Problem: Problem

Define a function $ f $ that starts with $ 1 $ and takes a sequence of finite lengths as an argument as follows.

$ \ displaystyle f (\\ {a_1, a_2, \ ldots, a_n \\}) = \ sum_ {i = 1} ^ n {a_i} ^ i $

Given a sequence of length $ N $, $ X = \\ {x_1, x_2, \ ldots, x_N \\} $, $ f (X) for all subsequences $ X'$ except empty columns. ') Find $ and output the sum of them divided by $ 998244353 $. However, the subsequence subsequences shall be renumbered starting from $ 1 $ while maintaining the relative order in the original sequence. Also, even if two subsequences are the same as columns, if they are taken out at different positions, they shall be counted separately.

Constraints

The input satisfies the following conditions.

* $ 1 \ leq N \ leq 10 ^ 6 $
* $ 1 \ leq x_i \ leq 10 ^ 6 $
* All inputs are integers

Input

The input is given in the following format.


$ N $
$ x_1 $ $ \ ldots $ $ x_N $


The first line is given the length $ N $. In the second row, the elements of the sequence $ X $ are given, separated by blanks.

Output

Find $ f (X') $ for all subsequences $ X'$ except empty columns, and divide the sum by $ 998244353 $ to output the remainder.

Examples

Input

3
1 2 3


Output

64


Input

5
100 200 300 400 500


Output

935740429

Solution (in CPP):

Solution:
// includes {{{
#include<iostream>
#include<iomanip>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<map>
#include<set>
#include<tuple>
#include<cmath>
#include<random>
#include<cassert>
#include<bitset>
#include<cstdlib>
// #include<deque>
// #include<multiset>
// #include<cstring>
// #include<bits/stdc++.h>
// }}}
using namespace std;
using ll = long long;

constexpr ll mod = 998244353;

/// --- Modulo Integer {{{ ///
#include <ostream>
template < long long mod = static_cast< long long >(1e9 + 7) >
struct ModuloInteger {
  static_assert(mod > 0, "mod must be positive");
  static_assert(mod <= 3037000499, "mod is too big");
  using integer = long long;
  static ModuloInteger unused;
  // math {{{
  static inline integer extgcd(integer a, integer b, integer &x, integer &y) {
    integer d;
    return b == 0 ? (x = a < 0 ? -1 : 1, y = 0, a < 0 ? -a : a)
      : (d = extgcd(b, a % b, y, x), y -= a / b * x, d);
  }
  static inline integer modinv(integer a) {
    integer x = 0, y = 0;
    extgcd(a, mod, x, y);
    if(x < 0)
      x += mod;
    else if(x == mod)
      x = 0;
    return x;
  }
  static inline integer modpow(integer a, long long b) {
    if(b < 0) b = -b, a = modinv(a);
    integer r = 1;
    a %= mod;
    while(b) {
      if(b & 1) r = r * a % mod;
      a = a * a % mod;
      b >>= 1;
    }
    return r;
  }
  // }}}

  integer val;
  constexpr ModuloInteger() : val(0) {}
  constexpr ModuloInteger(integer t) {
    val = t % mod;
    if(val < 0) val += mod;
  }

private:
  // strict constructor
  constexpr ModuloInteger(integer t, int) : val(t) {}

