結果
| 問題 | No.1510 Simple Integral |
| ユーザー |
 noimi
|
| 提出日時 | 2021-05-14 23:46:53 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 133 ms / 2,000 ms |
| コード長 | 29,729 bytes |
| コンパイル時間 | 4,329 ms |
| コンパイル使用メモリ | 251,260 KB |
| 最終ジャッジ日時 | 2025-01-21 12:33:10 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 43 |
ソースコード
#pragma region Macros
// #pragma GCC target("avx2")
#pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define rep2(i, a, b) for(ll i = a; i <= b; ++i)
#define rep(i, n) for(ll i = 0; i < n; ++i)
#define rep3(i, a, b) for(ll i = a; i >= b; --i)
#define pii pair<int, int>
#define pll pair<ll, ll>
#define pb push_back
#define eb emplace_back
#define vi vector<int>
#define vll vector<ll>
#define vpi vector<pii>
#define vpll vector<pll>
#define overload2(_1, _2, name, ...) name
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
IN(name)
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
IN(name)
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
#define mt make_tuple
#define fi first
#define se second
#define all(c) begin(c), end(c)
#define SUM(v) accumulate(all(v), 0LL)
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
using namespace std;
constexpr pii dx4[4] = {pii{1, 0}, pii{0, 1}, pii{-1, 0}, pii{0, -1}};
constexpr pii dx8[8] = {{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
const string yesno[2] = {"no", "yes"};
void YES(bool t = 1) { cout << YESNO[t] << endl; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { cout << YesNo[t] << endl; }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { cout << yesno[t] << endl; }
void no(bool t = 1) { yes(!t); }
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
#define si(c) (int)(c).size()
#define INT(...) \
int __VA_ARGS__; \
IN(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
IN(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
IN(__VA_ARGS__)
#define CHR(...) \
char __VA_ARGS__; \
IN(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
IN(__VA_ARGS__)
int scan() { return getchar(); }
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T, class S> void scan(pair<T, S> &p) { scan(p.first), scan(p.second); }
template <class T> void scan(vector<T> &);
template <class T> void scan(vector<T> &a) {
for(auto &i : a) scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail> void IN(Head &head, Tail &...tail) {
scan(head);
IN(tail...);
}
template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); }
template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); }
vi iota(int n) {
vi a(n);
iota(all(a), 0);
return a;
}
template <typename T> vi iota(vector<T> &a, bool greater = false) {
vi res(a.size());
iota(all(res), 0);
sort(all(res), [&](int i, int j) {
if(greater) return a[i] > a[j];
return a[i] < a[j];
});
return res;
}
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
template <class T> T ceil(T x, T y) {
assert(y >= 1);
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
assert(y >= 1);
return (x > 0 ? x / y : (x + y - 1) / y);
}
template <class T> T POW(T x, int n) {
T res = 1;
for(; n; n >>= 1, x *= x)
if(n & 1) res *= x;
return res;
}
vector<pll> factor(ll x) {
vector<pll> ans;
for(ll i = 2; i * i <= x; i++)
if(x % i == 0) {
ans.push_back({i, 1});
while((x /= i) % i == 0) ans.back().second++;
}
if(x != 1) ans.push_back({x, 1});
return ans;
}
template <class T> vector<T> divisor(T x) {
vector<T> ans;
for(T i = 1; i * i <= x; i++)
if(x % i == 0) {
ans.pb(i);
if(i * i != x) ans.pb(x / i);
}
return ans;
}
template <typename T> void zip(vector<T> &x) {
vector<T> y = x;
sort(all(y));
for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }
}
template <class S> void fold_in(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void fold_in(vector<S> &v, Head &&a, Tail &&...tail) {
for(auto e : a) v.emplace_back(e);
fold_in(v, tail...);
}
template <class S> void renumber(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void renumber(vector<S> &v, Head &&a, Tail &&...tail) {
