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: Accepted)

#pragma region Macros
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define rep2(i, a, b) for(ll i = a; i <= b; ++i)
#define rep(i, n) for(ll i = 0; i < n; ++i)
#define rep3(i, a, b) for(ll i = a; i >= b; --i)
#define pii pair<int, int>
#define pll pair<ll, ll>
#define pb push_back
#define eb emplace_back
#define vi vector<int>
#define vll vector<ll>
#define vpi vector<pii>
#define vpll vector<pll>
#define overload2(_1, _2, name, ...) name
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size)                                                                                                                                  \
    vector<type> name(size);                                                                                                                                   \
    IN(name)
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w)                                                                                                                                   \
    vector<vector<type>> name(h, vector<type>(w));                                                                                                             \
    IN(name)
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define fi first
#define se second
#define all(c) begin(c), end(c)
#define ios ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
using namespace std;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
#define Size(c) (int)(c).size()
#define INT(...)                                                                                                                                               \
    int __VA_ARGS__;                                                                                                                                           \
    IN(__VA_ARGS__)
#define LL(...)                                                                                                                                                \
    ll __VA_ARGS__;                                                                                                                                            \
    IN(__VA_ARGS__)
#define ULL(...)                                                                                                                                               \
    ull __VA_ARGS__;                                                                                                                                           \
    IN(__VA_ARGS__)
#define STR(...)                                                                                                                                               \
    string __VA_ARGS__;                                                                                                                                        \
    IN(__VA_ARGS__)
#define CHR(...)                                                                                                                                               \
    char __VA_ARGS__;                                                                                                                                          \
    IN(__VA_ARGS__)
#define DBL(...)                                                                                                                                               \
    double __VA_ARGS__;                                                                                                                                        \
    IN(__VA_ARGS__)
#define LD(...)                                                                                                                                                \
    ld __VA_ARGS__;                                                                                                                                            \
    IN(__VA_ARGS__)
int scan() { return getchar(); }
template <class T> void scan(T a) { cin >> a; }
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(long double &a) { cin >> a; }
void scan(char a[]) { scanf("%s", a); }
void scan(string &a) { cin >> a; }
template <class T> void scan(vector<T> &);
template <class T, size_t size> void scan(array<T, size> &);
template <class T, class L> void scan(pair<T, L> &);
template <class T, size_t size> void scan(T (&)[size]);
template <class T> void scan(vector<T> &a) {
    for(auto &i : a) scan(i);
}
template <class T> void scan(deque<T> &a) {
    for(auto &i : a) scan(i);
}
template <class T, size_t size> void scan(array<T, size> &a) {
    for(auto &i : a) scan(i);
}
template <class T, class L> void scan(pair<T, L> &p) {
    scan(p.first);
    scan(p.second);
}
template <class T, size_t size> void scan(T (&a)[size]) {
    for(auto &i : a) scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail> void IN(Head &head, Tail &... tail) {
    scan(head);
    IN(tail...);
}
string stin() {
    string s;
    cin >> s;
    return s;
}
template <class T, class S> inline bool chmax(T &a, S b) {
    if(a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T, class S> inline bool chmin(T &a, S b) {
    if(a > b) {
        a = b;
        return 1;
    }
    return 0;
}
vi iota(int n) {
    vi a(n);
    iota(all(a), 0);
    return a;
}
template <class T> void UNIQUE(vector<T> &x) {
    sort(all(x));
    x.erase(unique(all(x)), x.end());
}
int in() {
    int x;
    cin >> x;
    return x;
}
ll lin() {
    unsigned long long x;
    cin >> x;
    return x;
}
void print() { putchar(' '); }
void print(bool a) { cout << a; }
void print(int a) { cout << a; }
void print(long long a) { cout << a; }
void print(char a) { cout << a; }
void print(string &a) { cout << a; }
void print(double a) { cout << a; }
template <class T> void print(const vector<T> &);
template <class T, size_t size> void print(const array<T, size> &);
template <class T, class L> void print(const pair<T, L> &p);
template <class T, size_t size> void print(const T (&)[size]);
template <class T> void print(const vector<T> &a) {
    if(a.empty()) return;
    print(a[0]);
    for(auto i = a.begin(); ++i != a.end();) {
        cout << " ";
        print(*i);
    }
    cout << endl;
}
template <class T> void print(const deque<T> &a) {
    if(a.empty()) return;
    print(a[0]);
    for(auto i = a.begin(); ++i != a.end();) {
        cout << " ";
        print(*i);
    }
}
template <class T, size_t size> void print(const array<T, size> &a) {
    print(a[0]);
    for(auto i = a.begin(); ++i != a.end();) {
        cout << " ";
        print(*i);
    }
}
template <class T, class L> void print(const pair<T, L> &p) {
    cout << '(';
    print(p.first);
    cout << ",";
    print(p.second);
    cout << ')';
}
template <class T> void print(set<T> &x) {
    for(auto e : x) print(e), cout << " ";
    cout << endl;
}
template <class T> void print(multiset<T> &x) {
    for(auto e : x) print(e), cout << " ";
    cout << endl;
}
template <class T, size_t size> void print(const T (&a)[size]) {
    print(a[0]);
    for(auto i = a; ++i != end(a);) {
        cout << " ";
        print(*i);
    }
}
template <class T> void print(const T &a) { cout << a; }
int out() {
    putchar('\n');
    return 0;
}
template <class T> int out(const T &t) {
    print(t);
    putchar('\n');
    return 0;
}
template <class Head, class... Tail> int out(const Head &head, const Tail &... tail) {
    print(head);
    putchar(' ');
    out(tail...);
    return 0;
}
ll gcd(ll a, ll b) {
    while(b) {
        ll c = b;
        b = a % b;
        a = c;
    }
    return a;
}
ll lcm(ll a, ll b) {
    if(!a || !b) return 0;
    return a * b / gcd(a, b);
}
vector<pll> factor(ll x) {
    vector<pll> ans;
    for(ll i = 2; i * i <= x; i++)
        if(x % i == 0) {
            ans.push_back({i, 1});
            while((x /= i) % i == 0) ans.back().second++;
        }
    if(x != 1) ans.push_back({x, 1});
    return ans;
}
vector<int> divisor(int x) {
    vector<int> ans;
    for(int i = 1; i * i <= x; i++)
        if(x % i == 0) {
            ans.pb(i);
            if(i * i != x) ans.pb(x / i);
        }
    return ans;
}
template <typename T> void zip(vector<T> &x) {
    vector<T> y = x;
    sort(all(y));
    for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }
}
int popcount(ll x) { return __builtin_popcountll(x); }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int n) { return uniform_int_distribution<int>(0, n - 1)(rng); }
template <typename T> void shuffle(vector<T> &v) {
    rep3(i, v.size() - 1, 1) { swap(v[i], v[rnd(i)]); }
}
#define endl '\n'
vector<string> YES{"NO", "YES"};
vector<string> Yes{"No", "Yes"};
vector<string> yes{"no", "yes"};

