// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/courses/lesson/8/ITP2/all/ITP2_5_C
#include "../../../src/edh/cantor/inv/lib.hpp"
#include "../../../src/edh/cantor/seq/lib.hpp"
#include "../../../src/edh/cantor/seq2val/lib.hpp"
#include "../../../src/edh/cantor/val2seq/lib.hpp"
#include "../../../src/io/container/lib.hpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 n;
std::cin >> n;
vecu p(n);
std::cin >> p;
auto s = cantor_seq(p);
auto fact = gen_fact((u32)s.size(), -1_u64);
u64 v = cantor_seq2val(s, fact);
if (v > 1) std::cout << cantor_inv_seq(cantor_val2seq(v - 1, fact)) << '\n';
std::cout << p << '\n';
if (v < fact.back() * n) std::cout << cantor_inv_seq(cantor_val2seq(v + 1, fact)) << '\n';
return 0;
}
#line 1 "test/cpv/aizu-itp2/itp2_5_c.cpp"
// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/courses/lesson/8/ITP2/all/ITP2_5_C
#line 2 "src/edh/cantor/inv/lib.hpp"
#line 2 "src/ds/segtree/w/lib.hpp"
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<T>;
template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>; template <class T, usz N> using carr = std::array<const T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>; template <class U, class T> using vvecp = vvec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, T)
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 4 "src/ds/segtree/w/lib.hpp"
namespace tifa_libs {
class weighted_segtree {
cu32 n;
vecu t;
public:
CEXPE weighted_segtree(u32 N) NE : n(N), t(N * 4) {}
CEXP void ins(u32 pos) NE { ins_(1, 0, n - 1, pos); }
CEXP void del(u32 pos) NE { del_(1, 0, n - 1, pos); }
CEXP u32 kth_min(u32 k) NE { return kth_min_(1, 0, n - 1, k); }
CEXP u32 kth_max(u32 k) NE { return kth_max_(1, 0, n - 1, k); }
CEXP u32 frequency(u32 k) NE { return frequency_(1, 0, n - 1, k, k); }
CEXP u32 frequency(u32 l, u32 r) NE { return frequency_(1, 0, n - 1, l, r); }
private:
CEXP void ins_(u32 x, u32 l, u32 r, u32 pos) NE {
if (l == r) return void(++t[x]);
if (cu32 mid = l + (r - l) / 2; pos <= mid) ins_(x * 2, l, mid, pos);
else ins_(x * 2 + 1, mid + 1, r, pos);
t[x] = t[x * 2] + t[x * 2 + 1];
}
CEXP void del_(u32 x, u32 l, u32 r, u32 pos) NE {
if (l == r) return void(--t[x]);
if (cu32 mid = l + (r - l) / 2; pos <= mid) del_(x * 2, l, mid, pos);
else del_(x * 2 + 1, mid + 1, r, pos);
t[x] = t[x * 2] + t[x * 2 + 1];
}
ND CEXP u32 kth_min_(u32 x, u32 l, u32 r, u32 k) CNE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2; k <= t[x * 2]) return kth_min_(x * 2, l, mid, k);
else return kth_min_(x * 2 + 1, mid + 1, r, k - t[x * 2]);
}
ND CEXP u32 kth_max_(u32 x, u32 l, u32 r, u32 k) CNE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2; k <= t[x * 2 + 1]) return kth_max_(x * 2 + 1, mid + 1, r, k);
else return kth_max_(x * 2, l, mid, k - t[x * 2 + 1]);
}
ND CEXP u32 frequency_(u32 x, u32 l, u32 r, u32 L, u32 R) CNE {
if (L <= l && R >= r) return t[x];
cu32 mid = l + (r - l) / 2;