for(auto &&e : a) e = lb(v, e);
renumber(v, tail...);
}
template <class S, class... Args> vector<S> zip(vector<S> &head, Args &&...args) {
vector<S> v;
fold_in(v, head, args...);
sort(all(v)), v.erase(unique(all(v)), v.end());
renumber(v, head, args...);
return v;
}
// bit 演算系
ll pow2(int i) { return 1LL << i; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int lowbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }
// int allbit(int n) { return (1 << n) - 1; }
ll allbit(ll n) { return (1LL << n) - 1; }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
int in() {
int x;
cin >> x;
return x;
}
ll lin() {
unsigned long long x;
cin >> x;
return x;
}
template <class T> pair<T, T> operator-(const pair<T, T> &x, const pair<T, T> &y) { return pair<T, T>(x.fi - y.fi, x.se - y.se); }
template <class T> pair<T, T> operator+(const pair<T, T> &x, const pair<T, T> &y) { return pair<T, T>(x.fi + y.fi, x.se + y.se); }
template <class T> pair<T, T> operator&(const pair<T, T> &l, const pair<T, T> &r) { return pair<T, T>(max(l.fi, r.fi), min(l.se, r.se)); }
// template <class T> pair<T, T> &operator+=(pair<T, T> x, const pair<T, T> &y) {
// x = x + y;
// return &x;
// }
// template <class T> pair<T, T> &operator-=(pair<T, T> x, const pair<T, T> &y) {
// x = x - y;
// return &x;
// }
template <class T> ll operator*(const pair<T, T> &x, const pair<T, T> &y) { return (ll)x.fi * y.fi + (ll)x.se * y.se; }
template <typename T> struct edge {
int from, to;
T cost;
int id;
edge(int to, T cost) : from(-1), to(to), cost(cost) {}
edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {}
constexpr bool operator<(const edge<T> &rhs) const noexcept { return cost < rhs.cost; }
edge &operator=(const int &x) {
to = x;
return *this;
}
operator int() const { return to; }
};
template <typename T> using Edges = vector<edge<T>>;
using Tree = vector<vector<int>>;
using Graph = vector<vector<int>>;
template <class T> using Wgraph = vector<vector<edge<T>>>;
Graph getG(int n, int m = -1, bool directed = false, int margin = 1) {
Tree res(n);
if(m == -1) m = n - 1;
while(m--) {
int a, b;
cin >> a >> b;
a -= margin, b -= margin;
res[a].emplace_back(b);
if(!directed) res[b].emplace_back(a);
}
return move(res);
}
template <class T> Wgraph<T> getWg(int n, int m = -1, bool directed = false, int margin = 1) {
Wgraph<T> res(n);
if(m == -1) m = n - 1;
while(m--) {
int a, b;
T c;
cin >> a >> b >> c;
a -= margin, b -= margin;
res[a].emplace_back(b, c);
if(!directed) res[b].emplace_back(a, c);
}
return move(res);
}
void add(Graph &G, int x, int y) { G[x].eb(y), G[y].eb(x); }
template <class S> void add(Wgraph<S> &G, int x, int y, S c) { G[x].eb(y, c), G[y].eb(x, c); }
#define i128 __int128_t
#define ull unsigned long long int
#define TEST \
INT(testcases); \
while(testcases--)
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
for(auto it = begin(v); it != end(v); ++it) {
if(it == begin(v))
os << *it;
else
os << " " << *it;
}
return os;
}
template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {
os << p.first << " " << p.second;
return os;
}
template <class S, class T> string to_string(pair<S, T> p) { return "(" + to_string(p.first) + "," + to_string(p.second) + ")"; }
template <class A> string to_string(A v) {
if(v.empty()) return "{}";
string ret = "{";
for(auto &x : v) ret += to_string(x) + ",";
ret.back() = '}';
return ret;
}
string to_string(string s) { return "\"" + s + "\""; }
string to_string(char c) { return string(1, c); }
#ifdef _LOCAL
void dump() { cerr << endl; }
template <class Head, class... Tail> void dump(Head head, Tail... tail) {
cerr << to_string(head) << " ";
dump(tail...);
}
#define endl '\n'
#undef endl
#define debug(x) \
cout << #x << ": "; \
dump(x)
#else
void dump() {}
template <class Head, class... Tail> void dump(Head head, Tail... tail) {}
#define debug(x)
#endif
