結果
| 問題 | No.2556 Increasing Matrix |
| ユーザー |
 hitonanode
|
| 提出日時 | 2023-12-02 22:28:31 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 28,769 bytes |
| コンパイル時間 | 3,734 ms |
| コンパイル使用メモリ | 237,200 KB |
| 実行使用メモリ | 29,112 KB |
| 最終ジャッジ日時 | 2024-09-26 21:42:35 |
| 合計ジャッジ時間 | 26,220 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 2 ms
5,376 KB |
| testcase_04 | AC | 2 ms
5,376 KB |
| testcase_05 | AC | 2 ms
5,376 KB |
| testcase_06 | AC | 3 ms
5,376 KB |
| testcase_07 | AC | 2 ms
5,376 KB |
| testcase_08 | AC | 3 ms
5,376 KB |
| testcase_09 | AC | 8 ms
5,376 KB |
| testcase_10 | AC | 4 ms
5,376 KB |
| testcase_11 | AC | 6 ms
5,376 KB |
| testcase_12 | AC | 4 ms
5,376 KB |
| testcase_13 | AC | 17 ms
5,376 KB |
| testcase_14 | AC | 42 ms
5,376 KB |
| testcase_15 | AC | 37 ms
5,376 KB |
| testcase_16 | AC | 29 ms
5,376 KB |
| testcase_17 | AC | 53 ms
5,376 KB |
| testcase_18 | AC | 3,104 ms
18,716 KB |
| testcase_19 | AC | 3,694 ms
22,512 KB |
| testcase_20 | AC | 4,293 ms
24,008 KB |
| testcase_21 | AC | 2,216 ms
16,560 KB |
| testcase_22 | AC | 80 ms
5,376 KB |
| testcase_23 | TLE | - |
| testcase_24 | TLE | - |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <cassert>
#include <iostream>
#include <set>
#include <vector>
template <int md> struct ModInt {
using lint = long long;
constexpr static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
constexpr ModInt() : val_(0) {}
constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
constexpr ModInt(lint v) { _setval(v % md + md); }
constexpr explicit operator bool() const { return val_ != 0; }
constexpr ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
constexpr ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
constexpr ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
constexpr ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) {
return ModInt()._setval(a % md + x.val_);
}
friend constexpr ModInt operator-(lint a, const ModInt &x) {
return ModInt()._setval(a % md - x.val_ + md);
}
friend constexpr ModInt operator*(lint a, const ModInt &x) {
return ModInt()._setval(a % md * x.val_ % md);
}
friend constexpr ModInt operator/(lint a, const ModInt &x) {
return ModInt()._setval(a % md * x.inv().val() % md);
}
constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
constexpr bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
constexpr ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static constexpr int cache_limit = std::min(md, 1 << 21);
static std::vector<ModInt> facs, facinvs, invs;
constexpr static void _precalculation(int N) {
const int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
constexpr ModInt inv() const {
if (this->val_ < cache_limit) {
if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
constexpr ModInt fac() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[this->val_];
}
constexpr ModInt facinv() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[this->val_];
}
constexpr ModInt doublefac() const {
lint k = (this->val_ + 1) / 2;
return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
: ModInt(k).fac() * ModInt(2).pow(k);
}
constexpr ModInt nCr(int r) const {
if (r < 0 or this->val_ < r) return ModInt(0);
return this->fac() * (*this - r).facinv() * ModInt(r).facinv();
}
constexpr ModInt nPr(int r) const {
if (r < 0 or this->val_ < r) return ModInt(0);
return this->fac() * (*this - r).facinv();
}
static ModInt binom(int n, int r) {
static long long bruteforce_times = 0;
if (r < 0 or n < r) return ModInt(0);
if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r);
r = std::min(r, n - r);
ModInt ret = ModInt(r).facinv();
for (int i = 0; i < r; ++i) ret *= n - i;
bruteforce_times += r;
return ret;
}
// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
// Complexity: O(sum(ks))
