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)

// AtCoder Regular Contest 080 C - 4-adjacent
// 2018.1.11 bal4u

#include <stdio.h>
#include <string.h>

#define getchar_unlocked()  getchar()
int in()
{
	int n = 0;
	int c = getchar_unlocked();
	do n = (n<<3)+(n<<1) + (c & 0xf), c = getchar_unlocked();
	while (c >= '0');
	return n;
}

int main()
{
	int N, a;
	int i, n4, odd, ans;			// n4: 4の倍数

	odd = n4 = 0;
	N = in();
	for (i = 0; i < N; i++) {
		a = in();
		if (a & 1) odd++;
		else if (!(a & 3)) n4++;
	}
	ans = 0;
	if (n4 >= odd) ans = 1;
	else if (n4 == odd-1 && odd + n4 == N) ans = 1;
	puts(ans? "Yes": "No");
	return 0;
}