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)

integer N
integer,allocatable,dimension(:)::A
integer cnt4,cnt2,cntodd
read*,N
allocate(A(N))
read*,A
cnt4=0;cnt2=0;cntodd=0
do i=1,N
  select case(mod(A(i),4))
    case(0)
      cnt4=cnt4+1
    case(2)
      cnt2=cnt2+1
    case default 
      cntodd=cntodd+1
  end select
end do
if(cnt2>0)cntodd=cntodd+1
print"(A)",trim(merge("Yes","No ",cntodd<=cnt4+1))
end