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 Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

module module_sort
    use iso_fortran_env
    implicit none

    interface quicksort
        module procedure :: int32_qsort
        module procedure :: int64_qsort
    end interface quicksort
contains

    recursive function int32_qsort(m) result(res)
        integer(int32), intent(in) :: m(:)
        integer(int32) :: res(size(m)) 

        if (size(m) <= 1) then; res = m
        else; res = [int32_qsort( pack(m(2:), m(2:) >= m(1)) ), m(1), int32_qsort( pack(m(2:), m(2:) < m(1)) )]
        end if

    end function int32_qsort

    recursive function int64_qsort(m) result(res)
        integer(int64), intent(in) :: m(:)
        integer(int64) :: res(size(m)) 

        if (size(m) <= 1) then; res = m
        else; res = [int64_qsort( pack(m(2:), m(2:) >= m(1)) ), m(1), int64_qsort( pack(m(2:), m(2:) < m(1)) )]
        end if

    end function int64_qsort

end module module_sort

program main
    use module_sort
    use iso_fortran_env
    implicit none
    integer(int32) :: n
    integer(int32), allocatable :: ai(:)
    integer(int32) :: i, ie
    integer(int32) :: ans

    read *, n
    allocate( ai(n) )
    read *, ai( 1:n )
    ai = quicksort( ai )
!    call qsort( ai )
!    ai(n:1:-1) = ai(1:n)
!    ai = intQsort( ai )
!    ai(n:1:-1) = ai(1:n)

    if ( mod((n-1), 2) == 0 ) then
        ie = (n-1) / 2
        ans = ai(1) + ai(ie + 1)
    else
        ie = n / 2
        ans = ai(1)
    endif

    do i = 2, ie
        ans = ans + ai(i) * 2
    enddo

    print *, ans

contains

recursive subroutine qsort(a)
  implicit none
  integer(8),intent(inout) :: a(:)
  integer(8)::i,j,toobig,toosmall,pv,n

  n = size(a)
i = 1
j = n
pv = a((i+j)/2)
do
   do
     if (a(i) < pv) then
       i = i+1
     else
       exit
     end if
   end do
   do
     if(a(j) > pv) then
       j = j-1
     else
       exit
     end if
   end do
   if (i>=j) then
     exit
   else
     toobig = a(j)
     toosmall = a(i)
     a(i) = toobig
     a(j) = toosmall
     i = i+1
     j = j-1
   end if
 end do
 if (i > 2) then
   call qsort(a(1:i-1))
 end if
 if (j < n-1) then
   call qsort(a(j+1:n))
 end if
end subroutine qsort

pure recursive function intQsort( a ) result( r )
implicit none
integer(16), intent(in) :: a(:)
integer(16) :: r( size(a) )
integer(16) :: sample(3), len, i,j

len = size( a(:) )
if( len<=1 )then
  r = a
else
  !select pivot
  sample(1:3) = [a(1), a(len/2), a(len)]
  do i = 1,2
    do j = 2,3
      if( sample(i)>sample(j) )then
        len = sample(i) !len is buffer
        sample(i) = sample(j)
        sample(j) = len
      end if
    end do
  end do
  
  r = [ intQsort( pack(a(:), a(:)< sample(2)) ), &
                  pack(a(:), a(:)==sample(2))  , &
        intQsort( pack(a(:), a(:)> sample(2)) ) ]
end if
end function intQsort

end program main