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 Ruby (2.3.3) (judge verdict: Wrong Answer)

#!/usr/bin/ruby
N,*A=`dd`.split.map &:to_i
h=Hash.new 0
A.each{|e|
	if e%4==0
		h[2]+=1
	elsif e%2==0
		h[1]+=1
	else
		h[0]+=1
	end
}
a=nil
if h[0]>0
	a=0
	h[0]-=1
elsif h[1]>0
	a=1
	h[1]-=1
else
	a=2
	h[2]-=1
end
while h.values.any?{|e|e>0}
	if a==0&&h[2]>0
		a=2
		h[2]-=1
	elsif a==1&&h[1]>0
		a=1
		h[0]-=1
	elsif a==1&&h[2]>0
		a=2
		h[2]-=1
	elsif h[0]>0
		a=0
		h[0]-=1
	elsif h[1]>0
		a=1
		h[1]-=1
	elsif h[2]>0
		a=2
		h[2]-=1
	else
		puts :No
		exit
	end
end
puts :Yes