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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main(int argc, char *argv[])
{
	int i, N, kisu = 0, time2 = 0, time4 = 0;
	scanf("%d", &N);
	for ( i = 0; i < N; i++ ){
		int a;
		scanf("%d", &a);
		if ( a%2 == 1 ){
			kisu++;
		} else if ( a%4 == 0 ){
			time4++;
		} else {
			time2++;
		}
	}
	if ( kisu > time4 + 1 ){
		printf("No\n");
	} else if ( kisu == time4 + 1 ){
		if ( time2 > 0 ){
			printf("No\n");
		} else {
			printf("Yes\n");
		}
	} else {
		printf("Yes\n");
	}
	return 0;
}