Problem:
Score: 400 points

Problem Statement

Quickly after finishing the tutorial of the online game ATChat, you have decided to visit a particular place with N-1 players who happen to be there. These N players, including you, are numbered 1 through N, and the friendliness of Player i is A_i.

The N players will arrive at the place one by one in some order. To make sure nobody gets lost, you have set the following rule: players who have already arrived there should form a circle, and a player who has just arrived there should cut into the circle somewhere.

When each player, except the first one to arrive, arrives at the place, the player gets comfort equal to the smaller of the friendliness of the clockwise adjacent player and that of the counter-clockwise adjacent player. The first player to arrive there gets the comfort of 0.

What is the maximum total comfort the N players can get by optimally choosing the order of arrivals and the positions in the circle to cut into?

Constraints

All values in input are integers.

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

Print the maximum total comfort the N players can get.

Sample Input 1

4
2 2 1 3

Sample Output 1

7

By arriving at the place in the order Player 4, 2, 1, 3, and cutting into the circle as shown in the figure, they can get the total comfort of 7.

They cannot get the total comfort greater than 7, so the answer is 7.

Sample Input 2

7
1 1 1 1 1 1 1

Sample Output 2

6

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <algorithm>
#include <utility>
#include <cassert>

template <unsigned int modulus> struct modInt{
    static_assert(modulus > 0, "modulus must be a positive integer.");
    int val; // 値本体

    // コンストラクタ
    constexpr modInt():val(0){}
    template <class T> constexpr modInt(T v){
        val = v % (int)(modulus); 
        if(val < 0) val += modulus;
    }
    constexpr modInt& operator+= (const modInt<modulus> other) noexcept {
        val += other.val; if(val >= modulus) val -= modulus;
        return *this;
    }
    constexpr modInt& operator -= (const modInt<modulus> other) noexcept {
        val -= other.val; if(val < 0) val += modulus;
        return *this;
    }
    constexpr modInt& operator *= (const modInt<modulus> other) noexcept {
        val = (unsigned long long int)(val) * other.val % modulus;
        return *this; 
    }
    constexpr modInt& operator /= (const modInt<modulus> other) noexcept {
        val = (unsigned long long int)(val) * other.inverse() % modulus;
        return *this;
    }
    constexpr bool operator == (const modInt<modulus> other) const noexcept {
        return val == other.val;
    }
    constexpr modInt operator +(const modInt<modulus> v)const noexcept{
        return modInt<modulus>(*this) += v;
    }
    constexpr modInt operator -(const modInt<modulus> v)const noexcept{
        return modInt<modulus>(*this) -= v;
    }
    constexpr modInt operator *(const modInt<modulus> v)const noexcept{
        return modInt<modulus>(*this) *= v;
    }
    constexpr modInt operator /(const modInt<modulus> v)const noexcept{
        return modInt<modulus>(*this) /= v;
    }
    constexpr modInt& operator ++(void) noexcept {
        if(++val == modulus) val = 0;
        return *this;
    }
    constexpr modInt& operator --(void) noexcept {
        if(val-- == 0) val = modulus - 1;
        return *this;
    }
    constexpr modInt operator -()const noexcept{
        return modInt<modulus>((val == 0 ? 0 : modulus - val));
    }

    // aの逆元を求める関数
    constexpr unsigned int inverse(unsigned int a) const noexcept {
        unsigned int b = modulus;
                 int u = 1,   v = 0;
        while (b != 0) {
            unsigned int t = a / b; 
            a -= t * b; std::swap(a, b);
            u -= t * v; std::swap(u, v);
        }
        if(u < 0) u += modulus;
        return u;
    }
    constexpr unsigned int inverse(void) const noexcept {return inverse(val);}
    // a^nを返す関数 : nは負の数でも可
    constexpr unsigned int power(unsigned long long int a, long long int n)const noexcept{
        if(n == 0) return 1;
        unsigned long long res = 1, waiting = a;
        if(n < 0) waiting = inverse(), n = -n;
        while(n != 0){ 
            if((n & 1UL) != 0){ res *= waiting; res %= modulus; }
            waiting *= waiting; waiting %= modulus; 
            n /= 2;
        }
        return res;
    }
    constexpr unsigned int power(long long int n) const noexcept {return power(val, n);}
};


int main(void){
    std::cin.tie(nullptr); std::cin.sync_with_stdio(false);
    int n; std::cin >> n;
    std::vector<int> A(n); for(int i = 0; i < n; ++i) std::cin >> A[i];
    std::sort(A.begin(), A.end(), std::greater<int>());
    long long int res = 0;
    for(int i = 0; i + 1 < n; ++i){
        res += A[i];
    }
    std::cout << res << '\n';



    return 0;
}