結果
| 問題 |
No.287 場合の数
|
| コンテスト | |
| ユーザー |
 Ajayreddy17
|
| 提出日時 | 2023-07-06 19:57:10 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 5,000 ms |
| コード長 | 27,433 bytes |
| コンパイル時間 | 5,416 ms |
| コンパイル使用メモリ | 413,004 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-07-20 15:23:38 |
| 合計ジャッジ時間 | 6,478 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 22 |
ソースコード
#include <x86intrin.h>
#include <bits/stdc++.h>
using namespace std;
using str = string;
using ll = long long;
using ld = long double;
using u64 = unsigned long long;
template <class T>
using pr = pair<T, T>;
template <class T>
using vt = vector<T>;
template <class T>
using vvt = vector<vt<T>>;
#define ar array
#define pb push_back
#define fi first
#define se second
#define all(c) (c).begin(), (c).end()
#define len(x) (int)(x).size()
#define elif else if
#define def function
#define F_OR(i, a, b, s) for (int i=(a); (s)>0?i<(b):i>(b); i+=(s))
#define F_OR1(e) F_OR(i, 0, e, 1)
#define F_OR2(i, e) F_OR(i, 0, e, 1)
#define F_OR3(i, b, e) F_OR(i, b, e, 1)
#define F_OR4(i, b, e, s) F_OR(i, b, e, s)
#define GET5(a, b, c, d, e, ...) e
#define F_ORC(...) GET5(__VA_ARGS__, F_OR4, F_OR3, F_OR2, F_OR1)
#define rep(...) F_ORC(__VA_ARGS__)(__VA_ARGS__)
#define each(x, a) for (auto& x: a)
template <class T>
constexpr T inf = 0;
template <>
constexpr int inf<int> = 1'000'000'005;
template <>
constexpr long long inf<long long> = (long long)(inf<int>) * inf<int> * 2;
template <>
constexpr unsigned int inf<unsigned int> = inf<int>;
template <>
constexpr unsigned long long inf<unsigned long long> = inf<long long>;
template <>
constexpr __int128 inf<__int128> = __int128(inf<long long>) * inf<long long>;
template <>
constexpr double inf<double> = inf<long long>;
template <>
constexpr long double inf<long double> = inf<long long>;
template <class T, class S>
inline bool ctmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); }
template <class T, class S>
inline bool ctmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); }
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; }
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; }
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; }
template <typename T>
istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; }
void read() {}
template <typename T, class... U>
void read(T &t, U &...u) { cin >> t; read(u...); }
void print() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void print(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; print(u...); }
void write() { cout << " "; }
template <typename T, class... U, char sep = ' '>
void write(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; write(u...); }
#define Int(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define Ll(...) \
long long __VA_ARGS__; \
read(__VA_ARGS__)
#define Str(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define Vt(type, name, size) \
vector<type> name(size); \
read(name)
#define Die(...) \
do { \
print(__VA_ARGS__); \
return 0; \
} while (0)
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long Pw(int n) { return 1LL << n; }
constexpr long long Msk(int n) { return (1LL << n) - 1; }
struct has_mod_impl {
template <class T>
static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (len(dat) <= n) {
int k = len(dat);
int q = (mod + k - 1) / k;
dat.eb(dat[k * q - mod] * mint(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n);
if (n >= mod) return 0;
static vector<mint> dat = {1, 1};
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint(len(dat)));
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static vector<mint> dat = {1, 1};
if (n < 0) return mint(0);
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
static vector<vector<mint>> C;
static int H = 0, W = 0;