template <class Vec> static ModInt multinomial(const Vec &ks) {
ModInt ret{1};
int sum = 0;
for (int k : ks) {
assert(k >= 0);
ret *= ModInt(k).facinv(), sum += k;
}
return ret * ModInt(sum).fac();
}
// Catalan number, C_n = binom(2n, n) / (n + 1)
// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
// https://oeis.org/A000108
// Complexity: O(n)
static ModInt catalan(int n) {
if (n < 0) return ModInt(0);
return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv();
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using mint = ModInt<998244353>;
// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner);
constexpr int nttprimes[3] = {998244353, 167772161, 469762049};
// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) {
int n = a.size();
if (n == 1) return;
static const int mod = MODINT::mod();
static const MODINT root = MODINT::get_primitive_root();
assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);
static std::vector<MODINT> w{1}, iw{1};
for (int m = w.size(); m < n / 2; m *= 2) {
MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw;
w.resize(m * 2), iw.resize(m * 2);
for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
}
if (!is_inverse) {
for (int m = n; m >>= 1;) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m] * w[k];
a[i] = x + y, a[i + m] = x - y;
}
}
}
} else {
for (int m = 1; m < n; m *= 2) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m];
a[i] = x + y, a[i + m] = (x - y) * iw[k];
}
}
}
int n_inv = MODINT(n).inv().val();
for (auto &v : a) v *= n_inv;
}
}
template <int MOD>
std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {
int sz = a.size();
assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
std::vector<ModInt<MOD>> ap(sz), bp(sz);
for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
ntt(ap, false);
if (a == b)
bp = ap;
else
ntt(bp, false);
for (int i = 0; i < sz; i++) ap[i] *= bp[i];
ntt(ap, true);
return ap;
}
long long garner_ntt_(int r0, int r1, int r2, int mod) {
using mint2 = ModInt<nttprimes[2]>;
static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv().val();
static const long long m01_inv_m2 = mint2(m01).inv().val();
int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;
return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val()) % mod;
}
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) {
if (a.empty() or b.empty()) return {};
int sz = 1, n = a.size(), m = b.size();
while (sz < n + m) sz <<= 1;
if (sz <= 16) {
std::vector<MODINT> ret(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];
}
return ret;
}
int mod = MODINT::mod();
if (skip_garner or
std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) {
a.resize(sz), b.resize(sz);
if (a == b) {
ntt(a, false);
b = a;
} else {
ntt(a, false), ntt(b, false);
}
for (int i = 0; i < sz; i++) a[i] *= b[i];
ntt(a, true);
a.resize(n + m - 1);
} else {
std::vector<int> ai(sz), bi(sz);
for (int i = 0; i < n; i++) ai[i] = a[i].val();
for (int i = 0; i < m; i++) bi[i] = b[i].val();
auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
a.resize(n + m - 1);
for (int i = 0; i < n + m - 1; i++)
a[i] = garner_ntt_(ntt0[i].val(), ntt1[i].val(), ntt2[i].val(), mod);
}
return a;
}
template <typename MODINT>
std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {
return nttconv<MODINT>(a, b, false);
}
#include <algorithm>
#include <cassert>
#include <vector>
// Formal Power Series (形式的冪級数) based on ModInt<mod> / ModIntRuntime
// Reference: https://ei1333.github.io/luzhiled/snippets/math/formal-power-series.html
template <typename T> struct FormalPowerSeries : std::vector<T> {
using std::vector<T>::vector;
using P = FormalPowerSeries;
void shrink() {
while (this->size() and this->back() == T(0)) this->pop_back();
}
P operator+(const P &r) const { return P(*this) += r; }
