Problem:
Score : 400 points

Problem Statement

Snuke found N strange creatures.
Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.

Every creature can absorb another creature whose size is at most twice the size of itself.
When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B.
Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.

Snuke has been watching these creatures merge over and over and ultimately become one creature.
Find the number of the possible colors of this creature.

Constraints

2 \leq N \leq 100000

1 \leq A_i \leq 10^9

A_i is an integer.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 … A_N

Output

Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.

Sample Input 1

3
3 1 4

Sample Output 1

2

The possible colors of the last remaining creature are colors 1 and 3.
For example, when the creature of color 3 absorbs the creature of color 2, then the creature of color 1 absorbs the creature of color 3, the color of the last remaining creature will be color 1.

Sample Input 2

5
1 1 1 1 1

Sample Output 2

5

There may be multiple creatures of the same size.

Sample Input 3

6
40 1 30 2 7 20

Sample Output 3

4

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

module merge_sort_mod
    use,intrinsic :: iso_fortran_env
    implicit none
    private
    public:: merge_sort, double_merge_sort
    interface merge_sort
        module procedure ms32, ms64
    end interface

    interface double_merge_sort
        module procedure msd3232, msd6464
    end interface
contains
    recursive subroutine ms32(ar, fst, lst)
        integer(int32),intent(inout):: ar(:)
        integer(int32),intent(in):: fst,lst
        integer(int32):: mdl

        if (lst-fst < 2) then
            if (ar(fst) > ar(lst)) call swap32(ar(fst),ar(lst))
            return
        end if

        mdl = (fst+lst)/2
        call ms32(ar, fst, mdl)
        call ms32(ar, mdl+1, lst)
        call merge32(ar, fst, mdl, lst)
    end subroutine


    subroutine merge32(ar, fst, mdl, lst)
        integer(int32),intent(inout):: ar(:)
        integer(int32),intent(in):: fst, mdl, lst
        integer(int32),allocatable:: tmp(:)
        integer(int32):: li, ri, ti

        allocate(tmp(lst-fst+1))

        li=fst
        ri=mdl+1   
        ti=1

        do while (li <= mdl .and. ri <= lst)
            if (ar(li) <= ar(ri)) then
                tmp(ti) = ar(li)
                li=li+1
            else
                tmp(ti) = ar(ri)
                ri=ri+1
            end if
            ti=ti+1
        end do

        if (li <= mdl) then
            tmp(ti:) = ar(li:mdl)
        else
            tmp(ti:) = ar(ri:lst)
        end if

        ar(fst:lst) = tmp(:)
        deallocate(tmp)
    end subroutine


    subroutine swap32(x,y)
        integer(int32),intent(inout):: x,y
        integer(int32):: tmp
        tmp = x
        x = y
        y = tmp
    end subroutine


    recursive subroutine ms64(ar, fst, lst)
        integer(int64),intent(inout):: ar(:)
        integer(int64),intent(in):: fst,lst
        integer(int64):: mdl

        if (lst-fst < 2) then
            if (ar(fst) > ar(lst)) call swap64(ar(fst),ar(lst))
            return
        end if

        mdl = (fst+lst)/2
        call ms64(ar, fst, mdl)
        call ms64(ar, mdl+1, lst)
        call merge64(ar, fst, mdl, lst)
    end subroutine


    subroutine merge64(ar, fst, mdl, lst)
        integer(int64),intent(inout):: ar(:)
        integer(int64),intent(in):: fst, mdl, lst
        integer(int64),allocatable:: tmp(:)
        integer(int64):: li, ri, ti

        allocate(tmp(lst-fst+1))

        li=fst
        ri=mdl+1   
        ti=1

        do while (li <= mdl .and. ri <= lst)
            if (ar(li) <= ar(ri)) then
                tmp(ti) = ar(li)
                li=li+1
            else
                tmp(ti) = ar(ri)
                ri=ri+1
            end if
            ti=ti+1
        end do

        if (li <= mdl) then
            tmp(ti:) = ar(li:mdl)
        else
            tmp(ti:) = ar(ri:lst)
        end if

        ar(fst:lst) = tmp(:)
        deallocate(tmp)
    end subroutine


    subroutine swap64(x,y)
        integer(int64),intent(inout):: x,y
        integer(int64):: tmp
        tmp = x
        x = y
        y = tmp
    end subroutine