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
for(int i = 0; i < H; i++) {
C[i].resize(k + 1);
for(int j = W; j < k + 1; j++) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
for(int i = H; i < n + 1; i++) {
C[i].resize(W);
for(int j = 0; j < W; j++) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(long long n, long long k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if (dense) return C_dense<mint>(n, k);
if (!large) return multinomial<mint>(n, k, n - k);
k = min(k, n - k);
mint x(1);
for(int i = 0; i < k; i++) x *= mint(n - i);
return x * fact_inv<mint>(k);
}
template <typename mint, bool large = false>
mint C_inv(long long n, long long k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d] (1-x) ^ {-n} の計算
template <typename mint, bool large = false, bool dense = false>
mint C_negative(long long n, long long d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
return C<mint, large, dense>(n + d - 1, d);
}
template <int mod>
struct modint {
static_assert(mod < (1 << 30));
int val;
constexpr modint(const long long val = 0) noexcept
: val(val >= 0 ? val % mod : (mod - (-val) % mod) % mod) {}
bool operator<(const modint &other) const {
return val < other.val;
} // To use std::map
modint &operator+=(const modint &p) {
if ((val += p.val) >= mod) val -= mod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += mod - p.val) >= mod) val -= mod;
return *this;
}
modint &operator*=(const modint &p) {
val = (int)(1LL * val * p.val % mod);
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint(-val); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(long long n) const {
assert(n >= 0);
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
void write() { write(val); }
void read() {
read(val);
val = (val >= 0 ? val % mod : (mod - (-val) % mod) % mod);
}
static constexpr int get_mod() { return mod; }
// (n, r), r は 1 の 2^n 乗根
static constexpr pair<int, int> ntt_info() {
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 880803841) return {23, 211};
if (mod == 998244353) return {23, 31};
if (mod == 1045430273) return {20, 363};
if (mod == 1051721729) return {20, 330};
if (mod == 1053818881) return {20, 2789};
return {-1, -1};
}
static constexpr bool can_ntt() { return ntt_info().first != -1; }
};
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
// long でも大丈夫
// (val * x - 1) が mod の倍数になるようにする
// 特に mod=0 なら x=0 が満たす
long long mod_inv(long long val, long long mod) {
if (mod == 0) return 0;
mod = abs(mod);
val %= mod;
if (val < 0) val += mod;
long long a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
if (u < 0) u += mod;
return u;
}
template <class T>
vector<T> convolution_naive(const vector<T>& a, const vector<T>& b) {
int n = int(a.size()), m = int(b.size());
vector<T> ans(n + m - 1);
if (n < m) {
for(int j = 0; j < m; j++) for(int i = 0; i < n; i++) ans[i + j] += a[i] * b[j];
} else {
for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];
}
return ans;
}
template <class mint>
void ntt(vector<mint>& a, bool inverse) {
assert(mint::can_ntt());
const int rank2 = mint::ntt_info().first;
const int mod = mint::get_mod();
static array<mint, 30> root, iroot;
static array<mint, 30> rate2, irate2;
static array<mint, 30> rate3, irate3;
static bool prepared = 0;
if (!prepared) {
prepared = 1;
root[rank2] = mint::ntt_info().second;
iroot[rank2] = mint(1) / root[rank2];
for(int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
int n = int(a.size());
int h = (n == 0 ? -1 : 31 - __builtin_clz(n));
assert(n == 1 << h);
if (!inverse) {
int len = 0;
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
for(int s = 0; s < 1 << len; s++) {
int offset = s << (h - len);
for(int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