template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
struct Setup_io {
Setup_io() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
cout << fixed << setprecision(15);
}
} setup_io;
#define drop(s) cout << #s << endl, exit(0)
template <int N> struct ndFORarray {
std::array<int, N> v;
ndFORarray(std::array<int, N> v_) : v(v_) {}
struct ndFORitr {
const std::array<int, N> &v;
std::array<int, N> tmp;
bool is_end;
ndFORitr(const std::array<int, N> &v_) : v(v_), tmp(), is_end(false) {}
bool operator!=(const ndFORitr &) const { return !is_end; }
void operator++() {
int pos = N - 1;
while(pos != -1) {
tmp[pos] += 1;
if(tmp[pos] == v[pos]) {
tmp[pos] = 0;
pos -= 1;
} else {
break;
}
}
if(pos == -1) { is_end = true; }
}
const std::array<int, N> &operator*() const { return tmp; }
};
ndFORitr begin() const { return ndFORitr(v); }
ndFORitr end() const { return ndFORitr(v); }
};
struct ndFORvector {
std::vector<int> v;
ndFORvector(std::vector<int> v_) : v(v_) {}
struct ndFORitr {
const std::vector<int> &v;
std::vector<int> tmp;
bool is_end;
ndFORitr(const std::vector<int> &v_) : v(v_), tmp(v.size(), 0), is_end(false) {}
bool operator!=(const ndFORitr &) const { return !is_end; }
void operator++() {
int pos = v.size() - 1;
while(pos != -1) {
tmp[pos] += 1;
if(tmp[pos] == v[pos]) {
tmp[pos] = 0;
pos -= 1;
} else {
break;
}
}
if(pos == -1) { is_end = true; }
}
const std::vector<int> &operator*() const { return tmp; }
};
ndFORitr begin() const { return ndFORitr(v); }
ndFORitr end() const { return ndFORitr(v); }
};
auto ndFOR(std::vector<int> v) { return ndFORvector(v); }
template <class... Ts> auto ndFOR(Ts... v) { return ndFORarray<std::tuple_size<std::tuple<Ts...>>::value>({v...}); }
template <class F> struct REC {
F f;
REC(F &&f_) : f(std::forward<F>(f_)) {}
template <class... Args> auto operator()(Args &&...args) const { return f(*this, std::forward<Args>(args)...); }
};
#pragma endregion
namespace modular {
constexpr ll MOD = 998244353;
const int MAXN = 11000000;
template <ll Modulus> class modint;
using mint = modint<MOD>;
using vmint = vector<mint>;
vector<mint> Inv;
mint inv(int x);
template <ll Modulus> class modint {
public:
static constexpr int mod() { return Modulus; }
ll a;
constexpr modint(const ll x = 0) noexcept : a(((x % Modulus) + Modulus) % Modulus) {}
constexpr ll &val() noexcept { return a; }
constexpr const ll &val() const noexcept { return a; }
constexpr modint operator-() const noexcept { return modint() - *this; }
constexpr modint operator+() const noexcept { return *this; }
constexpr modint &operator++() noexcept {
if(++a == MOD) a = 0;
return *this;
}
constexpr modint &operator--() noexcept {
if(!a) a = MOD;
a--;
return *this;
}
constexpr modint operator++(int) {
modint res = *this;
++*this;
return res;
}
constexpr modint operator--(int) {
mint res = *this;
--*this;
return res;
}
constexpr modint &operator+=(const modint rhs) noexcept {
a += rhs.a;
if(a >= Modulus) { a -= Modulus; }
return *this;
}
constexpr modint &operator-=(const modint rhs) noexcept {
if(a < rhs.a) { a += Modulus; }
a -= rhs.a;
return *this;
}
constexpr modint &operator*=(const modint rhs) noexcept {
a = a * rhs.a % Modulus;
return *this;
}
constexpr modint &operator/=(const modint rhs) noexcept {
a = a * (modular::inv(rhs.a)).a % Modulus;
return *this;
}
constexpr modint pow(long long n) const noexcept {
if(n < 0) {
n %= Modulus - 1;
n = (Modulus - 1) + n;
}
modint x = *this, r = 1;
while(n) {
if(n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr modint inv() const noexcept { return pow(Modulus - 2); }
constexpr friend modint operator+(const modint &lhs, const modint &rhs) { return modint(lhs) += modint(rhs); }
constexpr friend modint operator-(const modint &lhs, const modint &rhs) { return modint(lhs) -= modint(rhs); }
constexpr friend modint operator*(const modint &lhs, const modint &rhs) { return modint(lhs) *= modint(rhs); }
