#ifndef CLASS_MODINT_64321 #define CLASS_MODINT_64321 #include #include class modint_64321 { private: static constexpr std::uint64_t mod = std::uint64_t(1) - (std::uint64_t(1) << 32); std::uint64_t n; public: modint_64321() noexcept : n(0) {}; modint_64321(std::uint64_t n_) noexcept : n(n_ < mod ? n_ : n_ - mod) {}; modint_64321(std::uint32_t n_) noexcept : n(n_) {}; modint_64321(std::int64_t n_) noexcept : n(n_ >= 0 ? n_ : std::uint64_t(n_) + mod) {}; modint_64321(std::int32_t n_) noexcept : n(n_ >= 0 ? n_ : std::uint64_t(n_) + mod) {}; static constexpr std::uint64_t get_mod() noexcept { return mod; } std::uint64_t get() const noexcept { return n; } bool operator==(const modint_64321& m) const noexcept { return n == m.n; } bool operator!=(const modint_64321& m) const noexcept { return n != m.n; } modint_64321& operator+=(const modint_64321& m) noexcept { n = (n < mod - m.n ? n + m.n : n + m.n - mod); return *this; } modint_64321& operator-=(const modint_64321& m) noexcept { n = (n >= m.n ? n - m.n : n - m.n + mod); return *this; } #ifdef __SIZEOF_INT128__ modint_64321& operator*=(const modint_64321& m) noexcept { __uint128_t g = __int128_t(n) * m.n; std::uint64_t g0 = g & 4294967295; std::uint64_t g1 = (g >> 32) & 4294967295; std::uint64_t g2 = (g >> 64) & 4294967295; std::uint64_t g3 = (g >> 96); n = ((g1 + g2) << 32) - (g1 + g2 < 4294967296 ? 0 : mod) + g0 - g2 - g3; n = (n < mod ? n : (g1 + g2 != 4294967295 ? n + mod : n - mod)); return *this; } #else modint_64321& operator*=(const modint_64321& m) noexcept { std::uint64_t la = n & 4294967295, lb = (n >> 32); std::uint64_t ra = m.n & 4294967295, rb = (m.n >> 32); std::uint64_t g0 = 0, g1 = 0, g2 = 0, g3 = 0; g0 += la * ra; g1 += (g0 >> 32); g0 &= 4294967295; g1 += la * rb; g2 += (g1 >> 32); g1 &= 4294967295; g1 += lb * ra; g2 += (g1 >> 32); g1 &= 4294967295; g2 += lb * rb; g3 += (g2 >> 32); g2 &= 4294967295; n = ((g1 + g2) << 32) - (g1 + g2 < 4294967296 ? 0 : mod) + g0 - g2 - g3; n = (n < mod ? n : (g1 + g2 != 4294967295 ? n + mod : n - mod)); return *this; } #endif modint_64321 operator+(const modint_64321& m) const noexcept { return modint_64321(*this) += m; } modint_64321 operator-(const modint_64321& m) const noexcept { return modint_64321(*this) -= m; } modint_64321 operator*(const modint_64321& m) const noexcept { return modint_64321(*this) *= m; } modint_64321 inv() const { assert(n != 0); return pow(mod - 2); } modint_64321 pow(std::uint64_t b) const noexcept { modint_64321 ans(1), m(*this); while (b) { if (b & 1) ans *= m; m *= m; b >>= 1; } return ans; } }; #endif // CLASS_MODINT_64321 #ifndef CLASS_POLYNOMIAL_NTT_64321 #define CLASS_POLYNOMIAL_NTT_64321 #include #include class polynomial_ntt_64321 { public: using modulo = modint_64321; private: static constexpr std::uint64_t primroot = 7; static constexpr std::uint64_t mod = modulo::get_mod(); public: static void fourier_transform(std::vector& v) { std::vector base_pw(33); base_pw[32] = modulo(primroot).pow((mod - 1) >> 32); for (int i = 31; i >= 0; --i) { base_pw[i] = base_pw[i + 1] * base_pw[i + 1]; } for (int i = 32; i >= 0; --i) { base_pw[i] *= modulo(-1); } std::size_t s = v.size(); for (std::size_t i = (s >> 1); i >= 1; i >>= 1) { modulo w(1); std::size_t cnt = 0; for (std::size_t j = 0; j < s; j += i * 2) { for (std::size_t k = j; k < j + i; ++k) { modulo va(v[k]), vb(v[k + i] * w); v[k] = va + vb; v[k + i] = va - vb; } w *= base_pw[__builtin_ctz(++cnt) + 2]; } } } static void fourier_transform_inverse(std::vector& v) { std::vector base_pw(33); base_pw[32] = modulo(primroot).pow((mod - 1) - ((mod - 1) >> 32)); for (int i = 31; i >= 0; --i) { base_pw[i] = base_pw[i + 1] * base_pw[i + 1]; } for (int i = 32; i >= 0; --i) { base_pw[i] *= modulo(-1); } std::size_t s = v.size(); for (std::size_t i = 1; i < s; i <<= 1) { modulo w(1); std::size_t cnt = 0; for (std::size_t j = 0; j < s; j += i * 2) { for (std::size_t k = j; k < j + i; ++k) { modulo va(v[k]), vb(v[k + i]); v[k] = va + vb; v[k + i] = (va - vb) * w; } w *= base_pw[__builtin_ctz(++cnt) + 2]; } } modulo powinv = modulo(s).inv(); for (std::size_t i = 0; i < s; ++i) { v[i] *= powinv; } } static std::vector convolve(std::vector v1, std::vector v2) { if (v1.empty() || v2.empty()) { return std::vector(); } if (v1.size() <= 64 || v2.size() <= 64) { std::vector ans_naive(v1.size() + v2.size() - 1); for (std::size_t i = 0; i < v1.size(); ++i) { for (std::size_t j = 0; j < v2.size(); ++j) { ans_naive[i + j] += v1[i] * v2[j]; } } return ans_naive; } if (v1.size() < v2.size()) { swap(v1, v2); } std::size_t fsize = v1.size() + v2.size() - 1; std::size_t step = v2.size(); while (step & (step - 1)) { step += step & (-step); // step to become minimum 2^k >= v2.size() } v1.resize((v1.size() + step - 1) / step * step); // change v1.size() to multiple of step v2.resize(step * 2); std::vector ans(fsize); std::vector pv1(step * 2); fourier_transform(v2); for (std::size_t i = 0; i < v1.size(); i += step) { std::copy(v1.begin() + i, v1.begin() + i + step, pv1.begin()); std::fill(pv1.begin() + step, pv1.end(), modulo(0)); fourier_transform(pv1); for (std::size_t j = 0; j < step * 2; ++j) { pv1[j] *= v2[j]; } fourier_transform_inverse(pv1); for (std::size_t j = 0; j < step * 2 && i + j < fsize; ++j) { ans[j + i] += pv1[j]; } } return ans; } }; #endif // CLASS_POLYNOMIAL_NTT_64321 #ifndef CLASS_BASICINT #define CLASS_BASICINT #include #include #include #include template class basic_int { // 2 <= base < max(base_type)^(2/3) = 2,642,245 protected: using base_type = std::uint32_t; // base type using base_type_d = std::uint64_t; // double of base type std::size_t capacity; std::vector digit; void resize(std::size_t capacity_) { if (capacity != capacity_) { assert(capacity_ >= 1); capacity = capacity_; digit.resize(capacity_); } } void minimize() { std::size_t d = digits(); while (d & (d - 1)) { d += d & (-d); } resize(d); } std::size_t digits() const { for (std::size_t i = capacity - 1; i >= 1; --i) { if (digit[i] != 0) { return i + 1; } } return 1; } public: // ----- #1. Costructors ----- // explicit basic_int() : capacity(1), digit(1, base_type(0)) {}; explicit basic_int(std::vector digit_) : digit(digit_) { assert(!digit.empty()); for (base_type i : digit) { assert(0 <= i && i < base); } capacity = 1; while (capacity < digit.size()) { capacity <<= 1; } digit.resize(capacity, 0); }; // ----- #2. Comparing Operators ----- // bool operator==(const basic_int& b) const noexcept { return digit == b.digit; } bool operator!