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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

program ec12;
var 
	a,j,t,s:array[1..100001] of longint;
	n,m,i,tot1,tot2,tot3:longint;
begin 
	readln(n);
	tot1:=0;
	tot2:=0;
	tot3:=0;
	for i:=1 to n do 
	begin 
		read(a[i]);	
		if a[i] mod 2=1 then 
		inc(tot1)
		else
		begin 
			if a[i] mod 4=0 then 
			inc(tot3)
			else
			inc(tot2);
		end;
	end;
	if tot3<tot1-1 then 
	begin 
		writeln('No');
		halt;
	end;
	if (tot3=tot1-1) and (tot2>0) then 
	begin 
		writeln('No');
		halt;
	end;
	writeln('Yes');
end.