += vi;
return s;
}
template <class T, class V>
T SUM(const V &v)
{
T s{};
fec(vi : v) s += vi;
return s;
}
template <class V>
auto MAX(const V &v) { return *max_element(ALL(v)); }
template <class V>
auto MIN(const V &v) { return *min_element(ALL(v)); }
template <class I = ll, class V>
I ARGMAX(const V &v) { return max_element(ALL(v)) - v.begin(); }
template <class I = ll, class V>
I ARGMIN(const V &v) { return min_element(ALL(v)) - v.begin(); }
template<class T = ll, class V>
T mex(const V &a)
{
int n = a.size();
vector<bool> exists(n, false);
repi(i, n) if (0 <= a[i] && a[i] < n) exists[a[i]] = true;
repi(x, n) if (!exists[x]) return x;
return n;
}
// (0, 1. ..., n-1) の順列か判定
template <class I>
bool is_permutation(const vc<I> &p)
{
const int n = p.size();
vc<bool> b(n, false);
repi(i, n)
{
if (!(0 <= p[i] && p[i] < n))
return false;
b[p[i]] = true;
}
return all_of(ALL(b), [](bool bi)
{ return bi; });
}
template <class T = ll>
vc<T> permid(const int &n, const int &base_index = 0)
{
vc<T> p(n);
repi(i, n) p[i] = i + base_index;
return p;
}
template <class T>
vc<T> perminv(const vc<T> &p)
{
if (p.empty())
return {};
const int n = p.size();
vc<T> q(MAX(p) + 1);
repi(i, n) if (p[i] >= 0) q[p[i]] = i;
return q;
}
// a[p[i]] for all i
template <class T, class U>
vc<T> permuted(const vc<T> &a, const vc<U> &p)
{
const int n = p.size();
vc<T> res(n);
repi(i, n)
{
assert(0 <= p[i] && p[i] < U(a.size()));
res[i] = a[p[i]];
}
return res;
}
// p[q[r[i]]] for all i など
template <class T, class U, class... Ts>
vc<T> permuted(const vc<T> &p, const vc<U> &q, const vc<Ts> &...rs)
{
return permuted(permuted(p, q), rs...);
}
template <class V>
V reversed(const V &v) { return V(v.rbegin(), v.rend()); }
#if __cplusplus < 202002L
template <class V, class... Args>
V sorted(V v, Args&&... args)
{
sort(ALL(v), forward<Args>(args)...);
return v;
}
#else
template <class V, class... Args>
V sorted(V v, Args&&... args)
{
ranges::sort(v, forward<Args>(args)...);
return v;
}
#endif
template <class V>
void unique(V &v) { v.erase(std::unique(ALL(v)), v.end()); }
template <class V>
V uniqued(V v) { unique(v); return v; }
template <class V>
void sortunique(V &v)
{
sort(ALL(v));
unique(v);
}
template <class V>
V sortuniqued(V v) { sortunique(v); return v; }
// 引数: vc<pair<T, U>>
// 返り値: vc<pair<T, vc<U>>
// T ごとに U をまとめたもの
// T は比較可能である必要がある
template <class T, class U>
vc<pair<T, vc<U>>> sortuniqued_group(vc<pair<T, U>> v)
{
stable_sort(ALL(v), [&](cauto &p1, cauto &p2)
{ return p1.first < p2.first; });
vc<pair<T, vc<U>>> res;
fec([x, y] : v)
{
if (res.empty() || res.back().first != x)
res.eb(x, vc{y});
else
res.back().second.eb(y);
}
return res;
}
// 01234 -> 12340
template <class V, class U>
void rotate(V &v, U k)
{
const U n = v.size();
k = (k % n + n) % n;
std::rotate(v.begin(), v.begin() + k, v.end());
}
// 01234 -> 12340
template <class V, class U>
V rotated(V v, U k) { rotate(v, k); return v; }
template <class T>
vvc<T> top(const vvc<T> &a)
{
if (a.empty())
return {};
const int n = a.size(), m = a[0].size();
vvc<T> b(m, vc<T>(n));
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[j][i] = a[i][j];
}
return b;
}
vstr top(const vstr &a)
{
vvc<char> a_(a.size());
repi(i, SZ<int>(a)) a_[i] = {ALL(a[i])};
vvc<char> b_ = top(a_);
vstr b(b_.size());
repi(i, SZ<int>(b)) b[i] = {ALL(b_[i])};
return b;
}
// 12
// 34 -> 246
// 56 135
// (反時計回り)
template <class VV, class U = ll>
VV rot90(const VV &a, U k = 1)
{
if (a.empty())
return {};
const int n = a.size(), m = a[0].size();
k = (k % 4 + 4) % 4;
if (k == 0)
return a;
else if (k == 1)
{
VV b(m);
repi(j, m) b[j].resize(n);
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[m - 1 - j][i] = a[i][j];
}
return b;
}
else if (k == 2)
{
VV b(n);
repi(i, n) b[i].resize(m);
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[n - 1 - i][m - 1 - j] = a[i][j];
}
return b;
}
else
{
VV b(m);
repi(j, m) b[j].resize(n);
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[j][n - 1 - i] = a[i][j];
}
return b;
}
}
template <class T>
struct MonoidAdd
{
using S = T;
static constexpr S op(S a, S b) { return a + b; }
static constexpr S e() { return 0; }
};
template <class T, const T infty = INF>
struct MonoidMin
{
using S = T;
static constexpr S op(S a, S b) { return min(a, b); }
static constexpr S e() { return infty; }
};
template <class T, const T infty = INF>
struct MonoidMax
{
using S = T;
static constexpr S op(S a, S b) { return max(a, b); }
static constexpr S e() { return -infty; }
};
// left_index が 0 なら、長さ n+1 で a.front() が e()
// left_index が 1 なら、長さ n で e() がない
template <class M>
vc<typename M::S> cuml(const vc<typename M::S> &v, int left_index = 0)
{
const int n = v.size();
vc<typename M::S> res(n + 1);
res[0] = M::e();
repi(i, n) res[i + 1] = M::op(res[i], v[i]);
res.erase(res.begin(), res.begin() + left_index);
return res;
}
// right_index が 0 なら、長さ n+1 で a.back() が e()
// right_index が 1 なら、長さ n で e() がない
template <class M>
vc<typename M::S> cumr(const vc<typename M::S> &v, int right_index = 0)
{ return reversed(cuml<M>(reversed(v), right_index)); }
template <class T>
vc<T> cumlsum(const vc<T> &v, int left_index = 0)
{ return cuml<MonoidAdd<T>>(v, left_index); }
template <class T>
vc<T> cumrsum(const vc<T> &v, int right_index = 0)
{ return cumr<MonoidAdd<T>>(v, right_index); }
template <class T>
vc<T> cumlmin(const vc<T> &v, int left_index = 0)
{ return cuml<MonoidMin<T>>(v, left_index); }
template <class T>
vc<T> cumrmin(const vc<T> &v, int right_index = 0)
{ return cumr<MonoidMin<T>>(v, right_index); }
template <class T>
vc<T> cumlmax(const vc<T> &v, int left_index = 0)
{ return cuml<MonoidMax<T>>(v, left_index); }
template <class T>
vc<T> cumrmax(const vc<T> &v, int right_index = 0)
{ return cumr<MonoidMax<T>>(v, right_index); }
// デフォルトでは長さ n+1
// left_index, right_index をそれぞれ 1 にすると、左右が削除される
template <class T>
vc<T> adjd(const vc<T> &v, int left_index = 0, int right_index = 0)
{
int n = v.size();
vc<T> res(n + 1);
res[0] = v[0];
repi(i, 1, n) res[i] = v[i] - v[i - 1];
res[n] = -v[n - 1];
res.erase(res.end() - right_index, res.end());
res.erase(res.begin(), res.begin() + left_index);
return res;
}
const vpll DRULgrid = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
const vpll DRULplane = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}};
/**
* @brief テンプレート（二分探索）