P operator+(const T &v) const { return P(*this) += v; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator-(const T &v) const { return P(*this) -= v; }
P operator*(const P &r) const { return P(*this) *= r; }
P operator*(const T &v) const { return P(*this) *= v; }
P operator/(const P &r) const { return P(*this) /= r; }
P operator/(const T &v) const { return P(*this) /= v; }
P operator%(const P &r) const { return P(*this) %= r; }
P &operator+=(const P &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
return *this;
}
P &operator+=(const T &v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
return *this;
}
P &operator-=(const P &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
return *this;
}
P &operator-=(const T &v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
return *this;
}
P &operator*=(const T &v) {
for (auto &x : (*this)) x *= v;
return *this;
}
P &operator*=(const P &r) {
if (this->empty() || r.empty())
this->clear();
else {
auto ret = nttconv(*this, r);
*this = P(ret.begin(), ret.end());
}
return *this;
}
P &operator%=(const P &r) {
*this -= *this / r * r;
return *this;
}
P operator-() const {
P ret = *this;
for (auto &v : ret) v = -v;
return ret;
}
P &operator/=(const T &v) {
assert(v != T(0));
for (auto &x : (*this)) x /= v;
return *this;
}
P &operator/=(const P &r) {
if (this->size() < r.size()) {
this->clear();
return *this;
}
int n = (int)this->size() - r.size() + 1;
return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n);
}
P pre(int sz) const {
P ret(this->begin(), this->begin() + std::min((int)this->size(), sz));
return ret;
}
P operator>>(int sz) const {
if ((int)this->size() <= sz) return {};
return P(this->begin() + sz, this->end());
}
P operator<<(int sz) const {
if (this->empty()) return {};
P ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
P reversed(int sz = -1) const {
assert(sz >= -1);
P ret(*this);
if (sz != -1) ret.resize(sz, T());
std::reverse(ret.begin(), ret.end());
return ret;
}
P differential() const { // formal derivative (differential) of f.p.s.
const int n = (int)this->size();
P ret(std::max(0, n - 1));
for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
return ret;
}
P integral() const {
const int n = (int)this->size();
P ret(n + 1);
ret[0] = T(0);
for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
return ret;
}
/**
* @brief f(x)g(x) = 1 (mod x^deg)
*
* @param deg
* @return P ret.size() == deg
*/
P inv(int deg) const {
assert(deg >= -1);
if (deg == 0) return {};
assert(this->size() and this->at(0) != T()); // Requirement: F(0) != 0
const int n = this->size();
if (deg == -1) deg = n;
P ret({T(1) / this->at(0)});
for (int i = 1; i < deg; i <<= 1) {
auto h = (pre(i << 1) * ret).pre(i << 1) >> i;
auto tmp = (-h * ret).pre(i);
ret.insert(ret.end(), tmp.cbegin(), tmp.cend());
ret.resize(i << 1);
}
return ret.pre(deg);
}
P log(int len = -1) const {
assert(len >= -1);
if (len == 0) return {};
assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1
const int n = (int)this->size();
if (len == 0) return {};
if (len == -1) len = n;
return (this->differential() * this->inv(len)).pre(len - 1).integral();
}
P sqrt(int deg = -1) const {
assert(deg >= -1);
const int n = (int)this->size();
if (deg == -1) deg = n;
if (this->empty()) return {};
if ((*this)[0] == T(0)) {
for (int i = 1; i < n; i++)
if ((*this)[i] != T(0)) {
if ((i & 1) or deg - i / 2 <= 0) return {};
return (*this >> i).sqrt(deg - i / 2) << (i / 2);
}
return {};
}
T sqrtf0 = (*this)[0].sqrt();
if (sqrtf0 == T(0)) return {};
P y = (*this) / (*this)[0], ret({T(1)});
T inv2 = T(1) / T(2);
for (int i = 1; i < deg; i <<= 1) ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2;
return ret.pre(deg) * sqrtf0;
}
P exp(int deg = -1) const {
assert(deg >= -1);
assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0
const int n = (int)this->size();
