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90 lines
2.3 KiB
C++
90 lines
2.3 KiB
C++
#include <iostream>
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#include <array>
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#include <type_traits>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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const int N = 5005;
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const int mod = 998244353;
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template <int x>
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using number = std::integral_constant<int, x>;
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template <int n>
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struct factorial : number<static_cast<long long>(n) * factorial<n - 1>::value % mod> {};
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template <>
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struct factorial<0> : number<1> {};
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template <int... S>
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constexpr std::array<int, sizeof...(S)> get_factorial_table_impl(std::integer_sequence<int, S...>) {
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return {factorial<S>::value...};
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}
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template <int S>
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constexpr auto get_factorial_table() {
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return get_factorial_table_impl(std::make_integer_sequence<int, S>{});
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}
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template <int n>
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struct inverse : number<static_cast<long long>(mod - (mod / n)) * inverse<mod % n>::value % mod> {};
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template <>
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struct inverse<1> : number<1> {};
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template <>
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struct inverse<0> : number<1> {};
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template <int n>
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struct factorial_inverse : number<static_cast<long long>(factorial_inverse<n - 1>::value) * inverse<n>::value % mod> {};
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template <>
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struct factorial_inverse<1> : number<1> {};
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template <>
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struct factorial_inverse<0> : number<1> {};
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template <int... S>
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constexpr std::array<int, sizeof...(S)> get_factorial_inverse_table_impl(std::integer_sequence<int, S...>) {
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return {factorial_inverse<S>::value...};
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}
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template <int S>
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constexpr auto get_factorial_inverse_table() {
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return get_factorial_inverse_table_impl(std::make_integer_sequence<int, S>{});
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}
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int a, b, c, ab, ac, bc, ans;
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constexpr auto fac = get_factorial_table<N>(),
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fac_inv = get_factorial_inverse_table<N>();
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inline int C(int n, int m) {
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return static_cast<long long>(fac[n]) * fac_inv[m] % mod * fac_inv[n - m] % mod;
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}
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int main() {
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std::ios::sync_with_stdio(false);
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cin.tie(nullptr);
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cin >> a >> b >> c;
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for (int i = 0; i <= std::min(a, b); i++) {
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ab = (ab + static_cast<long long>(C(a, i)) * C(b, i) % mod * fac[i] % mod) % mod;
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}
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for (int i = 0; i <= std::min(a, c); i++) {
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ac = (ac + static_cast<long long>(C(a, i)) * C(c, i) % mod * fac[i] % mod) % mod;
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}
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for (int i = 0; i <= std::min(b, c); i++) {
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bc = (bc + static_cast<long long>(C(b, i)) * C(c, i) % mod * fac[i] % mod) % mod;
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}
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cout << (((static_cast<long long>(ab) * ac) % mod * bc) % mod) % mod << endl;
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return 0;
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}
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