rot *= rate2[((~s & -~s) == 0 ? -1 : 31 - __builtin_clz(~s & -~s))];
}
len++;
} else {
int p = 1 << (h - len - 2);
mint rot = 1, imag = root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
unsigned long long mod2 = (unsigned long long)(mod) * mod;
unsigned long long a0 = a[i + offset].val;
unsigned long long a1 = (unsigned long long)(a[i + offset + p].val) * rot.val;
unsigned long long a2 = (unsigned long long)(a[i + offset + 2 * p].val) * rot2.val;
unsigned long long a3 = (unsigned long long)(a[i + offset + 3 * p].val) * rot3.val;
unsigned long long a1na3imag = (a1 + mod2 - a3) % mod * imag.val;
unsigned long long na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
rot *= rate3[((~s & -~s) == 0 ? -1 : 31 - __builtin_clz(~s & -~s))];
}
len += 2;
}
}
} else {
mint coef = mint(1) / mint((int) a.size());
for(int i = 0; i < (int) a.size(); i++) a[i] *= coef;
int len = h;
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for(int s = 0; s < 1 << (len - 1); s++) {
int offset = s << (h - len + 1);
for(int i = 0; i < p; i++) {
unsigned long long l = a[i + offset].val;
unsigned long long r = a[i + offset + p].val;
a[i + offset] = l + r;
a[i + offset + p] = (mod + l - r) * irot.val;
}
irot *= irate2[((~s & -~s) == 0 ? -1 : 31 - __builtin_clz(~s & -~s))];
}
len--;
} else {
int p = 1 << (h - len);
mint irot = 1, iimag = iroot[2];
for(int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
unsigned long long a0 = a[i + offset + 0 * p].val;
unsigned long long a1 = a[i + offset + 1 * p].val;
unsigned long long a2 = a[i + offset + 2 * p].val;
unsigned long long a3 = a[i + offset + 3 * p].val;
unsigned long long x = (mod + a2 - a3) * iimag.val % mod;
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] = (a0 + mod - a1 + x) * irot.val;
a[i + offset + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * irot2.val;
a[i + offset + 3 * p] = (a0 + 2 * mod - a1 - x) * irot3.val;
}
irot *= irate3[((~s & -~s) == 0 ? -1 : 31 - __builtin_clz(~s & -~s))];
}
len -= 2;
}
}
}
}
namespace CFFT {
using real = double;
struct C {
real x, y;
C() : x(0), y(0) {}
C(real x, real y) : x(x), y(y) {}
inline C operator+(const C& c) const { return C(x + c.x, y + c.y); }
inline C operator-(const C& c) const { return C(x - c.x, y - c.y); }
inline C operator*(const C& c) const {
return C(x * c.x - y * c.y, x * c.y + y * c.x);
}
inline C conj() const { return C(x, -y); }
};
const real PI = acosl(-1);
int base = 1;
vector<C> rts = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
void ensure_base(int nbase) {
if (nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
while (base < nbase) {
real angle = PI * 2.0 / (1 << (base + 1));
for (int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
real angle_i = angle * (2 * i + 1 - (1 << base));
rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
}
++base;
}
}
void fft(vector<C>& a, int n) {
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); }
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
C z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
} // namespace CFFT
template <class mint>
vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {
if (a.empty() || b.empty()) return {};
int n = int(a.size()), m = int(b.size());
int sz = 1;
while (sz < n + m - 1) sz *= 2;
// sz = 2^k のときの高速化。分割統治的なやつで損しまくるので。
if ((n + m - 3) <= sz / 2) {
auto a_last = a.back(), b_last = b.back();
a.pop_back(), b.pop_back();
auto c = convolution(a, b);
c.resize(n + m - 1);
c[n + m - 2] = a_last * b_last;
for(int i = 0; i < (int) a.size(); i++) c[i + (int) b.size()] += a[i] * b_last;
for(int i = 0; i < (int) b.size(); i++) c[i + (int) a.size()] += b[i] * a_last;
return c;
}
a.resize(sz), b.resize(sz);
bool same = a == b;
ntt(a, 0);
if (same) {
b = a;
} else {
ntt(b, 0);
}
for(int i = 0; i < sz; i++) a[i] *= b[i];