* @docs docs/template/template_binsearch.md
*/
template <class T>
struct is_random_access_iterator
{
static constexpr bool value = is_same_v<
typename iterator_traits<T>::iterator_category,
random_access_iterator_tag
>;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;
// --- LB, UB ---
#if __cplusplus < 202002L
struct identity
{
template <class T>
constexpr T &&operator()(T &&t) const noexcept
{ return forward<T>(t); }
};
namespace internal
{
template <class T = ll, class V, class Judge>
inline T bound_helper(const V &v, Judge judge)
{
int l = -1, r = v.size();
while (r - l > 1)
{
int m = (l + r) / 2;
if (judge(m))
l = m;
else
r = m;
}
return r;
}
};
// val <= v[i] となる最小の i (val 未満の値の個数)
template <class T = ll, class V, class Value, class Comp = less<>, class Proj = identity>
inline T LB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{
return internal::bound_helper(v, [&](int i) -> bool
{ return comp(proj(*(v.begin() + i)), val); });
}
// val < v[i] となる最小の i (val 以下の値の個数)
template <class T = ll, class V, class Value, class Comp = less<>, class Proj = identity>
inline T UB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{
return internal::bound_helper(v, [&](int i) -> bool
{ return !comp(val, proj(*(v.begin() + i))); });
}
#define DEFAULT_COMP less<>
#else
// val <= v[i] となる最小の i (val 未満の値の個数)
template <class T = ll, class V, class Value, class Comp = ranges::less, class Proj = identity>
inline T LB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{ return ranges::lower_bound(v, val, comp, proj) - v.begin(); }
// val < v[i] となる最小の i (val 以下の値の個数)
template <class T = ll, class V, class Value, class Comp = ranges::less, class Proj = identity>
inline T UB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{ return ranges::upper_bound(v, val, comp, proj) - v.begin(); }
#define DEFAULT_COMP ranges::less
#endif
// --- vector 等の lt, leq, gt, geq ---
// v[i] < val となる最大の i (なければ -1)
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto lt_max(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return LB<T>(v, val, comp, proj) - 1; }
// v[i] <= val となる最大の i (なければ -1)
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto leq_max(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return UB<T>(v, val, comp, proj) - 1; }
// val < v[i] となる最小の i (なければ n)
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto gt_min(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return UB<T>(v, val, comp, proj); }
// val <= v[i] となる最小の i (なければ n)
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto geq_min(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return LB<T>(v, val, comp, proj); }
// v[i] < val となる i の個数
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto lt_cnt(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return LB<T>(v, val, comp, proj); }
// v[i] <= val となる i の個数
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto leq_cnt(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return UB<T>(v, val, comp, proj); }
// val < v[i] となる i の個数
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto gt_cnt(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return SZ<T>(v) - UB<T>(v, val, comp, proj); }
// val <= v[i] となる i の個数
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto geq_cnt(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return SZ<T>(v) - LB<T>(v, val, comp, proj); }
// l <= v[i] < r となる i の個数
template <class T = ll, class V, class L, class R, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto in_cnt(const V &v, L l, R r, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{
if (l > r)
return 0;
return lt_cnt<T>(v, r, comp, proj) - lt_cnt<T>(v, l, comp, proj);
}
// --- set 等の lt, leq, gt, geq ---
// *it < val となる最大の it (なければ end())
template <class V, class Value>
inline auto lt_max(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{
auto it = v.lower_bound(val);
return it == v.begin() ? v.end() : prev(it);
}
// *it <= val となる最大の it (なければ end())
template <class V, class Value>
inline auto leq_max(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{
auto it = v.upper_bound(val);
return it == v.begin() ? v.end() : prev(it);
}
// val < *it となる最小の it (なければ end())
template <class V, class Value>
inline auto gt_min(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{ return v.upper_bound(val); }
// val <= *it となる最小の it (なければ end())
template <class V, class Value>
inline auto geq_min(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{ return v.lower_bound(val); }
// --- 自作二分探索 ---
// (ok, ng)
template <class T = ll, class Judge, class InitOk, class InitNg>
pair<T, T> binsearch(const Judge &judge, const InitOk &init_ok, const InitNg &init_ng, bool check_ok = true, bool check_ng = true)
{
T ok(init_ok), ng(init_ng);
if (check_ok)
assert(judge(ok));
if (check_ng)
assert(!judge(ng));
while (ok - ng != 1 && ng - ok != 1)
{
T mid = (ok & ng) + ((ok ^ ng) >> 1);
(judge(mid) ? ok : ng) = mid;
}
return {ok, ng};
}
template <class T = ld, class Judge, class InitOk, class InitNg>
T binsearch_real(const Judge &judge, const InitOk &init_ok, const InitNg &init_ng, int iteration_count = 100, bool check_ok = true, bool check_ng = true)
{
T ok(init_ok), ng(init_ng);
if (check_ok)
assert(judge(ok));
if (check_ng)
assert(!judge(ng));
repi(_, iteration_count)
{
T mid = (ok + ng) / 2;
(judge(mid) ? ok : ng) = mid;
}
return ok;
}
// (ok, ng)
template <class T = ll, class Judge, class InitVal>
pair<T, T> expsearch(const Judge &judge, const InitVal &init_val, bool positive = true)
{
T ok, ng;
if (judge(init_val))
{
ok = init_val, ng = init_val + (positive ? 1 : -1);
for (int i = 1; judge(ng); i++)
ok = ng, ng = init_val + (positive ? 1 : -1) * (T(1) << i);
}
else
{
ng = init_val, ok = init_val + (positive ? 1 : -1);
for (int i = 1; !judge(ok); i++)
ng = ok, ok = init_val + (positive ? 1 : -1) * (T(1) << i);
}
while (ok - ng != 1 && ng - ok != 1)
{
T mid = (ok & ng) + ((ok ^ ng) >> 1);
(judge(mid) ? ok : ng) = mid;
}
return {ok, ng};
}
/**
* @brief テンプレート（ビット演算）
* @docs docs/template/template_bit.md
*/
template <class T>
inline constexpr ull pow2(T k) { return 1ULL << k; }
template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }
#if __cplusplus < 202002L
// x == 0 ならば 0、そうでなければ 1 + floor(log2(x))
// 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, ...
