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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <map>
#include <set>
#include <list>
#include <ctime>
#include <cmath>
#include <queue>
#include <stack>
#include <bitset>
#include <vector>
#include <cstdio>
#include <string>
#include <cstring>
#include <sstream>
#include <iomanip>
#include <cstdlib>
#include <utility>
#include <iostream>
#include <algorithm>
using namespace std;
int a[100005],b[5];
int main ( ) {
	int n,i;
	scanf("%d",&n);
	for (i=1;i<=n;i++) scanf("%d",&a[i]),a[i]%=4,b[a[i]]++;
	if (b[1]+b[3]>b[0]+1) {
		puts("No");return 0;
	}
	if (b[1]+b[3]==b[0]+1 && b[2]!=0) {
		puts("No");return 0;
	}
	if (b[2]==1 && b[0]==0) {
		puts("No");return 0;
	}
	puts("Yes");
	return 0;
}
/* 
3
1 10 100

Yes

4
1 2 3 4

No

3
1 4 1

Yes

2
1 1

No

6
2 7 1 8 2 8

Yes
*/