ntt(a, 1);
a.resize(n + m - 1);
return a;
}
template <typename mint>
vector<mint> convolution_garner(const vector<mint>& a, const vector<mint>& b) {
int n = (int) a.size(), m = (int) b.size();
if (!n || !m) return {};
static const long long nttprimes[] = {754974721, 167772161, 469762049};
using mint0 = modint<754974721>;
using mint1 = modint<167772161>;
using mint2 = modint<469762049>;
vector<mint0> a0(n), b0(m);
vector<mint1> a1(n), b1(m);
vector<mint2> a2(n), b2(m);
for(int i = 0; i < n; i++) a0[i] = a[i].val, a1[i] = a[i].val, a2[i] = a[i].val;
for(int i = 0; i < m; i++) b0[i] = b[i].val, b1[i] = b[i].val, b2[i] = b[i].val;
auto c0 = convolution_ntt<mint0>(a0, b0);
auto c1 = convolution_ntt<mint1>(a1, b1);
auto c2 = convolution_ntt<mint2>(a2, b2);
static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
static const long long m0_inv_m1 = mint1(nttprimes[0]).inverse().val;
static const long long m01_inv_m2 = mint2(m01).inverse().val;
const int mod = mint::get_mod();
auto garner = [&](mint0 x0, mint1 x1, mint2 x2) -> mint {
int r0 = x0.val, r1 = x1.val, r2 = x2.val;
int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * mint2(m01_inv_m2);
return mint(r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val);
};
vector<mint> c((int) c0.size());
for(int i = 0; i < (int) c.size(); i++) c[i] = garner(c0[i], c1[i], c2[i]);
return c;
}
template <typename R>
vector<double> convolution_fft(const vector<R>& a, const vector<R>& b) {
using C = CFFT::C;
int need = (int)a.size() + (int)b.size() - 1;
int nbase = 1;
while ((1 << nbase) < need) nbase++;
CFFT::ensure_base(nbase);
int sz = 1 << nbase;
vector<C> fa(sz);
for (int i = 0; i < sz; i++) {
int x = (i < (int)a.size() ? a[i] : 0);
int y = (i < (int)b.size() ? b[i] : 0);
fa[i] = C(x, y);
}
CFFT::fft(fa, sz);
C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
for (int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
fa[i] = z;
}
for (int i = 0; i < (sz >> 1); i++) {
C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * CFFT::rts[(sz >> 1) + i];
fa[i] = A0 + A1 * s;
}
CFFT::fft(fa, sz >> 1);
vector<double> ret(need);
for (int i = 0; i < need; i++) {
ret[i] = (i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
}
return ret;
}
vector<long long> convolution(const vector<long long>& a, const vector<long long>& b) {
int n = (int) a.size(), m = (int) b.size();
if (!n || !m) return {};
if (min(n, m) <= 60) return convolution_naive(a, b);
long long abs_sum_a = 0, abs_sum_b = 0;
long long LIM = 1e15;
for(int i = 0; i < n; i++) abs_sum_a = min(LIM, abs_sum_a + abs(a[i]));
for(int i = 0; i < m; i++) abs_sum_b = min(LIM, abs_sum_b + abs(b[i]));
if (__int128(abs_sum_a) * abs_sum_b < 1e15) {
vector<double> c = convolution_fft<long long>(a, b);
vector<long long> res((int) c.size());
for(int i = 0; i < (int) c.size(); i++) res[i] = (long long)(floor(c[i] + .5));
return res;
}
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static const unsigned long long i1 = mod_inv(MOD2 * MOD3, MOD1);
static const unsigned long long i2 = mod_inv(MOD1 * MOD3, MOD2);
static const unsigned long long i3 = mod_inv(MOD1 * MOD2, MOD3);
using mint1 = modint<MOD1>;
using mint2 = modint<MOD2>;
using mint3 = modint<MOD3>;
vector<mint1> a1(n), b1(m);
vector<mint2> a2(n), b2(m);
vector<mint3> a3(n), b3(m);
for(int i = 0; i < n; i++) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i];
for(int i = 0; i < m; i++) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i];
auto c1 = convolution_ntt<mint1>(a1, b1);
auto c2 = convolution_ntt<mint2>(a2, b2);
auto c3 = convolution_ntt<mint3>(a3, b3);
vector<long long> c(n + m - 1);
for(int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i].val * i1) % MOD1 * M2M3;
x += (c2[i].val * i2) % MOD2 * M1M3;
