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<fstream>
#include<bitset>
#include<string>
#include<vector>
#include<list>
#include<algorithm>
#include<cmath>
#include<map>
#include<set>
#include<iomanip>
#include<queue>
#include<stack>
#include<numeric>
#include<utility>
#include<regex>
#include<climits>
#include<ctime>

using namespace std;

void Init() {
	std::cin.tie(0); std::ios::sync_with_stdio(false);
	struct Init_caller { Init_caller() { Init(); } }caller;
}



#define int long long
#define rep(i,n) for(LL i=0;i<(n);i++)
#define rep1(i,n) for(LL i=1;i<(n);i++)
#define rrep(i,n) for(LL i=(n)-1;i>=0;i--)
#define all(a) (a).begin(),(a).end()
#define check() cout<<"! ! !"<<endl
#define endl "\n"
#define _y() cout<<"Yes"<<endl
#define _Y() cout<<"YES"<<endl
#define _n() cout<<"No"<<endl
#define _N() cout<<"NO"<<endl



constexpr long long INF = (long long)1e15;
constexpr long long MOD = 1000000007;



using LL = long long;
using st = string;
template<typename T>using vec = vector<T>;
template<typename T>using vvec = vec<vec<T>>;
template<typename T>using vvvec = vec<vvec<T>>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vd = vector<double>;
using vvd = vector<vd>;
using vvvd = vector<vvd>;
using vc = vector<char>;
using vvc = vector<vc>;
using vs = vector<st>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vvvb = vector<vvb>;
using pi = pair<int, int>;
using ppi = pair<pi, int>;
using vpi = vector<pi>;
using vppi = vector<ppi>;
using mii = map<int, int>;
using mpii = map<pi, int>;
using mib = map<int, bool>;
using mci = map<char, int>;
template<typename T>using pq_greater = priority_queue<T>;
template<typename T>using pq_smaller = priority_queue<T, vec<T>, greater<T>>;


//4,2,8,6,1,7,3,9,5 (x:right y:up is positive)
int dx[] = { -1,0,0,1,-1,-1,1,1,0 };
int dy[] = { 0,1,-1,0,1,-1,1,-1,0 };

template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
	rep(i, v.size()) {
		in >> v[i];
	}
	return in;
}

template<typename T, typename U>
istream &operator>>(istream&in, pair<T, U> &p) {

	in >> p.first >> p.second;
	return in;
}

template<typename T>
ostream &operator<<(ostream &out, vector<T> &v) {
	out << "{";
	rep(i, v.size()) {
		out << v[i] << ",";
	}
	out << "}" << endl;

	return out;
}

template<typename T, typename U>
ostream &operator<<(ostream&out, pair<T, U> &p) {

	out << "{" << p.first << "," << p.second << "}" << endl;
	return out;
}

struct mint {
	int x;
	mint(int x = 0) :x((x%MOD + MOD) % MOD) {}

	mint operator-() const { return mint(-x); }
	mint& operator+=(const mint a) {
		if ((x += a.x) >= MOD) x -= MOD;
		return *this;
	}
	mint& operator-=(const mint a) {
		if ((x += MOD - a.x) >= MOD) x -= MOD;
		return *this;
	}
	mint& operator*=(const mint a) {
		(x *= a.x) %= MOD;
		return *this;
	}
	mint operator+(const mint a) const {
		mint res(*this);
		return res += a;
	}
	mint operator-(const mint a) const {
		mint res(*this);
		return res -= a;
	}
	mint operator*(const mint a) const {
		mint res(*this);
		return res *= a;
	}
	mint pow(int t) const {
		if (!t) return 1;
		mint a = pow(t >> 1);
		a *= a;
		if (t & 1) a *= *this;
		return a;
	}

	mint inv() const {
		return pow(MOD - 2);
	}
	mint& operator/=(const mint a) {
		return (*this) *= a.inv();
	}
	mint operator/(const mint a) const {
		mint res(*this);
		return res /= a;
	}

};

void y_n(bool p) {
	p ? _y() : _n();
}

void Y_N(bool p) {
	p ? _Y() : _N();
}

//MAX,maxpos,MIN,minpos
template<typename T>
pair<pair<T, int>, pair<T, int>> vmaxmin(vector<T> v) {
	int MAX = -INF;
	int MIN = INF;
	int maxpos = 0;
	int minpos = 0;
	rep(i, v.size()) {
		if (MAX < v[i]) {
			maxpos = i;
			MAX = v[i];
		}
		if (MIN > v[i]) {
			minpos = i;
			MIN = v[i];
		}
	}
	return { {MAX,maxpos},{MIN,minpos} };
}

template<typename T>
T vsum(vector<T> v) {
	T sum = 0;
	rep(i, v.size()) {
		sum += v[i];
	}
	return sum;
}

int gcd(int a, int b) {
	if (b == 0) {
		swap(a, b);
	}
	int r;
	while ((r = a % b) != 0) {
		a = b;
		b = r;
	}
	return b;
}