inline constexpr ull bit_width(ull x) { return x == 0 ? 0 : 64 - __builtin_clzll(x); }
// 0, 1, 2, 2, 4, 4, 4, 4, 8, 8, ...
inline constexpr ull bit_floor(ull x) { return x == 0 ? 0ULL : 1ULL << (bit_width(x) - 1); }
// 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, ...
inline constexpr ull bit_ceil(ull x) { return x == 0 ? 1ULL : 1ULL << bit_width(x - 1); }
inline constexpr ull countr_zero(ull x) { assert(x != 0); return __builtin_ctzll(x); }
inline constexpr ull popcount(ull x) { return __builtin_popcountll(x); }
inline constexpr bool has_single_bit(ull x) { return popcount(x) == 1; }
#else
// 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, ...
inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); }
// 0, 1, 2, 2, 4, 4, 4, 4, 8, 8, ...
inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); }
// 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, ...
inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); }
inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }
inline constexpr ll popcount(ll x) { return std::popcount((ull)x); }
inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); }
#endif
inline constexpr ull lsb_pos(ull x) { assert(x != 0); return countr_zero(x); }
inline constexpr ull msb_pos(ull x) { assert(x != 0); return bit_width(x) - 1; }
inline constexpr ull lsb_mask(ull x) { assert(x != 0); return x & -x; }
inline constexpr ull msb_mask(ull x) { assert(x != 0); return bit_floor(x); }
inline constexpr bool btest(ull x, uint k) { return (x >> k) & 1; }
template <class T>
inline void bset(T &x, uint k, bool b = 1) { b ? x |= (1ULL << k) : x &= ~(1ULL << k); }
template <class T>
inline void bflip(T &x, uint k) { x ^= (1ULL << k); }
inline constexpr bool bsubset(ull x, ull y) { return (x & y) == x; }
inline constexpr bool bsupset(ull x, ull y) { return (x & y) == y; }
inline constexpr ull bsetminus(ull x, ull y) { return x & ~y; }
/**
* @brief テンプレート（dump）
* @docs docs/template/template_dump.md
*/
#ifdef LOCAL
#include <cpp-dump.hpp> // https://github.com/philip82148/cpp-dump
namespace cpp_dump::_detail
{
inline string export_var(
const i128 &x, const string &indent, size_t last_line_length,
size_t current_depth, bool fail_on_newline, const export_command &command
) {
return export_var(i128tos(x), indent, last_line_length, current_depth, fail_on_newline, command);
}
} // namespace cpp_dump::_detail
#define dump(...) cpp_dump(__VA_ARGS__)
namespace cp = cpp_dump;
CPP_DUMP_SET_OPTION_GLOBAL(log_label_func, cp::log_label::line());
CPP_DUMP_SET_OPTION_GLOBAL(max_iteration_count, 1000);
#define local(...) __VA_ARGS__
#define oj(...)
#define local_oj(a, b) (a)
#else
#define dump(...)
#define local(...)