x += (c3[i].val * i3) % MOD3 * M1M2;
long long diff = c1[i].val - ((long long)(x) % (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5]
= {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
template <typename mint>
vector<mint> convolution(const vector<mint>& a, const vector<mint>& b) {
int n = (int) a.size(), m = (int) b.size();
if (!n || !m) return {};
if (mint::can_ntt()) {
if (min(n, m) <= 50) return convolution_naive(a, b);
return convolution_ntt(a, b);
}
if (min(n, m) <= 200) return convolution_naive(a, b);
return convolution_garner(a, b);
}
namespace dbg{
// DEBUG BEGIN
#ifndef ONLINE_JUDGE
template<class L, class R> ostream &operator<<(ostream &out, const pair<L, R> &p){
return out << "{" << p.first << ", " << p.second << "}";
}
template<class Tuple, size_t N> struct _tuple_printer{
static ostream &_print(ostream &out, const Tuple &t){ return _tuple_printer<Tuple, N-1>::_print(out, t) << ", " << get<N-1>(t); }
};
template<class Tuple> struct _tuple_printer<Tuple, 1>{
static ostream &_print(ostream &out, const Tuple& t){ return out << get<0>(t); }
};
template<class... Args> ostream &_print_tuple(ostream &out, const tuple<Args...> &t){
return _tuple_printer<decltype(t), sizeof...(Args)>::_print(out << "{", t) << "}";
}
template<class ...Args> ostream &operator<<(ostream &out, const tuple<Args...> &t){
return _print_tuple(out, t);
}
template<class T> ostream &operator<<(class enable_if<!is_same<T, string>::value, ostream>::type &out, const T &arr){
if(arr.empty()) return out << "{}";
out << "{";
for(auto it = arr.begin(); it != arr.end(); ++ it){
out << *it;
next(it) != arr.end() ? out << ", " : out << "}";
}
return out;
}
ostream &operator<<(ostream &out, const _Bit_reference &bit){
return out << bool(bit);
}
template<class T, class A, class C>
ostream &operator<<(ostream &out, priority_queue<T, A, C> pq){
vector<T> a;
while(!pq.empty()) a.push_back(pq.top()), pq.pop();
return out << a;
}
template<class Head>
void debug_out(Head H){ cerr << H << endl; }
template<class Head, class... Tail>
void debug_out(Head H, Tail... T){ cerr << H << ", ", debug_out(T...); }
void debug2_out(){ }
template<class Head, class... Tail>
void debug2_out(Head H, Tail... T){ cerr << "\n"; for(auto x: H) cerr << x << ",\n"; debug2_out(T...); }
template<class Width, class Head>
void debugbin_out(Width w, Head H){
for(auto rep = w; rep; -- rep, H >>= 1) cerr << (H & 1);
cerr << endl;
}
template<class Width, class Head, class... Tail>
void debugbin_out(Width w, Head H, Tail... T){
for(auto rep = w; rep; -- rep, H >>= 1) cerr << (H & 1);
cerr << ", "; debugbin_out(w, T...);
}
enum CODE{ CCRED = 31, CCGREEN = 32, CCYELLOW = 33, CCBLUE = 34, CCDEFAULT = 39 };
#define debug_endl() cerr << endl
#define debug(...) cerr << "\033[" << (int)CODE(CCRED) << "m[" << #__VA_ARGS__ << "]: \033[" << (int)CODE(CCBLUE) << "m", debug_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
#define debug2(...) cerr << "\033[" << (int)CODE(CCRED) << "m[" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debug2_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
#define debugbin(...) cerr << "\033[" << (int)CODE(CCRED) << "m[" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debugbin_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
#else
#define debug_endl() 42
#define debug(...) 42
#define debug2(...) 42
#define debugbin(...) 42
#endif
// DEBUG END
} using namespace dbg;
signed main(){
cin.tie(0)->sync_with_stdio(0);
cin.exceptions(ios::badbit | ios::failbit);
auto __solve_tc = [&](auto __tc_num)->int {
Ll(n);
vt<ll> poly(n + 1, 1);
rep(3) poly = convolution(poly, poly);
print(poly[6 * n]);
return 0;
};
int __tc_cnt = 1;
for(auto __tc_num = 0; __tc_num < __tc_cnt; ++ __tc_num){
__solve_tc(__tc_num);
}
}