// +---------------------------------- // | BigInteger Library Version 1.1 // | Author: square1001, E869120 // | Date: July 24th, 2016 // | Language: C++11 / C++14 // +--------------------------------- #ifndef ___Class_BasicInteger #define ___Class_BasicInteger // ------ Includes ------ // #include #include #include #include #include #include #include // ------ BasicInteger ------ // class BasicInteger { private: // ------ Variable ------ // int size_; std::vector v; // ------ Private Function ------ // void resize(int size__) { size_ = size__; v.resize(size_, 0); } int digit() { int digit = 1; for (int i = size_ - 1; i >= 1; i--) { if (v[i] != 0) { digit = i + 1; break; } } return digit; } void revalue() { int r = digit(); while (size_ >= r * 2) size_ >>= 1; v.resize(size_); } public: // ------ Constants ------ // static const int maxdigit = 4; // maxdigit <= 4 static const int maxvalue = 10000; // maxvalue = pow(10, maxdigit) // ------ Constructor ------ // BasicInteger() { size_ = 1; v.resize(size_, 0); } BasicInteger(const std::string &b) { std::string s = b; int r = (s.size() + maxdigit - 1) / maxdigit; size_ = 1; while (size_ < r) size_ <<= 1; v.resize(size_); std::reverse(s.begin(), s.end()); int val = 0, cnt = 0, t = 0, p = 1; for (char c : s) { val += (c - 48) * p; p *= 10; if (++cnt == maxdigit) { v[t++] = val; val = 0, cnt = 0, p = 1; } } if (cnt > 0) v[t] = val; } BasicInteger(long long x) { assert(x >= 0); (*this) = x; } BasicInteger(const BasicInteger& b) { size_ = b.size_; v = b.v; } // ------ Functions ------ // int size() const { return size_; } int digit() const { for (int i = size_ - 1; i >= 1; i--) { if (v[i] > 0) return i + 1; } return 1; } std::string to_string() const { std::string ret = ""; for (int i = size_ - 1; i >= 0; i--) { std::string t = std::to_string(v[i]); while (t.size() < BasicInteger::maxdigit) t = "0" + t; ret += t; } int r = 0; while (r < size_ * 4 && ret[r] == '0') r++; if (r == size_ * 4) return "0"; return ret.substr(r, size_ * 4); } // ------ Basic Operators ------ // BasicInteger& operator=(const long long x) { (*this) = BasicInteger(std::to_string(x)); return (*this); } BasicInteger& operator=(const BasicInteger& b) { if (&b != this) { size_ = b.size_; v = b.v; } return (*this); } // ------ Comparision Operators ------ // friend bool operator==(const BasicInteger& b1, const BasicInteger& b2) { return b1.v == b2.v; } friend bool operator!=(const BasicInteger& b1, const BasicInteger& b2) { return b1.v != b2.v; } friend bool operator<(const BasicInteger& b1, const BasicInteger& b2) { if (b1.size_ != b2.size_) return b1.size_ < b2.size_; int n = b1.size_; for (int i = n - 1; i >= 0; i--) { if (b1.v[i] != b2.v[i]) return b1.v[i] < b2.v[i]; } return false; } friend bool operator>(const BasicInteger& b1, const BasicInteger& b2) { return b2 < b1; } friend bool operator<=(const BasicInteger& b1, const BasicInteger& b2) { return !(b1 > b2); } friend bool operator>=(const BasicInteger& b1, const BasicInteger& b2) { return !