#define oj(...) __VA_ARGS__
#define local_oj(a, b) (b)
#endif
template <class T, class Sequence>
vc<T> content(queue<T, Sequence> que)
{
vc<T> res;
while (!que.empty())
{
res.eb(que.front());
que.pop();
}
return res;
}
template <class T, class Sequence, class Compare>
vc<T> content(priority_queue<T, Sequence, Compare> pque)
{
vc<T> res;
while (!pque.empty())
{
res.eb(pque.top());
pque.pop();
}
return res;
}
/**
* @brief テンプレート（入出力）
* @docs docs/template/template_inout.md
*/
// https://judge.yosupo.jp/submission/170706 (maspy さん)
// https://judge.yosupo.jp/submission/21623 (Nyaan さん)
#if defined FAST_IO and not defined LOCAL
namespace fastio {
static constexpr uint32_t SIZ = 1 << 17;
char ibuf[SIZ];
char obuf[SIZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SIZ - pir + pil, stdin);
pil = 0;
if (pir < SIZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd1(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd1(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd1_real(T &x) {
string s;
rd1(s);
x = stod(s);
}
template <typename T>
void rd1_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd1(int &x) { rd1_integer(x); }
void rd1(ll &x) { rd1_integer(x); }
void rd1(i128 &x) { rd1_integer(x); }
void rd1(uint &x) { rd1_integer(x); }
void rd1(ull &x) { rd1_integer(x); }
void rd1(u128 &x) { rd1_integer(x); }
void rd1(double &x) { rd1_real(x); }
void rd1(long double &x) { rd1_real(x); }
// void rd1(f128 &x) { rd1_real(x); }
template <class T, class U>
void rd1(pair<T, U> &p) {
return rd1(p.first), rd1(p.second);
}
template <size_t N = 0, typename T>
void rd1_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd1(x);
rd1_tuple<N + 1>(t);
}
}
template <class... T>
void rd1(tuple<T...> &tpl) {
rd1_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd1(array<T, N> &x) {
for (auto &d: x) rd1(d);
}
template <class T>
void rd1(vc<T> &x) {
for (auto &d: x) rd1(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd1(h), read(t...);
}
void wt1(const char c) {
if (por == SIZ) flush();
obuf[por++] = c;
}
void wt1(const string s) {
for (char c: s) wt1(c);
}
void wt1(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt1(s[i]);
}
template <typename T>
void wt1_integer(T x) {
if (por > SIZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt1_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt1(s);
}
void wt1(int x) { wt1_integer(x); }
template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x) { wt1_integer(x); }
void wt1(i128 x) { wt1_integer(x); }
void wt1(u128 x) { wt1_integer(x); }
void wt1(double x) { wt1_real(x); }
void wt1(long double x) { wt1_real(x); }
// void wt1(f128 x) { wt1_real(x); }
template <class T, class U>
void wt1(const pair<T, U> &val) {
wt1(val.first);
wt1(' ');
wt1(val.second);
}
template <size_t N = 0, typename T>
void wt1_tuple(const T &t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt1(' '); }
const auto x = std::get<N>(t);
wt1(x);
wt1_tuple<N + 1>(t);
}
}
template <class... T>
void wt1(const tuple<T...> &tpl) {
wt1_tuple(tpl);
}
template <class T, size_t S>
void wt1(const array<T, S> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt1(' ');
wt1(val[i]);
}
}
template <class T>
void wt1(const vector<T> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt1(' ');
wt1(val[i]);
}
}
void write() {}
template <class Head, class... Tail>
void write(Head &&head, Tail &&... tail) {
wt1(head);
write(forward<Tail>(tail)...);
}
void print() { wt1('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt1(head);
if (sizeof...(Tail)) wt1(' ');
print(forward<Tail>(tail)...);
}
} // namespace fastio
#endif
#if defined FAST_IO and not defined LOCAL
struct Dummy {
Dummy() { atexit(fastio::flush); }
} dummy;
#endif
// https://trap.jp/post/1224/
// ---- 入力 ----
#if defined LOCAL or not defined FAST_IO
template <class T, class U>
istream &operator>>(istream &is, pair<T, U> &p)
{
is >> p.first >> p.second;
return is;
}
template <class... Ts>
istream &operator>>(istream &is, tuple<Ts...> &t)
{
apply([&](auto &...a)
{ (is >> ... >> a); }, t);
return is;
}
template <class T, size_t n>
istream &operator>>(istream &is, array<T, n> &a)
{
for (size_t i = 0; i < n; i++)
is >> a[i];
return is;
}
template <class T>
istream &operator>>(istream &is, vc<T> &a)
{
const size_t n = a.size();
for (size_t i = 0; i < n; i++)
is >> a[i];
return is;
}
#endif
namespace internal
{
#if defined LOCAL or not defined FAST_IO
template <class... Ts>
void CIN(Ts &...a) { (cin >> ... >> a); }
#endif
#if defined FAST_IO and not defined LOCAL
template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }
#else
template <class... Ts>
void READnodump(Ts &...a) { CIN(a...); }
#endif
template <class T>
void READVECnodump(int n, vc<T> &v)
{
v.resize(n);
READnodump(v);
}
template <class T, class... Ts>
void READVECnodump(int n, vc<T> &v, vc<Ts> &...vs)
{ READVECnodump(n, v), READVECnodump(n, vs...); }
template <class T>
void READVEC2nodump(int n, int m, vvc<T> &v)
{
v.assign(n, vc<T>(m));
READnodump(v);
}
template <class T, class... Ts>
void READVEC2nodump(int n, int m, vvc<T> &v, vvc<Ts> &...vs)