    recursive subroutine msd3232(ar1, ar2, fst, lst)
        integer(int32),intent(inout):: ar1(:),ar2(:)
        integer(int32),intent(in):: fst,lst
        integer(int32):: mdl

        if (lst - fst < 2) then
            if (ar1(fst) > ar1(lst)) then
                call swap32(ar1(fst), ar1(lst))
                call swap32(ar2(fst), ar2(lst))
            end if
            return
        end if

        mdl = (fst+lst)/2

        call msd3232(ar1,ar2,fst,mdl)
        call msd3232(ar1,ar2,mdl+1,lst)
        call merged3232(ar1,ar2,fst,mdl,lst)
    end subroutine


    subroutine merged3232(ar1,ar2,fst,mdl,lst)
        integer(int32),intent(inout):: ar1(:),ar2(:)
        integer(int32),intent(in):: fst,mdl,lst
        integer(int32),allocatable:: t1(:),t2(:)
        integer(int32):: li,ri,ti

        allocate(t1(lst-fst+1), t2(lst-fst+1))

        li=fst
        ri=mdl+1
        ti=1

        do while(li <= mdl .and. ri <= lst)
            if (ar1(li) <= ar1(ri)) then
                t1(ti) = ar1(li) 
                t2(ti) = ar2(li)
                li=li+1
            else
                t1(ti) = ar1(ri)
                t2(ti) = ar2(ri)
                ri=ri+1
            end if
            ti=ti+1
        end do

        if (li <= mdl) then
            t1(ti:) = ar1(li:mdl)
            t2(ti:) = ar2(li:mdl)
        else
            t1(ti:) = ar1(ri:lst)
            t2(ti:) = ar2(ri:lst)
        end if

        ar1(fst:lst) = t1(:)
        ar2(fst:lst) = t2(:)

        deallocate(t1,t2)
    end subroutine


    recursive subroutine msd6464(ar1, ar2, fst, lst)
        integer(int64),intent(inout):: ar1(:),ar2(:)
        integer(int64),intent(in):: fst,lst
        integer(int64):: mdl

        if (lst - fst < 2) then
            if (ar1(fst) > ar1(lst)) then
                call swap64(ar1(fst), ar1(lst))
                call swap64(ar2(fst), ar2(lst))
            end if
            return
        end if

        mdl = (fst+lst)/2

        call msd6464(ar1,ar2,fst,mdl)
        call msd6464(ar1,ar2,mdl+1,lst)
        call merged6464(ar1,ar2,fst,mdl,lst)
    end subroutine


    subroutine merged6464(ar1,ar2,fst,mdl,lst)
        integer(int64),intent(inout):: ar1(:),ar2(:)
        integer(int64),intent(in):: fst,mdl,lst
        integer(int64),allocatable:: t1(:),t2(:)
        integer(int64):: li,ri,ti

        allocate(t1(lst-fst+1), t2(lst-fst+1))

        li=fst
        ri=mdl+1
        ti=1

        do while(li <= mdl .and. ri <= lst)
            if (ar1(li) <= ar1(ri)) then
                t1(ti) = ar1(li) 
                t2(ti) = ar2(li)
                li=li+1
            else
                t1(ti) = ar1(ri)
                t2(ti) = ar2(ri)
                ri=ri+1
            end if
            ti=ti+1
        end do

        if (li <= mdl) then
            t1(ti:) = ar1(li:mdl)
            t2(ti:) = ar2(li:mdl)
        else
            t1(ti:) = ar1(ri:lst)
            t2(ti:) = ar2(ri:lst)
        end if

        ar1(fst:lst) = t1(:)
        ar2(fst:lst) = t2(:)

        deallocate(t1,t2)
    end subroutine
end module


program agc011
    use,intrinsic :: iso_fortran_env
    use merge_sort_mod
    implicit none
    integer(int32):: n,i
    integer(int64),allocatable:: a(:), cnt(:)

    read*, n
    allocate(a(n))
    allocate(cnt(n), source=1_8)
    read*, a(:)

    call merge_sort(a,1_8,int(n,kind=int64))

    do i=1,n-1
        if (a(i)*2 >= a(i+1)) cnt(i+1) = cnt(i)+cnt(i+1)
        a(i+1)=a(i+1)+a(i)
    end do
    print'(i0)', cnt(n)
end program agc011