#ifdef _LOCAL
#undef endl
#define debug(x)                                                                                                                                               \
    cout << #x << ": ";                                                                                                                                        \
    print(x);                                                                                                                                                  \
    cout << endl;
void err() {}
template <class T> void err(const T &t) {
    print(t);
    cout << " ";
}
template <class Head, class... Tail> void err(const Head &head, const Tail &... tail) {
    print(head);
    putchar(' ');
    out(tail...);
}
#else
#define debug(x)
template <class... T> void err(const T &...) {}
#endif

template <typename T> struct edge {
    int from, to;
    T cost;
    int id;
    edge(int to, T cost) : from(-1), to(to), cost(cost) {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
    // edge(int from,int to,T cost,int id):from(from),to(to),cost(cost),id(id){}
    edge &operator=(const int &x) {
        to = x;
        return *this;
    }
    operator int() const { return to; }
};
template <typename T> using Edges = vector<edge<T>>;

struct Graph : vector<vector<int>> {
    using vector<vector<int>>::vector;
    inline void add(int a, int b, bool directed = false) {
        (*this)[a].emplace_back(b);
        if(!directed) (*this)[b].emplace_back(a);
    }
    void read(int n = -1, int offset = 1) {
        if(n == -1) n = this->size() - 1;
        int a, b;
        while(n--) {
            cin >> a >> b;
            Graph::add(a - offset, b - offset);
        }
    }
};
template <typename T> struct WeightedGraph : vector<Edges<T>> {
    using vector<Edges<T>>::vector;
    inline void add(int a, int b, T c, bool directed = false) {
        (*this)[a].emplace_back(b, c);
        if(!directed) (*this)[b].emplace_back(a, c);
    }
    void read(int n = -1, int offset = 1) {
        if(n == -1) n = this->size() - 1;
        int a, b;
        while(n--) {
            cin >> a >> b;
            Graph::add(a - offset, b - offset);
        }
    }
};
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(15);
    }
} setup_io;
#pragma endregion

