#ifndef LOCAL #define FAST_IO #endif // ===== template.hpp ===== #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i) #define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i) #define ALL(x) begin(x), end(x) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using u128 = __uint128_t; using i32 = signed int; using i64 = signed long long; using i128 = __int128_t; using f64 = double; using f80 = long double; template using Vec = vector; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } istream &operator>>(istream &is, i128 &x) { i64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, i128 x) { os << (i64) x; return os; } istream &operator>>(istream &is, u128 &x) { u64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, u128 x) { os << (u64) x; return os; } template > Vec sort_index(i32 n, F f, Comp comp = Comp()) { Vec idx(n); iota(ALL(idx), 0); sort(ALL(idx), [&](i32 i, i32 j) -> bool { return comp(f(i), f(j)); }); return idx; } [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; #ifdef FAST_IO __attribute__((constructor)) void fast_io() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(10); } #endif // ===== template.hpp ===== #ifdef DEBUGF #include "cpl/template/debug.hpp" #else #define DBG(x) (void) 0 #endif // ===== mod_int.hpp ===== #include #include #include // ===== utils.hpp ===== constexpr bool is_prime(unsigned n) { if (n == 0 || n == 1) { return false; } for (unsigned i = 2; i * i <= n; ++i) { if (n % i == 0) { return false; } } return true; } constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) { unsigned ret = 1, self = x; while (y != 0) { if (y & 1) { ret = static_cast(static_cast(ret) * self % mod); } self = static_cast(static_cast(self) * self % mod); y /= 2; } return ret; } template constexpr unsigned primitive_root() { static_assert(is_prime(mod), "`mod` must be a prime number."); if (mod == 2) { return 1; } unsigned primes[32] = {}; int it = 0; { unsigned m = mod - 1; for (unsigned i = 2; i * i <= m; ++i) { if (m % i == 0) { primes[it++] = i; while (m % i == 0) { m /= i; } } } if (m != 1) { primes[it++] = m; } } for (unsigned i = 2; i < mod; ++i) { bool ok = true; for (int j = 0; j < it; ++j) { if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) { ok = false; break; } } if (ok) return i; } return 0; } // y >= 1 template constexpr T safe_mod(T x, T y) { x %= y; if (x < 0) { x += y; } return x; } // y != 0 template constexpr T floor_div(T x, T y) { if (y < 0) { x *= -1; y *= -1; } if (x >= 0) { return x / y; } else { return -((-x + y - 1) / y); } } // y != 0 template constexpr T ceil_div(T x, T y) { if (y < 0) { x *= -1; y *= -1; } if (x >= 0) { return (x + y - 1) / y; } else { return -(-x / y); } } // ===== utils.hpp ===== template class ModInt { static_assert(mod != 0, "`mod` must not be equal to 0."); static_assert( mod < (1u << 31), "`mod` must be less than (1u << 31) = 2147483648."); unsigned val; public: constexpr ModInt() : val(0) {} template constexpr ModInt(T x) : val(static_cast(safe_mod(x, static_cast(mod)))) {} static constexpr ModInt raw(unsigned x) { ModInt ret; ret.val = x; return ret; } constexpr unsigned get_val() const { return val; } constexpr ModInt operator+() const { return *this; } constexpr ModInt operator-() const { return ModInt(0u) - *this; } constexpr ModInt &operator+=(const ModInt &rhs) { val += rhs.val; if (val >= mod) val -= mod; return *this; } constexpr ModInt &operator-=(const ModInt &rhs) { if (val < rhs.val) val += mod; val -= rhs.val; return *this; } constexpr ModInt &operator*=(const ModInt &rhs) { val = (unsigned long long)val * rhs.val % mod; return *this; } constexpr ModInt &operator/=(const ModInt &rhs) { val = (unsigned long long)val * rhs.inv().val % mod; return *this; } friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) += rhs; } friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) -= rhs; } friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) *= rhs; } friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) /= rhs; } constexpr ModInt pow(unsigned long long x) const { ModInt ret = ModInt::raw(1); ModInt self = *this; while (x != 0) { if (x & 1) ret *= self; self *= self; x >>= 1; } return ret; } constexpr ModInt inv() const { static_assert(is_prime(mod), "`mod` must be a prime number."); assert(val != 0); return this->pow(mod - 2); } friend std::istream &operator>>(std::istream &is, ModInt &x) { is >> x.val; x.val %= mod; return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } friend bool operator==(const ModInt &lhs, const ModInt &rhs) { return lhs.val == rhs.val; } friend bool operator!