{ READVEC2nodump(n, m, v), READVEC2nodump(n, m, vs...); }
template <class T>
void READJAGnodump(int n, vvc<T> &v)
{
v.resize(n);
repi(i, n)
{
int k;
READnodump(k);
READVECnodump(k, v[i]);
}
}
template <class T, class... Ts>
void READJAGnodump(int n, vvc<T> &v, vvc<Ts> &...vs)
{ READJAGnodump(n, v), READJAGnodump(n, vs...); }
}; // namespace internal
#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define IN(T, ...) T __VA_ARGS__; READ(__VA_ARGS__)
#define CHAR(...) IN(char, __VA_ARGS__)
#define INT(...) IN(int, __VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define STR(...) IN(string, __VA_ARGS__)
#define ARR(T, n, ...) array<T, n> __VA_ARGS__; READ(__VA_ARGS__)
#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define READVEC2(...) internal::READVEC2nodump(__VA_ARGS__); dump(__VA_ARGS__)
#define VEC(T, n, ...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define VEC2(T, n, m, ...) vvc<T> __VA_ARGS__; READVEC2(n, m, __VA_ARGS__)
#define READJAG(...) internal::READJAGnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define JAG(T, n, ...) vvc<T> __VA_ARGS__; READJAG(n, __VA_ARGS__)
// ----------
// ----- 出力 -----
#ifdef INTERACTIVE
#define ENDL endl
#else
#define ENDL '\n'
#endif
#if defined LOCAL or not defined FAST_IO
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p)
{
os << p.first << ' ' << p.second;
return os;
}
namespace internal
{
template <size_t N = 0, typename T>
void cout_tuple(ostream &os, const T &t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { os << ' '; }
const auto x = std::get<N>(t);
os << x;
cout_tuple<N + 1>(os, t);
}
}
}; // namespace internal
template <class... Ts>
ostream &operator<<(ostream &os, const tuple<Ts...> &t)
{
internal::cout_tuple(os, t);
return os;
}
template <class T, size_t n>
ostream &operator<<(ostream &os, const array<T, n> &a)
{
for (size_t i = 0; i < n; i++)
{
if (i)
os << ' ';
os << a[i];
}
return os;
}
template <class T>
ostream &operator<<(ostream &os, const vc<T> &v)
{
const size_t n = v.size();
for (size_t i = 0; i < n; i++)
{
if (i)
os << ' ';
os << v[i];
}
return os;
}
namespace internal
{
template <class T>
void COUTW() {}
template <class... Ts>
void COUTW(const Ts &...a) { (cout << ... << a); }
template <class T>
void COUTP() { cout << ENDL; }
template <class T>
void COUTP(const T &a) { cout << a << ENDL; }
template <class T, class... Ts>
void COUTP(const T &a, const Ts &...b)
{
cout << a;
(cout << ... << (cout << ' ', b));
cout << ENDL;
}
}; // namespace internal
#endif
#if defined FAST_IO and not defined LOCAL
#define WRITE fastio::write
#define PRINT fastio::print
#else
#define WRITE internal::COUTW
#define PRINT internal::COUTP
#endif
#define PRINTEXIT(...) do { PRINT(__VA_ARGS__); exit(0); } while (false)
#define PRINTRETURN(...) do { PRINT(__VA_ARGS__); return; } while (false)
template <class T>
void PRINTV(const vc<T> &v) { for (auto &vi : v) PRINT(vi); }
#define PRINTVEXIT(...) do { PRINTV(__VA_ARGS__); exit(0); } while (false)
#define PRINTVRETURN(...) do { PRINTV(__VA_ARGS__); return; } while (false)
// ----------
// ----- 基準ずらし -----
template <class T, class U, class P>
pair<T, U> operator+=(pair<T, U> &a, const P &b)
{
a.first += b.first;
a.second += b.second;
return a;
}
template <class T, class U, class P>
pair<T, U> operator+(pair<T, U> &a, const P &b) { return a += b; }
template <class T, size_t n, class A>
array<T, n> operator+=(array<T, n> &a, const A &b)
{
for (size_t i = 0; i < n; i++)
a[i] += b[i];
return a;
}
template <class T, size_t n, class A>
array<T, n> operator+(array<T, n> &a, const A &b) { return a += b; }
namespace internal
{
template <size_t... I, class A, class B>
auto tuple_add_impl(A &a, const B &b, const index_sequence<I...>)
{
((get<I>(a) += get<I>(b)), ...);
return a;
}
}; // namespace internal
template <class... Ts, class Tp>
tuple<Ts...> operator+=(tuple<Ts...> &a, const Tp &b)
{ return internal::tuple_add_impl(a, b, make_index_sequence<tuple_size_v<tuple<Ts...>>>{}); }
template <class... Ts, class Tp>
tuple<Ts...> operator+(tuple<Ts...> &a, const Tp &b) { return a += b; }
template <class T, class Add>
void offset(vc<T> &v, const Add &add) { for (auto &vi : v) vi += add; }
template <class T, class Add>
void offset(vvc<T> &v, const Add &add) { for (auto &vi : v) for (auto &vij : vi) vij += add; }
// ----------
// ----- 転置 -----
template <class T, const size_t m>
array<vc<T>, m> top(const vc<array<T, m>> &vt)
{
const size_t n = vt.size();
array<vc<T>, m> tv;
tv.fill(vc<T>(n));
for (size_t i = 0; i < n; i++)
for (size_t j = 0; j < m; j++)
tv[j][i] = vt[i][j];
return tv;
}
template <class T, const size_t m>
vc<array<T, m>> top(const array<vc<T>, m> &tv)
{
if (tv.empty()) return {};
const size_t n = tv[0].size();
vc<array<T, m>> vt(n);
for (size_t j = 0; j < m; j++)
{
assert(tv[j].size() == n);
for (size_t i = 0; i < n; i++)
vt[i][j] = tv[j][i];
}
return vt;
}
template <class T, class U>
pair<vc<T>, vc<U>> top(const vc<pair<T, U>> &vt)
{
const size_t n = vt.size();
pair<vc<T>, vc<U>> tv;
tv.first.resize(n), tv.second.resize(n);