// _________コーディングはここから！！___________
namespace modular {
constexpr ll MOD = 1000000007;
const int MAXN = 1100000;
template <ll Modulus> class modint {
    using u64 = ll;

  public:
    u64 a;

    constexpr modint(const u64 x = 0) noexcept : a(((x % Modulus) + Modulus) % Modulus) {}
    constexpr u64 &value() noexcept { return a; }
    constexpr const u64 &value() const noexcept { return a; }
    constexpr modint operator+(const modint rhs) const noexcept { return modint(*this) += rhs; }
    constexpr modint operator-(const modint rhs) const noexcept { return modint(*this) -= rhs; }
    constexpr modint operator*(const modint rhs) const noexcept { return modint(*this) *= rhs; }
    template <typename T> constexpr modint operator^(T rhs) const noexcept { return modint(*this) ^= rhs; }
    constexpr modint &operator+=(const modint rhs) noexcept {
        a += rhs.a;
        if(a >= Modulus) { a -= Modulus; }
        return *this;
    }
    constexpr modint &operator-=(const modint rhs) noexcept {
        if(a < rhs.a) { a += Modulus; }
        a -= rhs.a;
        return *this;
    }
    constexpr modint &operator*=(const modint rhs) noexcept {
        a = a * rhs.a % Modulus;
        return *this;
    }
    constexpr bool operator==(const modint rhs) const noexcept { return a == rhs.a; }
    template <typename T> constexpr modint &operator^=(T n) noexcept {
        modint<Modulus> res = 1;
        modint<Modulus> x = a;
        while(n) {
            if(n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        a = res.a;
        return *this;
    }
};
#define mint modint<MOD>
#define vmint vector<mint>
vmint Inv{0, 1}, Prd{1, 1}, Invprd{1, 1};
mint inv(int n) {
    if(Inv.size() > n)
        return Inv[n];
    else {
        for(int i = Inv.size(); i <= n; ++i) Inv.emplace_back(Inv[MOD % i] * (-MOD / i));
        return Inv[n];
    }
}
mint prd(int n) {
    if(Prd.size() > n)
        return Prd[n];
    else
        for(int i = Prd.size(); i <= n; ++i) Prd.emplace_back(Prd[i - 1] * i);
    return Prd[n];
}
mint invprd(int n) {
    if(Invprd.size() > n)
        return Invprd[n];
    else
        for(int i = Invprd.size(); i <= n; ++i) Invprd.emplace_back(Invprd[i - 1] * inv(i));
    return Invprd[n];
}
mint modpow(ll a, ll n) {
    mint x = a;
    return x ^= n;
}
template <ll T> modint<T> operator/(modint<T> l, modint<T> r) {
    if(r.a < MAXN) return l * inv(r.a);
    return l * (r ^ (MOD - 2));
}
template <typename T, ll S> modint<S> operator/(T l, modint<S> r) { return modint<S>(l) / r; }
template <ll T> modint<T> operator/=(modint<T> &l, modint<T> r) { return l = l / r; }
mint C(int a, int b) {
    if(a < 0 || b < 0) return 0;
    if(a < b) return 0;
    return prd(a) * invprd(b) * invprd(a - b);
}
mint P(int a, int b) {
    if(a < 0 || b < 0) return 0;
    if(a < b) return 0;
    return prd(a) * invprd(a - b);
}
ostream &operator<<(ostream &os, mint a) {
    os << a.a;
    return os;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &a) {
    for(auto &e : a) os << e << " ";
    os << endl;
    return os;
}
istream &operator>>(istream &is, mint &a) {
    ll x;
    is >> x;
    a = x;
    return is;
}
} // namespace modular
using namespace modular;
main() {
    INT(n);
    VEC(ll, a, n);
    sort(all(a));
    ll ans = a.back();
    a.pop_back();
    n -= 2;
    while(n) {
        ans += a.back() * min(n, 2);
        a.pop_back();
        n -= min(n, 2);
    }
    cout << ans << endl;
}