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: Wrong Answer)

#include <stdio.h>                                                                                                                                                                                                                
#include <stdlib.h>                                                                                                                                                                                                               
#include <string.h>                                                                                                                                                                                                               
                                                                                                                                                                                                                                  
long long num, *list;                                                                                                                                                                                                             
                                                                                                                                                                                                                                                                                                                         
int dfs(long long a, long long b)                                                                                                                                                                                                 
{                                                                                                                                                                                                                                 
        if (b == num) {                                                                                                                                                                                                           
                return 0;                                                                                                                                                                                                         
        }                                                                                                                                                                                                                         
                                                                                                                                                                                                                                  
        if ((list[a] * list[b]) % 4 == 0) {                                                                                                                                                                                       
                return 1;                                                                                                                                                                                                         
        }                                                                                                                                                                                                                         
                                                                                                                                                                                                                                  
        if (dfs(a, b + 1)) {                                                                                                                                                                                                       
                return 1;                                                                                                                                                                                                         
        }                                                                                                                                                                                                                         
        return 0;                                                                                                                                                                                                                 
}                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                  
int main(void)                                                                                                                                                                                                                    
{                                                                                                                                                                                                                                 
        long long i;                                                                                                                                                                                                              
        int ret;                                                                                                                                                                                                                  
                                                                                                                                                                                                                                  
        scanf("%lld", &num);                                                                                                                                                                                                      
        list = calloc(sizeof(long long), num);                                                                                                                                                                                    
        for (i = 0; i < num; i++) {                                                                                                                                                                                               
                scanf("%lld", &list[i]);                                                                                                                                                                                          
        }                                                                                                                                                                                                                         
                                                                                                                                                                                                                                  
        for (i = 0; i < num - 1; i++) {                                                                                                                                                                                           
                if ((ret = dfs(i, i + 1)) == 1) {                                                                                                                                                                                 
                        break;                                                                                                                                                                                                    
                }                                                                                                                                                                                                                 
        }                                                                                                                                                                                                                         
        if (ret == 1) {                                                                                                                                                                                                           
                printf("Yes\n");                                                                                                                                                                                                  
        } else {                                                                                                                                                                                                                  
                printf("No\n");                                                                                                                                                                                                   
        }                                                                                                                                                                                                                         
        return 0;                                                                                                                                                                                                                 
}