=(const basic_int& b) const noexcept { return digit != b.digit; } bool operator<(const basic_int& b) const noexcept { if (capacity != b.capacity) { return capacity < b.capacity; } for (std::size_t i = capacity - 1; i >= 1; --i) { if (digit[i] != b.digit[i]) { return digit[i] < b.digit[i]; } } return digit[0] < b.digit[0]; } bool operator>(const basic_int& b) const noexcept { if (capacity != b.capacity) { return capacity > b.capacity; } for (std::size_t i = capacity - 1; i >= 1; --i) { if (digit[i] != b.digit[i]) { return digit[i] > b.digit[i]; } } return digit[0] > b.digit[0]; } bool operator<=(const basic_int& b) const noexcept { return basic_int(*this) < b || basic_int(*this) == b; } bool operator>=(const basic_int& b) const noexcept { return basic_int(*this) > b || basic_int(*this) == b; } // ----- #3. Shifting ----- // basic_int& operator<<=(std::size_t s) noexcept { std::size_t d = digits(); if (d + s > capacity) { std::size_t nxtcap = d + s; while (nxtcap & (nxtcap - 1)) { nxtcap += nxtcap & (-nxtcap); } resize(nxtcap); } for (std::size_t i = d - 1; i != std::size_t(-1); --i) { digit[i + s] = digit[i]; } std::fill(digit.begin(), digit.begin() + s, 0); return *this; } basic_int& operator>>=(std::size_t s) noexcept { std::size_t d = digits(); if (d <= s) { (*this) = basic_int(); } else { for (std::size_t i = 0; i < d - s; ++i) { digit[i] = digit[i + s]; } std::fill(digit.begin() + d - s, digit.begin() + d, 0); minimize(); } return *this; } // ----- #4. Addition ----- // basic_int& operator+=(const basic_int& b) { resize(std::max(capacity, b.capacity)); bool carry = false; for (std::uint32_t i = 0; i < b.capacity; ++i) { digit[i] += b.digit[i] + (carry ? 1 : 0); carry = (digit[i] >= base); if (carry) digit[i] -= base; } for (std::uint32_t i = b.capacity; i < capacity; ++i) { digit[i] += (carry ? 1 : 0); carry = (digit[i] >= base); if (carry) digit[i] -= base; } if (carry) { resize(capacity << 1); digit[capacity >> 1] = 1; } return *this; } // ----- #5. Subtraction ----- // basic_int& operator-=(const basic_int& b) { bool carry = false; for (std::uint32_t i = 0; i < b.capacity; ++i) { digit[i] += base - b.digit[i] - (carry ? 1 : 0); carry = (digit[i] < base); if (!carry) digit[i] -= base; } for (std::uint32_t i = b.capacity; i < capacity; ++i) { digit[i] += base - (carry ? 1 : 0); carry = (digit[i] < base); if (!carry) digit[i] -= base; } // assert(!carry) // noexcept minimize(); return *this; } // ----- #6. Multiplication ----- // basic_int& operator*=(const basic_int& b) { using ntt = polynomial_ntt_64321; std::size_t nxtcap = std::max(capacity, b.capacity) * 2; std::vector nxtdigit = ntt::convolve(std::vector(digit.begin(), digit.end()), std::vector(b.digit.begin(), b.digit.end())); nxtdigit.resize(nxtcap); capacity = nxtcap; digit = std::vector(capacity, 0); std::uint64_t carry = 0; for (std::uint32_t i = 0; i < capacity; ++i) { std::uint64_t nxt = nxtdigit[i].get() + carry; carry = nxt / base; digit[i] = nxt - carry * base; } minimize(); return *this; } // ----- #7. Division ----- // basic_int& operator/=(const basic_int& b) { assert(b != basic_int()); if ((*this) < b) { (*this) = basic_int(); } else { std::size_t digit_a = digits(); std::size_t digit_b = b.digits(); std::size_t req_precis = digit_a - digit_b + 2; std::size_t set_precis = 1; while (set_precis < req_precis) set_precis <<= 1; // Find the inverse! std::uint64_t gen = (digit_b == 1 ? std::uint64_t(b.digit[0]) * base : std::uint64_t(b.digit[digit_b - 1]) * base + b.digit[digit_b - 2]); std::uint64_t gen_inv = std::uint64_t(base) * base * base / (gen + 1); std::size_t current_precis = 2; basic_int inv({ std::uint32_t(gen_inv % base), std::uint32_t(gen_inv / base) }); while (current_precis < set_precis) { std::size_t digit_nb = std::min(digit_b, current_precis * 2); basic_int nb = (digit_b == digit_nb ? b : b >> (digit_b - digit_nb)); inv = (((basic_int({ 2 }) << (current_precis + digit_nb - 1)) - inv * nb - basic_int({ 1 })) * inv) >> (digit_nb - 1); current_precis *= 2; } while (true) { basic_int next_inv = (((basic_int({ 2 }) << (current_precis + digit_b - 1)) - inv * b - basic_int({ 1 })) * inv) >> (set_precis + digit_b - 1); if (inv == next_inv) break; inv = next_inv; } basic_int val = (basic_int(*this) * inv) >> (set_precis + digit_b - 1); while (b * (val + basic_int({ 1 })) <= (*this)) { val += basic_int({ 1 }); } (*this) = val; } return *this; } // ----- #8. Operators ----- // basic_int operator<<(std::size_t s) const { return basic_int(*this) <<= s; } basic_int operator>>(std::size_t s) const { return basic_int(*this) >>= s; } basic_int operator+(const basic_int& b) const { return basic_int(*this) += b; } basic_int operator-(const basic_int& b) const { return basic_int(*this) -= b; } basic_int operator*(const basic_int& b) const { return basic_int(*this) *= b; } basic_int operator/(const basic_int& b) const { return basic_int(*this) /= b; } }; #endif // CLASS_BASICINT #ifndef CLASS_BIGINT #define CLASS_BIGINT #include #include // (digit / base_digit) * base_number^2 <= 2^64 - 2^32 + 1 = 18446744069414584321 // (digit / base_digit) < min(2^27, 2^26) = 67108864 // ---> max_digit = min(92233720, 335544320) = 92233720 constexpr std::size_t base_digit = 6; constexpr std::uint32_t base_number = 1000000; class bigint : private basic_int { private: bool sign; // positive/zero = false, negative = true bool is_number(std::string str) { if(str.empty() || str == "-" || !(('0' <= str[0] && str[0] <= '9') || str[0] == '-')) { return false; } for(std::uint64_t i = 1; i < str.size(); ++i) { if(!('0' <= str[i] && str[i] <= '9')) { return false; } } return true; } std::vector to_basic_expression(std::uint64_t x) { std::vector res; do { res.push_back(x % base_number); x /= base_number; } while(x != 0); return res; } public: // ----- #1. Constructors / String Functions ----- // bigint() : basic_int(), sign(false) {}; bigint(std::int64_t x) : basic_int(to_basic_expression(x >= 0 ? x : -x)), sign(x < 0) {}; bigint(const std::string& str) { assert(is_number(str)); sign = (str[0] == '-'); std::size_t initial = (sign ? 