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 LuaJIT (2.0.4) (judge verdict: Accepted)

local n = io.read("*n", "*l")
local str = io.read()
local t = {0, 0, 0}
for v in str:gmatch("%d+") do
  local a = tonumber(v)
  if a % 4 == 0 then
    t[1] = t[1] + 1
  elseif a % 2 == 0 then
    t[2] = t[2] + 1
  else
    t[3] = t[3] + 1
  end
end
if n == 1 then
  if t[3] == 1 then
    print("Yes")
  else
    print("No")
  end
elseif t[1] + 1 < t[3] then
  print("No")
elseif t[1] + 1 == t[3] then
  if t[2] == 0 then
    print("Yes")
  else
    print("No")
  end
else
  print("Yes")
end