u32 ret = 0_u32;
if (L <= mid) ret = frequency_(x * 2, l, mid, L, R);
if (R > mid) ret += frequency_(x * 2 + 1, mid + 1, r, L, R);
return ret;
}
};
} // namespace tifa_libs
#line 4 "src/edh/cantor/inv/lib.hpp"
namespace tifa_libs {
//! [0, n)
//! p \in [1, n], a_i == a_j \iff i == j
CEXP vecu cantor_inv_seq(spnu s) NE {
cu32 n = (u32)s.size();
weighted_segtree tr(n + 1);
flt_ (u32, i, 1, n + 1) tr.ins(i);
vecu p(n);
flt_ (u32, i, 0, n) tr.del(p[i] = tr.kth_min(s[i] + 1));
return p;
}
} // namespace tifa_libs
#line 2 "src/edh/cantor/seq/lib.hpp"
#line 2 "src/ds/fenwick/d1/lib.hpp"
#line 2 "src/bit/lowbit/lib.hpp"
#line 4 "src/bit/lowbit/lib.hpp"
namespace tifa_libs {
template <class T>
CEXP T lowbit(T x) NE { return T(1) << std::countr_zero(x); }
} // namespace tifa_libs
#line 5 "src/ds/fenwick/d1/lib.hpp"
namespace tifa_libs {
template <class T>
class fenwick {
vec<T> a;
public:
//! [1, sz)
CEXPE fenwick(u32 sz) NE : a(sz) { assert(sz > 1); }
//! [1, sz)
CEXP fenwick(spn<T> data) NE : fenwick((u32)data.size()) {
cu32 sz = (u32)data.size();
flt_ (u32, i, 1, sz) {
a[i] += data[i];
if (cu32 j = i + lowbit(i); j < sz) a[j] += a[i];
}
}
//! [pos, sz), pos > 0
CEXP void add(u32 pos, cT_(T) x) NE {
if (!pos) return;
for (; pos < a.size(); pos += lowbit(pos)) a[pos] += x;
}
//! [l, r], l > 0
CEXP void add(u32 l, u32 r, cT_(T) x) NE { add(l, x), add(r + 1, -x); }
//! [1, pos]
CEXP T sum(u32 pos) NE {
T ret = 0;
for (pos = min(pos, (u32)a.size() - 1); pos; pos -= lowbit(pos)) ret += a[pos];
return ret;
}
//! [l, r]
CEXP T sum(u32 l, u32 r) NE { return sum(r) - sum(l - 1); }
//! for weighted fenwick
CEXP T kth_max(u32 k) NE {
cu32 n = std::bit_ceil(a.size());
u32 now = 0;
T s{};
while (n)
if (cu32 to = now | n; to >= a.size()) continue;
else if (T x = s + a[to]; x < k) now = to, s = x;
return now + 1;
}
};
} // namespace tifa_libs
#line 4 "src/edh/cantor/seq/lib.hpp"
namespace tifa_libs {
//! [0, n)
//! p \in [1, n], a_i == a_j \iff i == j
CEXP vecu cantor_seq(spnu p) NE {
cu32 n = (u32)p.size();
fenwick<u32> tr(n + 1);
vecu s(n);
for (u32 i = n - 1; ~i; --i) s[i] = tr.sum(p[i]), tr.add(p[i], 1);
return s;
}
} // namespace tifa_libs
#line 2 "src/edh/cantor/seq2val/lib.hpp"
#line 2 "src/comb/seq/fact/lib.hpp"
#line 2 "src/math/mul_mod/lib.hpp"
#line 2 "src/math/safe_mod/lib.hpp"
#line 2 "src/util/traits/math/lib.hpp"
// clang-format off
#line 4 "src/util/traits/math/lib.hpp"
namespace tifa_libs {
template <class T> concept char_c = std::same_as<T, char> || std::same_as<T, signed char> || std::same_as<T, unsigned char>;
#pragma GCC diagnostic ignored "-Wpedantic"
template <class T> concept s128_c = std::same_as<T, __int128_t> || std::same_as<T, __int128>;
template <class T> concept u128_c = std::same_as<T, __uint128_t> || std::same_as<T, unsigned __int128>;
template <class T> concept i128_c = s128_c<T> || u128_c<T>;
#pragma GCC diagnostic warning "-Wpedantic"
