Problem:
Score : 400 points

Problem Statement

We have a sequence of length N, a = (a_1, a_2, ..., a_N).
Each a_i is a positive integer.

Snuke's objective is to permute the element in a so that the following condition is satisfied:

For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.

Determine whether Snuke can achieve his objective.

Constraints

2 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

If Snuke can achieve his objective, print Yes; otherwise, print No.

Sample Input 1

3
1 10 100

Sample Output 1

Yes

One solution is (1, 100, 10).

Sample Input 2

4
1 2 3 4

Sample Output 2

No

It is impossible to permute a so that the condition is satisfied.

Sample Input 3

3
1 4 1

Sample Output 3

Yes

The condition is already satisfied initially.

Sample Input 4

2
1 1

Sample Output 4

No

Sample Input 5

6
2 7 1 8 2 8

Sample Output 5

Yes

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

program ABC_069_C_4adjacent
   implicit none
   integer N, i, countN2, countN4
   integer(8), allocatable :: a(:)
   read(*, *) N
   allocate(a(1: N))
   read(*, *) a(1: N)
   countN2 = 0
   countN4 = 0
   do i = 1, N
       if(mod(a(i), 2) == 0) then
	       countN2 = countN2 + 1
	   end if
	   if(mod(a(i), 4) == 0) then
	       countN4 = countN4 + 1
	   end if
   end do
   if(N/2 <= countN4) then
       write(*, *) 'Yes' 
   else if(N - 2*countN4 <= countN2 - countN4) then
       write(*, *) 'Yes'
   else
       write(*, *) 'No'
   end if
end program ABC_069_C_4adjacent