Problem:
Score : 300 points

Problem Statement

There are N people, conveniently numbered 1 through N.
They were standing in a row yesterday, but now they are unsure of the order in which they were standing.
However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.
According to their reports, the difference above for person i is A_i.

Based on these reports, find the number of the possible orders in which they were standing.
Since it can be extremely large, print the answer modulo 10^9+7.
Note that the reports may be incorrect and thus there may be no consistent order.
In such a case, print 0.

Constraints

1≦N≦10^5

0≦A_i≦N-1

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 orders in which they were standing, modulo 10^9+7.

Sample Input 1

5
2 4 4 0 2

Sample Output 1

4

There are four possible orders, as follows:

2,1,4,5,3

2,5,4,1,3

3,1,4,5,2

3,5,4,1,2

Sample Input 2

7
6 4 0 2 4 0 2

Sample Output 2

0

Any order would be inconsistent with the reports, thus the answer is 0.

Sample Input 3

8
7 5 1 1 7 3 5 3

Sample Output 3

16

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

PROGRAM ATCODER

implicit none
integer(16) :: n,i,ans
integer(16),allocatable :: a(:)

read*, n
allocate(a(n))
read*, a(1:n)

call hs(n,a)

do i = n-1, 0, -2
  if ( i == 0 ) then
    if ( a(1) /= 0 ) stop
    exit
  end if
  if ( 2*i /= a(i)+a(i+1) ) then
    print'(i0)', 0
    stop
  end if
end do

ans = 1
do i = 1, n/2
  ans = mod(ans*2,10**9+7)
end do

print'(i0)', ans 

contains
!!!!!! サブルーチンは↓
subroutine hs(n,array)
  implicit none
  integer(16),intent(in)::n
  integer(16),intent(inout)::array(1:n)
  
  integer(16)::i,k,j,l,m
  integer(16)::t
  
  if(n.le.0)then
     write(6,*)"Error, at heapsort"; stop
  endif
  if(n.eq.1)return
 
  l=n/2+1
  k=n
  do while(k.ne.1)
     if(l.gt.1)then
        l=l-1
        t=array(l)
     else
        t=array(k)
        array(k)=array(1)
        k=k-1
        if(k.eq.1) then
           array(1)=t
           exit
        endif
     endif
     i=l
     j=l+l
     do while(j.le.k)
        if(j.lt.k)then
           if(array(j).lt.array(j+1))j=j+1
        endif
        if (t.lt.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
!!!!!!

END PROGRAM ATCODER