template <class T> concept imost64_c = std::integral<T> && sizeof(T) * __CHAR_BIT__ <= 64;
template <class T> concept smost64_c = imost64_c<T> && std::signed_integral<T>;
template <class T> concept umost64_c = imost64_c<T> && std::unsigned_integral<T>;
template <class T> concept int_c = i128_c<T> || imost64_c<T>;
template <class T> concept sint_c = s128_c<T> || smost64_c<T>;
template <class T> concept uint_c = u128_c<T> || umost64_c<T>;
template <class T> concept arithm_c = std::is_arithmetic_v<T> || int_c<T>;
template <class T> concept mint_c = requires(T x) { {x.mod()} -> uint_c; {x.val()} -> uint_c; };
template <class T> concept dft_c = requires(T x, std::vector<TPN T::data_t> v, u32 n) { {x.size()} -> std::same_as<u32>; x.bzr(n); x.dif(v, n); x.dit(v, n); };
template <class T> concept ntt_c = dft_c<T> && requires(T x) { T::max_size; T::G; };
template <class T> struct to_sint : std::make_signed<T> {};
template <> struct to_sint<u128> { using type = i128; };
template <> struct to_sint<i128> { using type = i128; };
template <class T> using to_sint_t = TPN to_sint<T>::type;
template <class T> struct to_uint : std::make_unsigned<T> {};
template <> struct to_uint<u128> { using type = u128; };
template <> struct to_uint<i128> { using type = u128; };
template <class T> using to_uint_t = TPN to_uint<T>::type;
template <arithm_c T> struct to_bigger : std::make_unsigned<T> {};
#define _(w,ww) template <> struct to_bigger<w> { using type = ww; }
#define _2(w,ww) _(i##w,i##ww); _(u##w,u##ww);
_2(8, 16); _2(16, 32); _2(32, 64); _2(64, 128); _(f32, f64); _(f64, f128);
#undef _2
#undef _
template <class T> using to_bigger_t = TPN to_bigger<T>::type;
template <arithm_c T> CEXP T inf_v = [] {
if CEXP(sint_c<T>) return T(to_uint_t<T>(-1) / 4 - 1);
else if CEXP(uint_c<T>) return T(-1) / 2 - 1;
else return std::numeric_limits<T>::max() / 2 - 1;
}();
} // namespace tifa_libs
// clang-format on
#line 4 "src/math/safe_mod/lib.hpp"
namespace tifa_libs {
template <int_c T>
CEXP T safe_mod(T x, to_uint_t<T> mod) NE {
if CEXP (sint_c<T>) {
if (x <= -(T)mod || x >= (T)mod) x %= (T)mod;
retif_((x < 0), x + (T)mod, x);
} else {
retif_((x >= mod), x % mod, x);
}
}
} // namespace tifa_libs
#line 4 "src/math/mul_mod/lib.hpp"
namespace tifa_libs {
CEXP i64 mul_mod_s(i64 a, i64 b, u64 mod) NE {
if (std::bit_width((u64)abs(a)) + std::bit_width((u64)abs(b)) < 64) return safe_mod(a * b % (i64)mod, mod);
return safe_mod((i64)((i128)a * b % mod), mod);
}
CEXP u64 mul_mod_u(u64 a, u64 b, u64 mod) NE {
if (std::bit_width(a) + std::bit_width(b) <= 64) return a * b % mod;
return (u64)((u128)a * b % mod);
}
} // namespace tifa_libs
#line 5 "src/comb/seq/fact/lib.hpp"
namespace tifa_libs {
// i! from i=0..n-1
CEXP vecuu gen_fact(u32 n, u64 mod) NE {
retif_((n <= 1) [[unlikely]], vecuu(n, 1));
vecuu ans(n);
ans[0] = ans[1] = 1;
flt_ (u32, i, 2, n) ans[i] = mul_mod_u(ans[i - 1], i, mod);