(b1 < b2); } // ------ Addition Operator ------ // friend BasicInteger operator+(const BasicInteger& b1, const BasicInteger& b2) { BasicInteger ret(b1); int n = std::max(b1.size_, b2.size_); ret.resize(n); for (int i = 0; i < b2.size_; i++) ret.v[i] += b2.v[i]; for (int i = 0; i < n - 1; i++) { if (ret.v[i] >= BasicInteger::maxvalue) { ret.v[i] -= BasicInteger::maxvalue; ret.v[i + 1]++; } } if (ret.v[n - 1] >= BasicInteger::maxvalue) { ret.resize(n << 1); ret.v[n - 1] -= BasicInteger::maxvalue; ret.v[n] = 1; } return ret; } // ------ Subtraction ------ // friend BasicInteger operator-(const BasicInteger& b1, const BasicInteger& b2) { assert(b1 >= b2); BasicInteger ret(b1); for (int i = 0; i < b2.size_; i++) ret.v[i] -= b2.v[i]; for (int i = 0; i < ret.size_; i++) { if (ret.v[i] < 0) { ret.v[i] += BasicInteger::maxvalue; ret.v[i + 1]--; } } ret.revalue(); return ret; } // ------ Multiplication ------ // friend BasicInteger operator*(const BasicInteger& b1, const BasicInteger& b2) { BasicInteger ret; BasicInteger b3(b1 < b2 ? b2 : b1); // large BasicInteger b4(b1 < b2 ? b1 : b2); // small int d1 = b3.size_, d2 = b4.size_; ret.resize(d1 << 1); for (int i = 0; i < d1; i += d2) { std::vector sub(b3.v.begin() + i, b3.v.begin() + i + d2); std::vector res; res = BasicInteger::NumberTheoreticConvolution(sub, b4.v); for (int j = 0; j < (d2 << 1); j++) { ret.v[j + i] += res[j]; if (ret.v[j + i] >= BasicInteger::maxvalue) { ret.v[j + i] -= BasicInteger::maxvalue; ret.v[j + i + 1]++; } } } ret.revalue(); return ret; } // ------ Normal Multiplication ------ // inline static std::vector NormalMul(const std::vector& b1, const std::vector& b2) { int n = b1.size(); // n <= 2^30, b1 and b2 is the same size! std::vector ret(n << 1); for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { ret[i + j] += 1LL * b1[i] * b2[j]; } } for (int i = 0; i < (n << 1) - 1; i++) { ret[i + 1] += ret[i] / BasicInteger::maxvalue; ret[i] %= BasicInteger::maxvalue; } std::vector res(ret.begin(), ret.end()); return res; } // ------ Fast Fourier Transform ------ // inline static void DiscreteFourierTransform(std::vector > &f, bool rev = false) { int n = f.size(); // n <= 8192 const double pi = acos(-1.0); for (int i = 0, j = 1; j < n - 1; j++) { for (int k = n >> 1; k >(i ^= k); k >>= 1); if (i > j) swap(f[i], f[j]); } for (int b = 2; b <= n; b <<= 1) { std::complex wr = std::polar(1.0, (rev ? -2.0 : 2.0) * pi / b); for (int i = 0; i < n; i += b) { std::complex w(1.0, 0.0); for (int j = 0; j < b >> 1; j++) { std::complex f0 = f[i + j], f1 = w * f[i + j + (b >> 1)]; f[i + j] = f0 + f1; f[i + j + (b >> 1)] = f0 - f1; w *= wr; } } } if (rev) { double mul = 1.0 / n; for (int i = 0; i < n; i++) f[i] *= mul; } } inline static std::vector FastFourierTransform(std::vector b1, std::vector b2) { int n = b1.size() * 2; // b1 and b2 is the same size! std::vector > f0(n), f1(n); for (int i = 0; i < n >> 1; i++) { f0[i] = b1[i]; f1[i] = b2[i]; } DiscreteFourierTransform(f0); DiscreteFourierTransform(f1); for (int i = 0; i < n; i++) f0[i] *= f1[i]; DiscreteFourierTransform(f0, true); std::vector res(n); for (int i = 0; i < n; i++) { res[i] = (long long)(f0[i].real() + 0.5); } for (int i = 0; i < n - 1; i++) { res[i + 1] += res[i] / BasicInteger::maxvalue; res[i] %= BasicInteger::maxvalue; } std::vector ret(res.begin(), res.end()); return ret; } // ------ Number Theoretic Transform ------ // inline static int modpow(int a, int b, int m) { int ret = 1; for (int