constexpr friend modint operator/(const modint &lhs, const modint &rhs) { return modint(lhs) /= modint(rhs); }
constexpr friend bool operator==(const modint &lhs, const modint &rhs) { return lhs.a == rhs.a; }
constexpr friend bool operator!=(const modint &lhs, const modint &rhs) { return lhs.a != rhs.a; }
// constexpr friend modint operator^=(const modint &lhs, const modint &rhs) { return modint(lhs) ^= modint(rhs); }
};
vmint Fact{1, 1}, Ifact{1, 1};
mint inv(int n) {
if(n > MAXN) return (mint(n)).pow(MOD - 2);
if(Inv.empty()) Inv.emplace_back(0), Inv.emplace_back(1);
if(Inv.size() > n)
return Inv[n];
else {
for(int i = Inv.size(); i <= n; ++i) {
auto [y, x] = div(int(MOD), i);
Inv.emplace_back(Inv[x] * (-y));
}
return Inv[n];
}
}
mint fact(int n) {
if(Fact.size() > n)
return Fact[n];
else
for(int i = Fact.size(); i <= n; ++i) Fact.emplace_back(Fact[i - 1] * i);
return Fact[n];
}
mint ifact(int n) {
if(Ifact.size() > n)
return Ifact[n];
else
for(int i = Ifact.size(); i <= n; ++i) Ifact.emplace_back(Ifact[i - 1] * inv(i));
return Ifact[n];
}
mint modpow(ll a, ll n) { return mint(a).pow(n); }
mint inv(mint a) { return inv(a.a); }
mint ifact(mint a) { return ifact(a.a); }
mint fact(mint a) { return fact(a.a); }
mint modpow(mint a, ll n) { return modpow(a.a, n); }
mint C(int a, int b) {
if(a < 0 || b < 0) return 0;
if(a < b) return 0;
if(a > MAXN) {
mint res = 1;
rep(i, b) res *= a - i, res /= i + 1;
return res;
}
return fact(a) * ifact(b) * ifact(a - b);
}
mint P(int a, int b) {
if(a < 0 || b < 0) return 0;
if(a < b) return 0;
if(a > MAXN) {
mint res = 1;
rep(i, b) res *= a - i;
return res;
}
return fact(a) * ifact(a - b);
}
ostream &operator<<(ostream &os, mint a) {
os << a.a;
return os;
}
istream &operator>>(istream &is, mint &a) {
ll x;
is >> x;
a = x;
return is;
}
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace convolution {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while((1U << x) < (unsigned int)(n)) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if(x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if(_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if(m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while(n) {
if(n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if(n <= 1) return false;
if(n == 2 || n == 7 || n == 61) return true;
if(n % 2 == 0) return false;
long long d = n - 1;
while(d % 2 == 0) d /= 2;
for(long long a : {2, 7, 61}) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while(t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if(y != n - 1 && t % 2 == 0) { return false; }
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if(a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while(t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if(m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if(m == 2) return 1;
if(m == 167772161) return 3;
if(m == 469762049) return 3;
if(m == 754974721) return 11;
if(m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while(x % 2 == 0) x /= 2;
for(int i = 3; (long long)(i)*i <= x; i += 2) {
if(x % i == 0) {
divs[cnt++] = i;
while(x % i == 0) { x /= i; }
}
}
if(x > 1) { divs[cnt++] = x; }
for(int g = 2;; g++) {
bool ok = true;
for(int i = 0; i < cnt; i++) {
if(pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if(ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
void butterfly(std::vector<mint> &a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if(first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for(int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for(int i = 0; i < cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for(int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for(int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for(int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