for (size_t i = 0; i < n; i++)
tie(tv.first[i], tv.second[i]) = vt[i];
return tv;
}
template <class T, class U>
vc<pair<T, U>> top(const pair<vc<T>, vc<U>> &tv)
{
const size_t n = tv.first.size();
assert(n == tv.second.size());
vc<pair<T, U>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = make_pair(tv.first[i], tv.second[i]);
return vt;
}
namespace internal
{
template <size_t... I, class V, class Tp>
auto vt_to_tv_impl(V &tv, const Tp &t, index_sequence<I...>, size_t index)
{ ((get<I>(tv)[index] = get<I>(t)), ...); }
template <size_t... I, class Tp>
auto tv_to_vt_impl(const Tp &tv, index_sequence<I...>, size_t index)
{ return make_tuple(get<I>(tv)[index]...); }
};
template <class... Ts>
auto top(const vc<tuple<Ts...>> &vt)
{
const size_t n = vt.size();
tuple<vc<Ts>...> tv;
apply([&](auto &...v)
{ ((v.resize(n)), ...); }, tv);
for (size_t i = 0; i < n; i++)
internal::vt_to_tv_impl(tv, vt[i], make_index_sequence<tuple_size_v<decltype(tv)>>{}, i);
return tv;
}
template <class... Ts>
auto top(const tuple<vc<Ts>...> &tv)
{
size_t n = get<0>(tv).size();
apply([&](auto &...v)
{ ((assert(v.size() == n)), ...); }, tv);
vc<tuple<Ts...>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = internal::tv_to_vt_impl(tv, index_sequence_for<Ts...>{}, i);
return vt;
}
// ----------
/**
* @brief テンプレート（ランダム生成）
* @docs docs/template/template_random.md
*/
mt19937_64 mt;
// [l, r] から等確率
template <class T = ll, class U1, class U2>
T randint(U1 l, U2 r)
{
assert(T(l) <= T(r));
return T(l) + mt() % (T(r) - T(l) + 1);
}
// [l, r) から等確率
template <class T = ll, class U1, class U2>
T randrange(U1 l, U2 r)
{
assert(T(l) < T(r));
return T(l) + mt() % (T(r) - T(l));
}
// [l, r) から相異なる k 個を選ぶ
// does_sort: ソートするかどうか
template <int k, bool does_sort, class T = ll, class U1, class U2>
array<T, k> random_sample_range_array(U1 l, U2 r)
{
assert(T(r) - T(l) >= T(k));
array<T, k> res;
repi(i, k) res[i] = randint<T>(T(l), T(r) - T(k));
sort(ALL(res));
repi(i, k) res[i] += i;
if (!does_sort)
shuffle(ALL(res), mt);
return res;
}
// [l, r) から相異なる k 個を選ぶ
// does_sort: ソートするかどうか
template <bool does_sort, class T = ll, class U1, class U2>
vc<T> random_sample_range_vector(U1 l, U2 r, int k)
{
assert(T(r) - T(l) >= T(k));
vc<T> res(k);
repi(i, k) res[i] = randint<T>(T(l), T(r) - T(k));
sort(ALL(res));
repi(i, k) res[i] += i;
if (!does_sort)
shuffle(ALL(res), mt);
return res;
}
/**
* @brief CSR
* @docs docs/ds/csr.md
*/
template <class T>
struct CSR
{
protected:
int n, m;
// i (0 <= i < n) 行目を表すのは elist の [start[i], start[i+1])
vc<int> start;
vc<T> elist;
vc<int> eid_to_elistid;
struct Row
{
using iterator = typename vc<T>::const_iterator;
private:
iterator begi, endi;
public:
Row(const iterator &begi, const iterator &endi) : begi(begi), endi(endi) {}
inline iterator begin() const { return begi; }
inline iterator end() const { return endi; }
template <class I = ll>
inline I size() const { return endi - begi; }
inline bool empty() const { return size() == 0; }
inline T operator[](int i) const { return *(begi + i); }
inline T at(int i) const
{
assert(0 <= i && i < size());
return *(begi + i);
}
inline T front() const
{
assert(!empty());
return *begi;
}
inline T back() const
{
assert(!empty());
return *prev(endi);
}
vc<T> to_v() const { return vc<T>(ALL(*this)); }
};
public:
CSR() {}
// (i, elem) が格納された vector
template <class I>
CSR(int n, const vc<pair<I, T>> &ies) : n(n), m(ies.size()), start(n, 0), elist(m), eid_to_elistid(m)
{
fec([ i, e ] : ies)
{
assert(0 <= i && i < n);
start[i]++;
}
start = cumlsum(start);
auto cnt = start;
repi(j, m)
{
cauto &[i, e] = ies[j];
int &k = cnt[i];
elist[k] = e;
eid_to_elistid[j] = k;
k++;
}
}
// vv[i] に elem たちが格納された vector
CSR(const vvc<T> &vv) : n(vv.size()), start(n + 1, 0)
{
m = 0;
fec(row : vv) m += row.size();
elist.resize(m);
eid_to_elistid.resize(m);
int k = 0;
for (int i = 0, j = 0; i < n; i++)
{
start[i] = k;
fec(e : vv[i])
{
elist[k] = e;
eid_to_elistid[j++] = k;
k++;
}
}
start.back() = m;
}
Row operator[](int i) const { return Row(elist.begin() + start[i], elist.begin() + start[i + 1]); }
Row at(int i) const
{
if (!(0 <= i && i < n))
return Row(elist.begin(), elist.begin());
return Row(elist.begin() + start[i], elist.begin() + start[i + 1]);
}
template <class I = ll>
I size() const { return n; }
const T &find_by_eid(int eid) const
{
assert(0 <= eid && eid < m);
return elist[eid_to_elistid[eid]];
}
vvc<T> to_vv() const
{
vvc<T> res(n);
repi(i, n) res[i] = {elist.begin() + start[i], elist.begin() + start[i + 1]};
return res;
}
};
/**
* @brief グラフクラス
* @docs docs/graph/graph.md
*/
template <class Cost>
struct Edge
{
int from, to;
Cost cost;
int index;
Edge() : from(-1), to(-1), index(-1) {}
Edge(int s, int t, Cost c, int i = -1) : from(s), to(t), cost(c), index(i) {}
operator int() const { return to; }
bool operator<(const Edge &rhs) const { return cost < rhs.cost; }
// 逆辺を返す (もとの辺は変更しない)
Edge rev() const { return Edge(to, from, cost, index); }
};
#ifdef LOCAL
CPP_DUMP_DEFINE_EXPORT_OBJECT(Edge<int>, from, to, cost)
CPP_DUMP_DEFINE_EXPORT_OBJECT(Edge<ll>, from, to, cost)