public:
  template < class T >
    explicit operator T() {
      return T(val);
    }
  // operator bool() { return bool(val); }
  // ModuloInteger <arithmetic-operator>[=] ModuloInteger {{{
  ModuloInteger operator+(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp += rhs;
    return tmp;
  }
  ModuloInteger operator-(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp -= rhs;
    return tmp;
  }
  ModuloInteger operator*(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp *= rhs;
    return tmp;
  }
  ModuloInteger operator/(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp /= rhs;
    return tmp;
  }
  ModuloInteger &operator+=(ModuloInteger const &rhs) {
    val = val + rhs.val;
    if(val >= mod) val -= mod;
    return *this;
  }
  ModuloInteger &operator-=(ModuloInteger const &rhs) { return *this += -rhs; }
  ModuloInteger &operator*=(ModuloInteger const &rhs) {
    val = val * rhs.val % mod;
    return *this;
  }
  ModuloInteger &operator/=(ModuloInteger const &rhs) { return *this *= rhs.inv(); }
  // }}}
  // increment, decrement {{{
  ModuloInteger operator++(int) {
    ModuloInteger tmp = *this;
    val = val + 1;
    if(val >= mod) val = 0;
    return tmp;
  }
  ModuloInteger operator--(int) {
    ModuloInteger tmp = *this;
    val = val == 0 ? mod - 1 : val - 1;
    return tmp;
  }
  ModuloInteger &operator++() {
    val = val + 1;
    if(val >= mod) val = 0;
    return *this;
  }
  ModuloInteger &operator--() {
    val = val == 0 ? mod - 1 : val - 1;
    return *this;
  }
  // }}}
  ModuloInteger operator-() const { return ModuloInteger(val == 0 ? 0 : mod - val, 0); }
  // ModuloInteger <arithmetic-operator>[=] T {{{
  template < typename T >
    ModuloInteger operator+(T const &rhs) const {
      return ModuloInteger(val + rhs % mod);
    }
  template < typename T >
    ModuloInteger operator-(T const &rhs) const {
      return ModuloInteger(mod + val - rhs % mod);
    }
  template < typename T >
    ModuloInteger operator*(T const &rhs) const {
      return ModuloInteger(val * (rhs % mod));
    }
  template < typename T >
    ModuloInteger operator/(T const &rhs) const {
      return ModuloInteger(val * modinv(rhs));
    }
  template < typename T >
    ModuloInteger &operator+=(T const &rhs) {
      val = (mod + val + rhs % mod) % mod;
      return *this;
    }
  template < typename T >
    ModuloInteger &operator-=(T const &rhs) {
      val = (mod + val - rhs % mod) % mod;
      return *this;
    }
  template < typename T >
    ModuloInteger &operator*=(T const &rhs) {
      val = val * (mod + rhs % mod) % mod;
      return *this;
    }
  template < typename T >
    ModuloInteger &operator/=(T const &rhs) {
      val = val * modinv(rhs) % mod;
      return *this;
    }
  // }}}
  ModuloInteger inv() const { return ModuloInteger(modinv(val), 0); }
  ModuloInteger operator~() const { return inv(); }
  friend std::ostream &operator<<(std::ostream &os, ModuloInteger const &mv) {
    os << mv.val;
    return os;
  }
  // equality operator {{{
  ModuloInteger operator==(const ModuloInteger &a) const { return val == a.val; }
  ModuloInteger operator!=(const ModuloInteger &a) const { return val != a.val; }
  ModuloInteger operator==(const integer &a) const { return val == ModuloInteger(a); }
  ModuloInteger operator!=(const integer &a) const { return val != ModuloInteger(a); }
  // }}}
  // T <arithmetic-operator> ModuloInteger {{{
  friend constexpr ModuloInteger operator+(integer a, ModuloInteger const &mv) {
    return ModuloInteger(a % mod + mv.val);
  }
  friend constexpr ModuloInteger operator-(integer a, ModuloInteger const &mv) {
    return ModuloInteger(a % mod - mv.val);
  }
  friend constexpr ModuloInteger operator*(integer a, ModuloInteger const &mv) {
    return ModuloInteger((mod + a % mod) * mv.val % mod, 0);
  }
  friend constexpr ModuloInteger operator/(integer a, ModuloInteger const &mv) {
    return ModuloInteger((mod + a % mod) * modinv(mv.val) % mod, 0);
  }
  // }}}
  // power {{{
  ModuloInteger operator^(integer x) const { return pow(*this, x); }
  ModuloInteger &operator^=(integer x) {
    val = modpow(val, x);
    return *this;
  }
  friend ModuloInteger pow(ModuloInteger x, integer y) {
    return ModuloInteger(modpow(x.val, y), 0);
  }
  // }}}
};
template < long long mod >
ModuloInteger< mod > ModuloInteger< mod >::unused(mod, 0);
/// }}}--- ///

using modint = ModuloInteger<mod>;

int main() {
  std::ios::sync_with_stdio(false), std::cin.tie(0);
  int n;
  cin >> n;
  modint ans;
  for(int i = 0; i < n; i++) {
    int x;
    cin >> x;
    ans += modint(x) * (modint(x + 1) ^ i) * (modint(2) ^ (n - i - 1));
  }
  cout << ans << endl;
  return 0;
}