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: Accepted)

require 'pp'

n = gets.chomp!.to_i
a_n = gets.chomp!.split(" ").map(&:to_i)

x = {0 => 0, 2 => 0, 4 => 0}.merge(a_n.group_by {|a|
    if a % 4 == 0
        4
    elsif a% 2 == 0
        2
    else
        0
    end
}.map {|k, v|
    [k, v.length]
}.to_h)

sum = 0
# 4の倍数だけでカバーできる数
if x[4] * 2 + 1 >= n
    puts "Yes"
else
    remain = n - (x[4] * 2)
    if x[2] >= remain
        puts "Yes"
    else
        puts "No"
    end
end