#endif
template <class Cost>
vc<Edge<Cost>> rev_path(const vc<Edge<Cost>> &path)
{
const int len = path.size();
vc<Edge<Cost>> res(len);
repi(i, len) res[i] = path[len - 1 - i].rev();
return res;
}
// コンストラクタ: n, es
template <bool is_directed, class Cost>
struct Graph
{
using E = Edge<Cost>;
protected:
int n, m;
CSR<E> g;
public:
Graph() {}
template <class I>
Graph(int n, const vc<pair<I, I>> &es, const Cost &dflt_cost = 1) : n(n), m(es.size())
{
if constexpr (is_directed)
{
vc<pair<int, E>> edges(m);
repi(i, m)
{
auto [u, v] = es[i];
assert(0 <= u && u < n);
assert(0 <= v && v < n);
edges[i] = {u, E(u, v, dflt_cost, i)};
}
g = CSR<E>(n, edges);
}
else
{
vc<pair<int, E>> edges(2 * m);
repi(i, m)
{
auto [u, v] = es[i];
assert(0 <= u && u < n);
assert(0 <= v && v < n);
edges[2 * i] = {u, E(u, v, dflt_cost, i)};
edges[2 * i + 1] = {v, E(v, u, dflt_cost, i)};
}
g = CSR<E>(n, edges);
}
}
template <class I>
Graph(int n, const vc<tuple<I, I, Cost>> &es) : n(n), m(es.size())
{
if constexpr (is_directed)
{
vc<pair<int, E>> edges(m);
repi(i, m)
{
auto [u, v, w] = es[i];
assert(0 <= u && u < n);
assert(0 <= v && v < n);
edges[i] = {u, E(u, v, w, i)};
}
g = CSR<E>(n, edges);
}
else
{
vc<pair<int, E>> edges(2 * m);
repi(i, m)
{
auto [u, v, w] = es[i];
assert(0 <= u && u < n);
assert(0 <= v && v < n);
edges[2 * i] = {u, E(u, v, w, i)};
edges[2 * i + 1] = {v, E(v, u, w, i)};
}
g = CSR<E>(n, edges);
}
}
// 頂点数
template <class I = ll>
I size() const { return n; }
// 辺数
template <class I = ll>
I num_of_edges() const { return m; }
// v から出る辺の集合
auto out_edges(int v) const { return g[v]; }
// 辺番号から辺を取得する
// 無向グラフの場合 from <= to を満たすように返す
E get_edge(int eid) const
{
if constexpr (is_directed)
return g.find_by_eid(eid);
else
{
E e = g.find_by_eid(eid * 2);
return e.from > e.to ? e.rev() : e;
}
}
// すべての辺を返す (辺番号順)
// 無向グラフの場合、各辺は from <= to を満たす
vc<E> edges() const
{
vc<E> res(m);
repi(i, m) res[i] = get_edge(i);
return res;
}
// 隣接リスト
vvc<E> adj_list() const { return g.to_vv(); }
// 隣接行列（辺の本数を格納）
template <class I = ll>
vvc<I> adj_matrix() const
{
vvc<I> res(n, vc<I>(n, 0));
fec(e : edges())
{
res[e.from][e.to]++;
if (!is_directed && e.from != e.to)
res[e.to][e.from]++;
}
return res;
}
// 入次数の列
template <class I = ll>
vc<I> indegs() const
{
vc<I> res(n);
fec(e : edges())
{
res[e.to]++;
if (!is_directed && e.from != e.to)
res[e.from]++;
}
return res;
}
// 出次数の列
template <class I = ll>
vc<I> outdegs() const
{
vc<I> res(n);
fec(e : edges())
{
res[e.from]++;
if (!is_directed && e.from != e.to)
res[e.to]++;
}
return res;
}
};
template <class Cost>
using GraphDirected = Graph<true, Cost>;
template <class Cost>
using GraphUndirected = Graph<false, Cost>;
template <class Cost>
GraphDirected<Cost> rev_graph(const GraphDirected<Cost> &g)
{
const int n = g.size(), m = g.num_of_edges();
vc<tuple<int, int, Cost>> uvw;
uvw.reserve(m);
fec(e : g.edges()) uvw.eb(e.to, e.from, e.cost);
return GraphDirected<Cost>(n, uvw);
}
/**
* @brief 自作 queue
* @docs docs/ds/my_queue.md
*/
template <class T>
struct MyQueue
{
private:
vc<T> d;
int pos = 0;
public:
void reserve(int n) { d.reserve(n); }
template <class I = ll>
I size() const { return SZ<I>(d) - pos; }
bool empty() const { return pos == SZ<int>(d); }
void push(const T &t) { d.eb(t); }
T front() const { return d[pos]; }
T &front() { return d[pos]; }
void clear()
{
d.clear();
pos = 0;
}
void pop() { pos++; }
T operator[](int i) const { return d[pos + i]; }
T &operator[](int i) { return d[pos + i]; }
T at(int i) const
{
assert(0 <= i && i < size<int>());
return d[pos + i];
}
T &at(int i)
{
assert(0 <= i && i < size<int>());
return d[pos + i];
}
vc<T> content() { return {d.begin() + pos, d.end()}; }
};
/**
* @brief 根つき木クラス
* @docs docs/graph/tree/rooted_tree.md
*/
// コンストラクタは
// - n, es, root
// - g, root
// - p
// のいずれか
template <class Cost, bool need_dist = true>
struct RootedTree
{
using E = Edge<Cost>;
protected:
int n, root_;
vc<E> par; // par[v] は v から親に向かう辺
CSR<E> chi;
// bfs_ordered_eid: 辺番号を BFS 順に並べた順列
vc<int> bfs_ordered_eid;
vc<int> dep;
vc<Cost> dis;
vc<int> siz;
void calc_siz()
{
siz.assign(n, 1);
repi(j, n - 2, -1, -1)
{
const E &e = get_edge(bfs_ordered_eid[j]);
siz[e.from] += siz[e.to];
}
}
public:
RootedTree() {}
// p[i] は i の親の頂点番号 (根は -1) を渡す
template <class I>
RootedTree(const vc<I> &p, const Cost &dflt_cost = 1) : n(p.size())
{
// par, chi を計算する
par.resize(n);
root_ = -1;
vc<pair<int, E>> edges(n - 1);
for (int i = 0, j = 0; i < n; i++)
{
if (p[i] < 0)
{
assert(root_ == -1 && "more than two roots exist");
par[i] = E(i, -1, dflt_cost, -1);
root_ = i;
}
else
{
assert(j < n - 1 && "the root does not exist");
par[i] = E(i, p[i], dflt_cost, j);
edges[j] = {p[i], E(p[i], i, dflt_cost, j)};
j++;
}
}
chi = CSR<E>(n, edges);
// bfs_ordered_eid, dep(, dist) を計算する
bfs_ordered_eid.reserve(n - 1);
MyQueue<int> que;
que.push(root_);
dep.assign(n, 0);
if constexpr (need_dist)
dis.assign(n, 0);
while (!que.empty())
{
int v = que.front();
que.pop();
fec(e : chi[v])
{
bfs_ordered_eid.eb(e.index);
dep[e.to] = dep[e.from] + 1;
if constexpr (need_dist)