int lcm(int a, int b) {
	return (a / gcd(a, b) * b);
}

bool is_square(int n) {
	if ((int)sqrt(n)*(int)sqrt(n) == n) {
		return true;
	}
	else {
		return false;
	}
}


bool is_prime(int n) {
	if (n <= 1) {
		return false;
	}
	else {
		for (int i = 2; i*i <= n; i++) {
			if (n % i == 0) {
				return false;
			}
		}
	}
	return true;
}

void dec_num(int n, vi &v) {
	int a = 2;
	v.push_back(1);
	v.push_back(n);
	while (a*a <= n) {
		if (n%a == 0) {
			v.push_back(a);
			v.push_back(n / a);
		}
		a++;
	}
	sort(all(v));
	v.erase(unique(all(v)), v.end());
}


void dec_prime(int n, vi &v) {
	//v.push_back(1);
	int a = 2;
	while (a*a <= n) {
		if (n % a == 0) {
			v.push_back(a);
			n /= a;
		}
		else {
			a++;
		}
	}
	v.push_back(n);
}

//n= ...*pow(p_i,m[p_i])*...
void dec_prime_e(int n, map<int, int> &m) {
	for (int i = 2; i*i <= n; i++) {
		if (n%i == 0) {
			int e = 0;
			while (n%i == 0) {
				e++;
				n /= i;
			}
			m[i] += e;
		}
	}
	if (n != 1) m[n]++;
}


int sieve_prime(int a, int b) {
	if (a > b)swap(a, b);
	vb s(b + 1, true);
	int cnt_a = 0, cnt_b = 0;
	for (int i = 2; i <= b; i++) {
		for (int j = 2; i*j <= b; j++) {
			s[i*j] = false;
		}
	}
	//return s;
	for (int i = 2; i <= b; i++) {
		if (s[i]) {
			//cout << i << " ";
			if (i < a) {
				cnt_a++;
			}
			cnt_b++;
		}
	}
	return cnt_b - cnt_a;

}


int factorial(int n) {
	int a = 1, ret = 1;
	while (a < n) {
		a++;
		ret *= a;
		//ret %= MOD;
	}
	return ret;
}

int bit_count(int n) {
	int k = (int)log2(n) + 1;
	int ret = 0;
	rep(i, k) {
		if (n&(1LL << i))ret++;
	}
	return ret;
}

//a^(a+1)^(a+2)^...^b
int XOR(int a, int b) {
	if (a == 0) {
		switch (b % 4) {
		case 0:	return b;
		case 1:	return 1;
		case 2:	return (b + 1);
		case 3:	return 0;
		}
	}
	int A = XOR(0, a - 1);
	int B = XOR(0, b);
	return (A ^ B);
}


const int COMBMAX = 4000;
int comb[COMBMAX + 5][COMBMAX + 5];

void init_comb() {
	comb[0][0] = 1;
	rep(i, COMBMAX) {
		rep(j, i + 1) {
			comb[i + 1][j] += comb[i][j];
			//comb[i + 1][j] %= MOD;
			comb[i + 1][j + 1] += comb[i][j];
			//comb[i + 1][j + 1] %= MOD;
		}
	}
}

int combination(int n, int k) {
	if (k<0 || k>n)return 0;
	else return comb[n][k];
}


const int COMBMODMAX = 5000000;
int fac[COMBMODMAX + 5], facinv[COMBMODMAX + 5], inv[COMBMODMAX + 5];

void init_comb_mod() {
	fac[0] = fac[1] = 1;
	facinv[0] = facinv[1] = 1;
	inv[1] = 1;
	for (int i = 2; i < COMBMODMAX; i++) {
		fac[i] = fac[i - 1] * i%MOD;
		inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
		facinv[i] = facinv[i - 1] * inv[i] % MOD;
	}
}

//nCk (mod p)
//nHk = n+k-1Ck
int comb_mod(int n, int k) {
	if (n < k)return 0;
	if (n < 0 || k < 0)return 0;
	return fac[n] * (facinv[k] * facinv[n - k] % MOD) % MOD;
}

//x^n (mod p)
int pow_mod(int x, int n, int p) {
	if (n == 0)return 1;
	int res = pow_mod(x*x%p, n / 2, p);
	if (n % 2 == 1)res = res * x % p;
	return res;
}

struct edge {
	int to;
	int cost;
};

using ve = vector<edge>;
using vve = vector<ve>;


/*****************************************************************************/

signed main() {



	int n;
	cin >> n;
	vi a(n);
	cin >> a;
	sort(all(a), greater<int>());
	mii m;
	rep(i, n) {
		m[a[i]]++;
	}
	a.erase(unique(all(a)), a.end());
	int ans = 0;
	ans += a[0] * (m[a[0]] - 1);
	rep1(i, a.size()) {
		ans += a[i - 1] * min(m[a[i - 1]], m[a[i]]);
		ans += a[i] * (m[a[i]] - 1);
	}
	cout << ans;







	
}