if (deg == -1) deg = n;
P ret({T(1)});
for (int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
P pow(long long k, int deg = -1) const {
assert(deg >= -1);
const int n = (int)this->size();
if (deg == -1) deg = n;
if (k == 0) {
P ret(deg);
if (deg >= 1) ret[0] = T(1);
ret.shrink();
return ret;
}
for (int i = 0; i < n; i++) {
if ((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P C = (*this) * rev, D(n - i);
for (int j = i; j < n; j++) D[j - i] = C.coeff(j);
D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].pow(k);
if (__int128(k) * i > deg) return {};
P E(deg);
long long S = i * k;
for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j];
E.shrink();
return E;
}
}
return *this;
}
// Calculate f(X + c) from f(X), O(NlogN)
P shift(T c) const {
const int n = (int)this->size();
P ret = *this;
for (int i = 0; i < n; i++) ret[i] *= T(i).fac();
std::reverse(ret.begin(), ret.end());
P exp_cx(n, 1);
for (int i = 1; i < n; i++) exp_cx[i] = exp_cx[i - 1] * c * T(i).inv();
ret = ret * exp_cx;
ret.resize(n);
std::reverse(ret.begin(), ret.end());
for (int i = 0; i < n; i++) ret[i] *= T(i).facinv();
return ret;
}
T coeff(int i) const {
if ((int)this->size() <= i or i < 0) return T(0);
return (*this)[i];
}
T eval(T x) const {
T ret = 0, w = 1;
for (auto &v : *this) ret += w * v, w *= x;
return ret;
}
};
// multipoint polynomial evaluation
// input: xs = [x_0, ..., x_{N - 1}]: points to evaluate
// f = \sum_i^M f_i x^i
// Complexity: O(N (lgN)^2) building, O(N (lgN)^2 + M lg M) evaluation
template <typename Tfield> struct MultipointEvaluation {
int nx;
using polynomial = FormalPowerSeries<Tfield>;
std::vector<polynomial> segtree;
MultipointEvaluation(const std::vector<Tfield> &xs) : nx(xs.size()) {
segtree.resize(nx * 2 - 1);
for (int i = 0; i < nx; i++) { segtree[nx - 1 + i] = {-xs[i], 1}; }
for (int i = nx - 2; i >= 0; i--) { segtree[i] = segtree[2 * i + 1] * segtree[2 * i + 2]; }
}
std::vector<Tfield> ret;
void _eval_rec(polynomial f, int now) {
f %= segtree[now];
f.shrink();
if (now - (nx - 1) >= 0) {
ret[now - (nx - 1)] = f.coeff(0);
return;
}
_eval_rec(f, 2 * now + 1);
_eval_rec(f, 2 * now + 2);
}
std::vector<Tfield> evaluate_polynomial(const polynomial &f) {
ret.resize(nx);
_eval_rec(f, 0);
return ret;
}
std::vector<Tfield> evaluate_polynomial(const std::vector<Tfield> &f) {
return evaluate_polynomial(polynomial(f.begin(), f.end()));
}
std::vector<Tfield> _interpolate_coeffs;
polynomial _rec_interpolation(int now, const std::vector<Tfield> &ys) const {
int i = now - (nx - 1);
if (i >= 0) return {ys[i]};
auto retl = _rec_interpolation(2 * now + 1, ys);
auto retr = _rec_interpolation(2 * now + 2, ys);
return retl * segtree[2 * now + 2] + retr * segtree[2 * now + 1];
}
std::vector<Tfield> polynomial_interpolation(std::vector<Tfield> ys) {
assert(nx == int(ys.size()));
if (_interpolate_coeffs.empty()) {
_interpolate_coeffs = evaluate_polynomial(segtree[0].differential());
for (auto &x : _interpolate_coeffs) x = x.inv();
}
for (int i = 0; i < nx; i++) ys[i] *= _interpolate_coeffs[i];
return _rec_interpolation(0, ys);
}
};
int main() {
int N;
cin >> N;
vector<mint> A(N);
cin >> A;
for (int i = 0; i < N; ++i) A.at(i) += i;
mint num = 1, den = 1;
for (int diff = 1; diff < N; ++diff) den *= mint(diff).pow(N - diff);
REP(i, N) FOR(j, i + 1, N) num *= A.at(j) - A.at(i);
auto rec = [&](auto &&self, int l, int r) -> vector<mint> {
if (l + 1 == r) return {-A.at(l), 1};
return nttconv(self(self, l, (l + r) / 2), self(self, (l + r) / 2, r));
};
auto f = rec(rec, 0, N);
for (int i = 1; i <= N; ++i) f.at(i) *= i;
f.erase(f.begin());
MultipointEvaluation<mint> me(A);
auto ret = me.evaluate_polynomial(f);
mint ans = mint(-1).pow(lint(N) * (N - 1) / 2);
for (auto v : ret) ans *= v;
cout << ans / (den * den) << '\n';
}