dep[e.to] = dep[e.from] + e.cost;
que.push(e.to);
}
}
// siz を計算する
calc_siz();
}
// g は木であることを想定、もとの g の index はそのまま保持される
template <bool is_directed>
RootedTree(const Graph<is_directed, Cost> &g, int root)
: n(g.size()), root_(root)
{
// par, chi, bfs_ordered_eid, dep(, dist) を計算する
par.resize(n);
par[root] = E(root, -1, {}, -1);
vc<pair<int, E>> edges(n - 1);
MyQueue<int> que;
que.push(root);
dep.assign(n, 0);
if constexpr (need_dist)
dis.assign(n, 0);
while (!que.empty())
{
int v = que.front();
que.pop();
fec(e : g.out_edges(v))
{
if (par[e.from] == e.to)
continue;
par[e.to] = e.rev();
edges[e.index] = {e.from, e};
bfs_ordered_eid.eb(e.index);
dep[e.to] = dep[e.from] + 1;
if constexpr (need_dist)
dis[e.to] = dis[e.from] + e.cost;
que.push(e.to);
}
}
chi = CSR<E>(n, edges);
// siz を計算する
calc_siz();
}
template <class I>
RootedTree(int n, const vc<pair<I, I>> &es, int root)
: RootedTree(GraphUndirected<Cost>(n, es), root) {}
template <class I>
RootedTree(int n, const vc<tuple<I, I, Cost>> &es, int root)
: RootedTree(GraphUndirected<Cost>(n, es), root) {}
// 頂点数を返す
template <class I = ll>
I size() const { return n; }
// 根を返す
int root() const { return root_; }
// v から親に向かう辺として返す (根なら to == -1)
const E &parent(int v) const
{
assert(0 <= v && v < n);
return par[v];
}
// v の子の集合
auto children(int v) const
{
assert(0 <= v && v < n);
return chi[v];
}
// v の深さ
template <class I = ll>
I depth(int v) const
{
assert(0 <= v && v < n);
return dep[v];
}
// 根から v への距離 (重みつき)
// need_dist == true が必要
Cost dist(int v) const
{
static_assert(need_dist);
assert(0 <= v && v < n);
return dis[v];
}
// v を根とする部分木のサイズ (v も含む)
template <class I = ll>
I subtree_size(int v) const
{
assert(0 <= v && v < n);
return siz[v];
}
// 辺 (u, v) が存在するとして、これを切ったときの
// u 側、v 側それぞれの連結成分サイズ
template <class I = ll>
pair<I, I> cut_and_subtree_size(int u, int v) const
{
assert(0 <= u && u < n);
assert(0 <= v && v < n);
if (dep[u] < dep[v])
return {n - siz[v], siz[v]};
else
return {siz[u], n - siz[u]};
}
// 辺番号から辺を取得する
// 辺は親から子
const E &get_edge(int eid) const { return chi.find_by_eid(eid); }
// すべての辺を返す
// 辺は親から子
vc<E> edges() const
{
vc<E> res(n - 1);
repi(i, n - 1) res[i] = get_edge(i);
return res;
}
// v から根までのパスを (辺の vector として) 返す
vc<E> path_to_root(int v) const
{
assert(0 <= v && v < n);
vc<E> res;
res.reserve(dep[v]);
while (v != root_)
{
res.eb(par[v]);
v = par[v].to;
}
return res;
}
// u から v までのパスを (辺の vector として) 返す
vc<E> path(int u, int v) const
{
assert(0 <= u && u < n);
assert(0 <= v && v < n);
vc<E> pu, pv;
while (u != v)
{
if (dep[u] > dep[v])
{
const E &e = parent(u);
pu.eb(e);
u = e.to;
}
else
{
const E &e = parent(v);
pv.eb(e);
v = e.to;
}
}
return concat(pu, rev_path(pv));
}
// BFS 順に頂点を並べた、長さ n の列を返す
template <class I = ll>
vc<I> bfs_ordered_vertices() const
{
vc<I> res(n);
res[0] = root_;
repi(i, n - 1) res[i + 1] = get_edge(bfs_ordered_eid[i]).to;
return res;
}
// BFS 順に辺を並べた、長さ n-1 の列を返す
// 辺は親から子
vc<E> bfs_ordered_edges() const
{
vc<E> res(n - 1);
repi(i, n - 1) res[i] = get_edge(bfs_ordered_eid[i]);
return res;
}
// 帰るのも含めた DFS 順に辺を並べた、長さ 2(n-1) の列を返す
vc<E> dfs_ordered_edges() const
{
vc<E> res(2 * (n - 1));
vc<int> dp(n, 0);
fec(eid : bfs_ordered_eid)
{
const E &e = get_edge(eid);
dp[e.to] = dp[e.from] + 1;
res[dp[e.to] - 1] = e;
dp[e.from] += 2 * siz[e.to];
res[dp[e.from] - 1] = e.rev();
}
return res;
}
// グラフや根つき木を作るための辺の vc<tuple>
template <class I = ll>
vc<tuple<I, I, Cost>> edges_vt() const
{
vc<tuple<I, I, Cost>> es(n - 1);
repi(i, n - 1)
{
const E &e = get_edge(i);
es[i] = {e.from, e.to, e.cost};
}
return es;
}
// 新たに根を付け替えた根つき木を返す
RootedTree<Cost, need_dist> rerooted_tree(int new_root) const
{
return RootedTree<Cost, need_dist>(n, edges_vt(), new_root);
}
// Graph として返す
template <bool is_directed>
Graph<is_directed, Cost> to_graph() const
{
return Graph<is_directed, Cost>(n, edges_vt());
}
};
void init()
{
oj(mt.seed(random_device()()));
}
void main2()
{
LL(N);
VEC(ll, N, P);
P.insert(P.begin(), -1);
RootedTree<bool> G(P);
ll ans = 0;
rep(i, N)
{
if (G.depth(i) == 3)
{
dump(i);
ans++;
}
}
PRINT(ans);
}
void test()
{
}
template <auto init, auto main2, auto test>
struct Main
{
Main()
{
cauto CERR = [](string val, string color)
{
string s = "\033[" + color + "m" + val + "\033[m";
#ifdef LOCAL
cerr << s;
#endif
/* コードテストで確認する際にコメントアウトを外す
cerr << val;
//*/
};
#if defined FAST_IO and not defined LOCAL
CERR("\n[FAST_IO]\n\n", "32");
#endif
#if defined FAST_CIO and not defined LOCAL
CERR("\n[FAST_CIO]\n\n", "32");
cin.tie(0);
ios::sync_with_stdio(false);
#endif
cout << fixed << setprecision(20);
init();
#ifdef LOCAL
test();
#endif
#if defined AOJ_TESTCASE or (defined LOCAL and defined SINGLE_TESTCASE)
CERR("\n[AOJ_TESTCASE]\n\n", "35");
while (true)
{
dump("new testcase");
main2();
}
#elif defined SINGLE_TESTCASE
CERR("\n[SINGLE_TESTCASE]\n\n", "36");
main2();
#elif defined MULTI_TESTCASE
CERR("\n[MULTI_TESTCASE]\n\n", "33");
local(while (true))
{
dump("T");
IN(uint, T);
while (T--)
{
dump("new testcase");
main2();
}
}
#endif
}
};
Main<init, main2, test> main_dummy;
int main() {}