i = 30; i >= 0; i--) { ret = 1LL * ret * ret % m; if (b & (1 << i)) ret = 1LL * ret * a % m; } return ret; } inline static void extgcd(int a, int b, int &x, int &y) { if (b) extgcd(b, a % b, y, x), y -= (a / b) * x; else x = 1, y = 0; } inline static unsigned long long modmul(unsigned long long a, unsigned long long b, unsigned long long m) { unsigned long long res = 0; a %= m, b %= m; while (a) { if (a & 1) res += b; a >>= 1; if (res >= m) res -= m; b <<= 1; if (b >= m) b -= m; } return res; } inline static void NumberTheoreticTransform(std::vector &f, int mod, int root, bool rev = false) { int n = f.size(); for (int i = 0, j = 1; j < n - 1; j++) { for (int k = n >> 1; k >(i ^= k); k >>= 1); if (i < j) std::swap(f[i], f[j]); } for (int b = 1; b < n; b <<= 1) { int wr = modpow(root, (mod - 1) / (b << 1), mod); if (rev) wr = modpow(wr, mod - 2, mod); for (int i = 0; i < n; i += (b << 1)) { int w = 1; for (int j = i; j < i + b; j++) { int f0 = f[j], f1 = 1LL * w * f[j + b] % mod; f[j] = f0 + f1; if (f[j] >= mod) f[j] -= mod; f[j + b] = f0 - f1; if (f[j + b] < 0) f[j + b] += mod; w = 1LL * w * wr % mod; } } } if (rev) { int mul = modpow(n, mod - 2, mod); for (int i = 0; i < n; i++) { f[i] = 1LL * f[i] * mul % mod; } } } inline static std::vector NumberTheoreticModularConvolution(std::vector f0, std::vector f1, int mod, int root) { int n = f0.size() * 2; // f0 and f1 is the same size! f0.resize(n); f1.resize(n); NumberTheoreticTransform(f0, mod, root); NumberTheoreticTransform(f1, mod, root); for (int i = 0; i < n; i++) f0[i] = 1LL * f0[i] * f1[i] % mod; NumberTheoreticTransform(f0, mod, root, true); return f0; } inline static std::vector NumberTheoreticConvolution(std::vector b1, std::vector b2) { int n = b1.size() * 2; // b1 and b2 is the same size! int mod1 = 469762049, r1 = 3; int mod2 = 754974721, r2 = 11; std::vector f0 = NumberTheoreticModularConvolution(b1, b2, mod1, r1); std::vector f1 = NumberTheoreticModularConvolution(b1, b2, mod2, r2); int t1, t2; extgcd(mod1, mod2, t1, t2); if (t1 < 0) t1 += mod2; if (t2 < 0) t2 += mod1; long long w0 = 1LL * mod1 * mod2; long long w1 = 1LL * mod2 * t2; long long w2 = 1LL * mod1 * t1; std::vector res(n); for (int i = 0; i < n; i++) { long long x1 = modmul(f0[i], w1, w0); long long x2 = modmul(f1[i], w2, w0); res[i] = (x1 + x2) % w0; } for (int i = 0; i < n - 1; i++) { res[i + 1] += res[i] / BasicInteger::maxvalue; res[i] %= BasicInteger::maxvalue; } std::vector ret(res.begin(), res.end()); return ret; } // ------ In / Out Operator ------ // friend std::istream& operator >> (std::istream& is, BasicInteger& b) { std::string res; is >> res; b = BasicInteger(res); return is; } friend std::ostream& operator<<(std::ostream& os, const BasicInteger& b) { os << b.to_string(); return os; } }; #endif #include #include using namespace std; int n, p[100009], bit[100009]; BasicInteger a[100009], b[100009]; int main() { cin.tie(0); ios_base::sync_with_stdio(false); cin >> 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; } int s = 1; while (2 << s < n) s++; for (int i = 0; i <= s; i++) { for (int j = 0; j + (1 << i) < n; j += (2 << i)) { a[j] = a[j] + b[j] * a[j + (1 << i)]; b[j] = b[j] * b[j + (1 << i)]; } } cout << a[0] + 1 << endl; return 0; }