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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(let* ((n (read))
       (a (make-array n))
       (four 0)
       (two 0))
  (dotimes (i n)
    (let ((ai (read)))
      (if (zerop (mod ai 4))
          (incf four)
          (when (zerop (mod ai 2))
            (incf two)))
      (setf (aref a i) ai)))
  (format t "~A~%"
          (if (<= (1- n) (max
                           (if (< 0 four) (min 2 (+ four 2)) 0)
                           (if (<= 2 two) two 0)
                           (if (and (< 0 four)
                                    (<= 2 two))
                             (+ (if (evenp n) 0 1) four (1- two))
                             0)
                         (if (and (<= 2 four)
                                  (<= 2 two))
                             (+ 2 four (1- two))
                             0)))
              "Yes" "No")))