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 name
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int32):: n,i,mul4=0, odd=0
    integer(int32), allocatable:: a(:)

    read*, n
    allocate(a(n))
    read*, a(:)
    do i=1,n
        if (btest(a(i),0))then
            odd=odd+1
        else if (mod(a(i),4) == 0) then
            mul4=mul4+1
        end if
    end do

    if (mul4 >= odd) then
        print'(a)', 'Yes'
    else
        if (mul4+1 == odd .and. mul4+odd == n) then
            print'(a)', 'Yes'
        else
            print'(a)', 'No'
        end if
    end if
end program name