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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <stdint.h>
#include <string.h>
#include <wchar.h>

#define MIN(a, b) (a < b ? a : b)
#define MAX(a, b) (a > b ? a : b)
#define ABSS(a, b) (a > b ? a - b : b - a)

int compare_f(const void *a, const void *b) {
	return (int)(*(uint32_t *)b) - (int)(*(uint32_t *)a);
}

static size_t comb(const size_t n, const size_t r) {
	size_t result = 1;

	for (size_t i = 0; i < r; i++) {
		result *= n - i;
		result /= i + 1;
	}

	return result;
}

int main(void) {
	size_t N;
	size_t cntOdd = 0;
	size_t cntMul4 = 0;

	scanf("%zu\n", &N);
	for (size_t idx = 0; idx < N; idx++) {
		size_t a;
		scanf((idx != N - 1 ? "%zu " : "%zu"), &a);
		if (a % 2 != 0) {
			cntOdd++;
		}
		else {
			if (a % 4 == 0) {
				cntMul4++;
			}
		}
	}

	puts((cntOdd <= cntMul4 || cntMul4 >= N/2 ? "Yes" : "No"));

	return 0;
}