Problem:
Score : 300 points

Problem Statement

There are N monsters, numbered 1, 2, ..., N.

Initially, the health of Monster i is A_i.

Below, a monster with at least 1 health is called alive.

Until there is only one alive monster, the following is repeated:

A random alive monster attacks another random alive monster.

As a result, the health of the monster attacked is reduced by the amount equal to the current health of the monster attacking.

Find the minimum possible final health of the last monster alive.

Constraints

All values in input are integers.

2 \leq N \leq 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 ... A_N

Output

Print the minimum possible final health of the last monster alive.

Sample Input 1

4
2 10 8 40

Sample Output 1

2

When only the first monster keeps on attacking, the final health of the last monster will be 2, which is minimum.

Sample Input 2

4
5 13 8 1000000000

Sample Output 2

1

Sample Input 3

3
1000000000 1000000000 1000000000

Sample Output 3

1000000000

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

PROGRAM ATCODER

implicit none
integer :: n, i, check
integer, allocatable :: a(:), m(:)

read(*,*) n
allocate (a(n), m(n-1))
read(*,*) (a(i), i=1,n)

call hs(n,a)

check = 0
do i = 1, n-1
	m(i) = mod(a(n),a(i))
    if(m(i) /= 0) then
    	check = 1
    end if
end do

if(check == 1)then
	write(*,'(i0)') 1
else
	write(*,'(i0)') a(1)
end if

END PROGRAM ATCODER

subroutine hs(n,array)
  implicit none
  integer,intent(in) :: n
  integer,intent(inout) :: array(1:n)
  
  integer ::i,k,j,l
  integer :: t
  
  if(n <= 0)then
     write(6,*)"Error, at heapsort"; stop
  endif
  if(n == 1)return
 
  l=n/2+1
  k=n
  do while(k /= 1)
     if(l > 1)then
        l=l-1
        t=array(L)
     else
        t=array(k)
        array(k)=array(1)
        k=k-1
        if(k == 1) then
           array(1)=t
           exit
        endif
     endif
     i=l
     j=l+l
     do while(j <= k)
        if(j < k)then
           if(array(j) < array(j+1))j=j+1
        endif
        if (t < array(j))then
           array(i)=array(j)
           i=j
           j=j+j
        else
           j=k+1
        endif
     enddo
     array(i)=t
  enddo
 
  return
end subroutine hs