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>
#include <stdlib.h>
#include <string.h>

#define type1 0 // 4の倍数
#define type2 1 // 4の倍数ではないが2の倍数
#define type3 2 // 奇数

int get_type(long int num) {
	if(num % 2 == 1)
		return 2;
	else if(num % 4 == 0)
		return 0;
	else
		return 1;
}

int main(void) {
	long int array[100000];
	int k, s, g, i = 0, N;
	char s1[2000000];
	char *tok;

	scanf("%d", &N);
	gets(s1);
	gets(s1);

	tok = strtok(s1, ". ");
	array[i++] = atol(tok);
	while(1) {
		tok = strtok(NULL, ". ");
		if(tok == NULL)
			break;
		array[i++] = atol(tok);
	}

	for(i = 0; i < N; i++) {
		array[i] = get_type(array[i]);
		switch(array[i]) {
			case type1:
				s++;
				break;
			case type2:
				g++;
				break;
			default:
				k++;
		}
	}
	
	if(k == s + 1) {
		if(k + s == N)
			printf("Yes");
		else
			printf("No");
	}
	else if(k == s) {
		printf("Yes");
	}
	else if(k > s) {
		printf("No");
	}
	else {
		printf("Yes");
	}

	return EXIT_SUCCESS;
}