1 : 0); while(initial + 1 != str.size() && str[initial] == '0') { ++initial; } std::size_t str_digits = str.size() - initial; capacity = 1; while(capacity * base_digit < str_digits) { capacity *= 2; } digit = std::vector(capacity, 0); for(std::size_t i = 0; (i + 1) * base_digit < str_digits; ++i) { digit[i] = std::stoi(str.substr(str.size() - i * base_digit - base_digit, base_digit)); } digit[(str_digits - 1) / base_digit] = std::stoi(str.substr(initial, (str.size() - (str_digits - 1) / base_digit * base_digit) - initial)); } std::string to_string() const { std::size_t d = digits(); std::string res = (sign ? "-" : "") + std::to_string(digit[d - 1]); for(std::size_t i = d - 2; i != std::size_t(-1); --i) { std::string digit_str = std::to_string(digit[i]); res += std::string(base_digit - digit_str.size(), '0') + digit_str; } return res; } // ----- #2. Operators ----- // bool operator==(const bigint& b) const noexcept { return sign == b.sign && basic_int::operator==(b); } bool operator!=(const bigint& b) const noexcept { return sign != b.sign || basic_int::operator!=(b); } bool operator<(const bigint& b) const noexcept { return sign != b.sign ? sign : basic_int::operator<(b); } bool operator>(const bigint& b) const noexcept { return sign != b.sign ? !sign : basic_int::operator>(b); } bool operator<=(const bigint& b) const noexcept { return sign != b.sign ? sign : basic_int::operator<=(b); } bool operator>=(const bigint& b) const noexcept { return sign != b.sign ? !sign : basic_int::operator>=(b); } bigint& operator+=(const bigint& b) { if(sign == b.sign) { basic_int::operator+=(b); } else if(basic_int(*this) >= basic_int(b)) { basic_int::operator-=(b); if(sign && basic_int(*this) == basic_int()) sign = false; } else { sign = !sign; (*this) = b - (*this); } return *this; } bigint& operator-=(const bigint& b) { if(sign != b.sign) { basic_int::operator+=(b); } else if(basic_int(*this) >= basic_int(b)) { basic_int::operator-=(b); if(sign && basic_int(*this) == basic_int()) sign = false; } else { sign = !sign; (*this) += b; sign = !sign; } return *this; } bigint& operator*=(const bigint& b) { basic_int::operator*=(b); if(b.sign) sign = !sign; if(sign && basic_int(*this) == basic_int()) sign = false; return *this; } bigint& operator/=(const bigint& b) { basic_int::operator/=(b); if(b.sign) sign = !sign; if(sign && basic_int(*this) == basic_int()) sign = false; return *this; } bigint operator%=(const bigint& b) { bigint itself(*this); (*this) = itself - itself / b * b; return *this; } bigint operator+(const bigint& b) const { return bigint(*this) += b; } bigint operator-(const bigint& b) const { return bigint(*this) -= b; } bigint operator*(const bigint& b) const { return bigint(*this) *= b; } bigint operator/(const bigint& b) const { return bigint(*this) /= b; } bigint operator%(const bigint& b) const { return bigint(*this) %= b; } friend std::istream& operator>>(std::istream& is, bigint& x) { std::string s; is >> s; x = bigint(s); return is; } friend std::ostream& operator<<(std::ostream& os, const bigint& x) { os << x.to_string(); return os; } }; #endif // CLASS_BIGINT #include #include using namespace std; int main() { cin.tie(0); ios_base::sync_with_stdio(false); int n; cin >> n; vector p(n), bit(n); vector a(n), b(n); for (int i = 0; i < n; i++) cin >> p[i]; for (int i = n - 1; i >= 0; i--) { int x = 0; for (int j = p[i] - 1; j >= 1; j -= j & (-j)) x += bit[j]; for (int j = p[i]; j < n; j += j & (-j)) bit[j]++; a[n - i - 1] = x; b[i] = i + 1; } for (int i = 1; i < n; i <<= 1) { for (int j = 0; j + i < n; j += 2 * i) { a[j] = a[j] + b[j] * a[j + i]; b[j] = b[j] * b[j + i]; } } cout << a[0] + 1 << endl; return 0; }