void butterfly_inv(std::vector<mint> &a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if(first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for(int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for(int i = 0; i < cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for(int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for(int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for(int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] = (unsigned long long)(mint::mod() + l.val() - r.val()) * inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
mint z = mint(n).inv();
for(int i = 0; i < n; i++) a[i] *= z;
}
} // namespace internal
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if(!n || !m) return {};
if(std::min(n, m) <= 60) {
if(n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) { ans[i + j] += a[i] * b[j]; }
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for(int i = 0; i < z; i++) { a[i] *= b[i]; }
internal::butterfly_inv(a);
a.resize(n + m - 1);
// mint iz = mint(z).inv();
// for(int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
} // namespace convolution
using Poly = vmint;
Poly low(const Poly &f, int s) { return Poly(f.begin(), f.begin() + min<int>(max(s, 1), f.size())); }
Poly operator-(Poly f) {
for(auto &&e : f) e = -e;
return f;
}
Poly &operator+=(Poly &l, const Poly &r) {
l.resize(max(l.size(), r.size()));
rep(i, r.size()) l[i] += r[i];
return l;
}
Poly operator+(Poly l, const Poly &r) { return l += r; }
Poly &operator-=(Poly &l, const Poly &r) {
l.resize(max(l.size(), r.size()));
rep(i, r.size()) l[i] -= r[i];
return l;
}
Poly operator-(Poly l, const Poly &r) { return l -= r; }
Poly &operator<<=(Poly &f, size_t n) { return f.insert(f.begin(), n, 0), f; }
Poly operator<<(Poly f, size_t n) { return f <<= n; }
Poly &operator>>=(Poly &f, size_t n) { return f.erase(f.begin(), f.begin() + min(f.size(), n)), f; }
Poly operator>>(Poly f, size_t n) { return f >>= n; }
Poly operator*(const Poly &l, const Poly &r) { return convolution::convolution(l, r); }
Poly &operator*=(Poly &l, const Poly &r) { return l = l * r; }
Poly inv(const Poly &f, int s = -1) {
if(s == -1) s = f.size();
Poly r(s);
r[0] = mint(1) / f[0];
for(int n = 1; n < s; n *= 2) {
auto F = low(f, 2 * n);
F.resize(2 * n);
convolution::internal::butterfly(F);
auto g = low(r, 2 * n);
g.resize(2 * n);
convolution::internal::butterfly(g);
rep(i, 2 * n) F[i] *= g[i];
convolution::internal::butterfly_inv(F);
rep(i, n) F[i] = 0;
convolution::internal::butterfly(F);
rep(i, 2 * n) F[i] *= g[i];
convolution::internal::butterfly_inv(F);
rep2(i, n, min(2 * n, s) - 1) r[i] -= F[i];
}
return r;
}
Poly integ(const Poly &f) {
Poly res(f.size() + 1);
for(int i = 1; i < (int)res.size(); ++i) res[i] = f[i - 1] / i;
return res;
}
Poly deriv(const Poly &f) {
if(f.size() == 0) return Poly();
Poly res(f.size() - 1);
rep(i, res.size()) res[i] = f[i + 1] * (i + 1);
return res;
}
Poly log(const Poly &f) {
Poly g = integ(inv(f) * deriv(f));
return Poly{g.begin(), g.begin() + f.size()};
}
Poly exp(const Poly &f) {
Poly g{1};
while(g.size() < f.size()) {
Poly x(f.begin(), f.begin() + min(f.size(), g.size() * 2));
x[0] += 1;
g.resize(2 * g.size());
x -= log(g);
x *= {g.begin(), g.begin() + g.size() / 2};
rep2(i, g.size() / 2, min<int>(x.size(), g.size()) - 1) g[i] = x[i];
}
return {g.begin(), g.begin() + f.size()};
}
} // namespace modular
using namespace modular;
int main() {
INT(n);
map<int, int> mp;
rep(i, n) { mp[in()]++; }
mint ans;
for(auto &[e, k] : mp) {
vmint dp(k);
dp[0] = 1;
auto f = [&](int i, int j) {
mint p = (i >= 0 ? inv(i) : -inv(-i));
vmint nxt(dp.size());
rep(x, si(dp)) {
mint now = p.pow(j);
rep(y, si(dp) - x) {
nxt[x + y] += dp[x] * now * C(si(dp) - 1 - x, y);
now *= p;
now *= j + y;
}
}
swap(dp, nxt);
};
for(auto [x, y] : mp) {
f(e + x, y);
if(e != x) { f(e - x, y); }
}
dp.back() /= fact(k - 1);
if((n + k) & 1)
ans -= dp.back() * 2;
else
ans += dp.back() * 2;
}
cout << ans << endl;
// cout << mint(3) / 8 << endl;
}