=(const ModInt &lhs, const ModInt &rhs) { return lhs.val != rhs.val; } }; [[maybe_unused]] constexpr unsigned mod998244353 = 998244353; [[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007; // ===== mod_int.hpp ===== using Mint = ModInt; // ===== fenwick_tree.hpp ===== #include #include // ===== operations.hpp ===== #include #include template struct Add { using Value = T; static Value id() { return T(0); } static Value op(const Value &lhs, const Value &rhs) { return lhs + rhs; } static Value inv(const Value &x) { return -x; } }; template struct Mul { using Value = T; static Value id() { return Value(1); } static Value op(const Value &lhs, const Value &rhs) { return lhs * rhs; } static Value inv(const Value &x) { return Value(1) / x; } }; template struct Min { using Value = T; static Value id() { return std::numeric_limits::max(); } static Value op(const Value &lhs, const Value &rhs) { return std::min(lhs, rhs); } }; template struct Max { using Value = T; static Value id() { return std::numeric_limits::min(); } static Value op(const Value &lhs, const Value &rhs) { return std::max(lhs, rhs); } }; template struct Xor { using Value = T; static Value id() { return T(0); } static Value op(const Value &lhs, const Value &rhs) { return lhs ^ rhs; } static Value inv(const Value &x) { return x; } }; template struct Reversible { using Value = std::pair; static Value id() { return Value(Monoid::id(), Monoid::id()); } static Value op(const Value &v1, const Value &v2) { return Value( Monoid::op(v1.first, v2.first), Monoid::op(v2.second, v1.second)); } }; // ===== operations.hpp ===== template class FenwickTree { public: using Value = typename CommutativeGroup::Value; private: std::vector data; public: FenwickTree(int n) : data(n, CommutativeGroup::id()) {} void add(int idx, const Value &x) { assert(idx >= 0 && idx < static_cast(data.size())); for (; idx < static_cast(data.size()); idx |= idx + 1) { data[idx] = CommutativeGroup::op(data[idx], x); } } Value sum(int r) const { assert(r >= 0 && r <= static_cast(data.size())); Value ret = CommutativeGroup::id(); for (; r > 0; r &= r - 1) { ret = CommutativeGroup::op(ret, data[r - 1]); } return ret; } Value sum(int l, int r) const { assert(l >= 0 && l <= r && r <= static_cast(data.size())); return CommutativeGroup::op(sum(r), CommutativeGroup::inv(sum(l))); } }; // ===== fenwick_tree.hpp ===== int main() { i32 n; cin >> n; Vec a(n); REP(i, n) { cin >> a[i]; } Vec pow2(n + 1); pow2[0] = Mint(1); REP(i, 1, n + 1) { pow2[i] = pow2[i - 1] * Mint(2); } DBG(pow2); Vec idx_l(n); iota(ALL(idx_l), 0); sort(ALL(idx_l), [&](i32 i, i32 j) -> bool { if (a[i] != a[j]) { return a[i] < a[j]; } else { return i < j; } }); Vec idx_r(n); iota(ALL(idx_r), 0); sort(ALL(idx_r), [&](i32 i, i32 j) -> bool { if (a[i] != a[j]) { return a[i] < a[j]; } else { return i > j; } }); DBG(idx_l); DBG(idx_r); Vec less_l(n), less_r(n), greater_l(n), greater_r(n); FenwickTree> fw(n); for (i32 i : idx_r) { fw.add(i, pow2[i]); less_l[i] = fw.sum(i); } fw = FenwickTree>(n); for (i32 i : idx_l) { fw.add(i, pow2[n - 1 - i]); less_r[i] = fw.sum(i + 1, n); } reverse(ALL(idx_l)); reverse(ALL(idx_r)); swap(idx_l, idx_r); fw = FenwickTree>(n); for (i32 i : idx_r) { fw.add(i, pow2[i]); greater_l[i] = fw.sum(i); } fw = FenwickTree>(n); for (i32 i : idx_l) { fw.add(i, pow2[n - 1 - i]); greater_r[i] = fw.sum(i + 1, n); } DBG(less_l); DBG(less_r); DBG(greater_l); DBG(greater_r); Mint ans; REP(i, n) { ans += less_l[i] * less_r[i] + greater_l[i] * greater_r[i]; } cout << ans << '\n'; }