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 <bits/stdc++.h>
#include <unistd.h>
//#include <ext/pb_ds/assoc_container.hpp> // Common file
//#include <ext/pb_ds/tree_policy.hpp> // Including seg_tree_order_statistics_node_update
#include <stdio.h>
#include <cassert>
using namespace std;
//using namespace __gnu_pbds;
typedef long long lo;
typedef long double ld;
#include <ctime>
typedef pair<lo, lo> ll; //pair
typedef vector<lo> vl;   //vector of long
typedef vector<ll> vll;  //vector of pair
typedef priority_queue<lo> p_q;
typedef vector<vl> vvl; //vector of vectors
#define X first
#define Y second
#define mp(a, b) make_pair((a), (b))
#define REP(a, b) for (lo i = (a); i < (lo)b; i++) //no need to declare variable i
#define REPE(a, b, c, d) \
    REP(a, b)            \
    for (lo j = (c); j < (lo)d; j++)                    //no need to declare vaiables i,j
#define REPV(a, b, c) for (lo(a) = b; (a) < (c); (a)++) //a is the variable
#define IREP(a, b) for (lo i = (a); i >= (b); i--)
#define IREPV(a, b, c) for (lo(a) = b; (a) >= (c); (a)--)
#define correct(x, y, n, m) (0 <= (x) && (x) < (n) && 0 <= (y) && (y) < (m))
#define all(v) (v).begin(), (v).end()
#define TRV(a) for (auto &it : a)
#define INF 500010
#define MOD 1000000007
#define MOD2 1000000009
#define BLOCK 300
#define CHECK_BIT(var, pos) ((var) & (1 << (pos)))
#define pb(a) push_back((a))
#define eps 1e-2
#define PI acos(-1.0)

#if _DEBUG
#define debug(x) cout << #x << "=" << x << endl
#define debug2(x, y) cout << #x << "=" << x << " " << #y << "=" << y << endl;
#define debug3(x, y, z) cout << #x << "=" << x << " " << #y << "=" << y << " " << #z << "=" << z << endl;
#define debug4(x, y, z, w) cout << #x << "=" << x << " " << #y << "=" << y << " " << #z << "=" << z << " " << #w << "=" << w << endl;
#define debug5(x, y, z, w, t)      \
    cout << #x << "=" << x << " "; \
    debug4(y, z, w, t);
#define debug6(p, x, y, z, w, t)                            \
    cout << #p << " " << p << " " << #x << "=" << x << " "; \
    debug4(y, z, w, t);
#define debug7(o, p, x, y, z, w, t) \
    cout << #o << " " << o << " ";  \
    debug6(p, x, y, z, w, t);
#define wait  \
    int xxxx; \
    cin >> xxxx;
#define derr(x) cerr << #x << "=" << x << endl;
#define derr2(x, y) cerr << #x << "=" << x << " " << #y << "=" << y << endl;
#define derr3(x, y, z) cerr << #x << "=" << x << " " << #y << "=" << y << " " << #z << "=" << z << endl;
#define derr4(x, y, z, w) cerr << #x << "=" << x << " " << #y << "=" << y << " " << #z << "=" << z << " " << #w << "=" << w << endl;
#define derr5(x, y, z, w, t)       \
    cerr << #x << "=" << x << " "; \
    derr4(y, z, w, t);
#define derr6(p, x, y, z, w, t)                             \
    cerr << #p << " " << p << " " << #x << "=" << x << " "; \
    derr4(y, z, w, t);
#define derr7(o, p, x, y, z, w, t) \
    cerr << #o << " " << o << " "; \
    derr6(p, x, y, z, w, t);
lo checkpoint_counter = 0;
#define checkpoint cerr << "At checkpoint : " << checkpoint_counter++ << endl;

#else
#define debug(x) ;
#define debug2(x, y) ;
#define debug3(x, y, z) ;
#define debug4(x, y, z, q) ;
#define debug5(x, y, z, r, t) ;
#define debug6(x, y, z, r, t, s) ;
#define debug7(x, y, z, r, t, s, u) ;
#define wait ;
#define derr(x) ;
#define derr2(x, y) ;
#define derr3(x, y, z) ;
#define derr4(x, y, z, q) ;
#define derr5(x, y, z, r, t) ;
#define derr6(x, y, z, r, t, s) ;
#define derr7(x, y, z, r, t, f, u) ;
#define checkpoint ;
#endif

#define print_matrix(a, n, m) \
    REPE(0, n, 0, m) { cout << (a)[i][j] << ((j == m - 1) ? '\n' : ' '); }
#define present(container, element) (container.find(element) != container.end())
#define endl "\n"
template <typename T>
ostream &operator<<(ostream &o, vector<T> v)
{
    if (v.size() > 0)
        o << v[0];
    for (unsigned i = 1; i < v.size(); i++)
        o << " " << v[i];
    return o << " ";
}
template <typename U, typename V>
ostream &operator<<(ostream &o, pair<U, V> p)
{
    return o << "(" << p.first << ", " << p.second << ") ";
}
template <typename T>
istream &operator>>(istream &in, vector<T> &v)
{
    for (unsigned i = 0; i < v.size(); i++)
        in >> v[i];
    return in;
}
template <typename T>
istream &operator>>(istream &in, pair<T, T> &p)
{
    in >> p.X;
    in >> p.Y;
    return in;
}
template <typename T>
ostream &operator<<(ostream &o, set<T> v)
{
    TRV(v)
    o << it << " ";
    return o << endl;
}
template <typename T, typename U>
ostream &operator<<(ostream &o, map<T, U> v)
{
    TRV(v)
    o << it << " ";
    return o << endl;
}
template <typename T>
T &&vmin(T &&val)
{
    return std::forward<T>(val);
}

template <typename T0, typename T1, typename... Ts>
auto vmin(T0 &&val1, T1 &&val2, Ts &&... vs)
{
    return (val1 < val2) ? vmin(val1, std::forward<Ts>(vs)...) : vmin(val2, std::forward<Ts>(vs)...);
}
template <typename T>
T &&vmax(T &&val)
{
    return std::forward<T>(val);
}

template <typename T0, typename T1, typename... Ts>
auto vmax(T0 &&val1, T1 &&val2, Ts &&... vs)
{
    return (val1 > val2) ? vmax(val1, std::forward<Ts>(vs)...) : vmax(val2, std::forward<Ts>(vs)...);
}
struct custom_hash
{
    static uint64_t splitmix64(uint64_t x)
    {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const
    {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};
lo Pow(lo x, lo n)
{
    lo res = 1;
    while (n > 0)
    {
        if (n & 1)
            res = (res * x) % MOD;
        x = (x * x) % MOD;
        n /= 2;
    }
    return res;
}
lo inv(lo n)
{
    return Pow(n, MOD - 2);
}
int main(int argc, char *argv[])
{
    std::ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cout.precision(20);
    lo n;
    cin >> n;
    vl A(n);
    cin >> A;
    cout << accumulate(all(A), 0LL) - *min_element(all(A)) << endl;
    return 0;
}