return ans;
}
// i! from i=0..n-1
template <class mint>
CEXP vec<mint> gen_fact(u32 n) NE {
vec<mint> ans(n);
auto _ = gen_fact(n, mint::mod());
flt_ (u32, i, 0, n) ans[i] = _[i];
return ans;
}
} // namespace tifa_libs
#line 4 "src/edh/cantor/seq2val/lib.hpp"
namespace tifa_libs {
CEXP u64 cantor_seq2val(spnu s, spnuu fact, u64 mod = -1_u64) NE {
cu32 n = (u32)s.size();
u64 ret = 1;
flt_ (u32, i, 0, n) (ret += mul_mod_u(s[i], fact[n - i - 1], mod)) %= mod;
return ret;
}
CEXP u64 cantor_seq2val(spnu s, u64 mod = -1_u64) NE { return cantor_seq2val(s, gen_fact((u32)s.size(), mod), mod); }
} // namespace tifa_libs
#line 2 "src/edh/cantor/val2seq/lib.hpp"
#line 4 "src/edh/cantor/val2seq/lib.hpp"
namespace tifa_libs {
CEXP vecu cantor_val2seq(u64 cv, spnuu fact) NE {
cu32 n = (u32)fact.size();
vecu s;
s.reserve(n), --cv;
for (u32 i = 0; i < n; cv %= fact[n - i - 1], ++i) s.push_back(u32(cv / fact[n - i - 1]));
return s;
}
CEXP vecu cantor_val2seq(u64 cv, u32 n) NE { return cantor_val2seq(cv, gen_fact(n, -1_u64)); }
} // namespace tifa_libs
#line 2 "src/io/container/lib.hpp"
#line 2 "src/util/traits/others/lib.hpp"
// clang-format off
#line 4 "src/util/traits/others/lib.hpp"
namespace tifa_libs {
//! only for template without non-type argument
template <class, template <class...> class> CEXP bool specialized_from_v = false;
template <template <class...> class T, class... Args> CEXP bool specialized_from_v<T<Args...>, T> = true;
static_assert(specialized_from_v<vecu, std::vector>);
template <class T> concept container_c = common_range<T> && !std::is_array_v<std::remove_cvref_t<T>> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;
template <class T> concept istream_c = std::derived_from<T, std::istream> || std::derived_from<T, std::wistream> || requires(T is) { is.peek(); };
template <class T> concept ostream_c = std::derived_from<T, std::ostream> || std::derived_from<T, std::wostream> || requires(T os) { os.flush(); };
} // namespace tifa_libs
// clang-format on
#line 4 "src/io/container/lib.hpp"
namespace tifa_libs {
auto& operator>>(tifa_libs::istream_c auto& is, tifa_libs::container_c auto& x) NE {
for (auto& i : x) is >> i;
return is;
}
auto& operator<<(tifa_libs::ostream_c auto& os, tifa_libs::container_c auto CR x) NE {
if (begin(x) == end(x)) [[unlikely]]
return os;
auto it = begin(x);
for (os << *it++; it != end(x); ++it) os << ' ' << *it;
return os;
}
} // namespace tifa_libs
#line 7 "test/cpv/aizu-itp2/itp2_5_c.cpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 n;
std::cin >> n;
vecu p(n);
std::cin >> p;
auto s = cantor_seq(p);
auto fact = gen_fact((u32)s.size(), -1_u64);
u64 v = cantor_seq2val(s, fact);
if (v > 1) std::cout << cantor_inv_seq(cantor_val2seq(v - 1, fact)) << '\n';
std::cout << p << '\n';
if (v < fact.back() * n) std::cout << cantor_inv_seq(cantor_val2seq(v + 1, fact)) << '\n';
return 0;
}
test/cpv/aizu-itp2/itp2_5_c.cpp