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<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<ctime>
#include<vector>
#include<queue>
#include<stack>
#include<map>
using namespace std;
#define FOR(i,s,e) for (int i=s;i<e;i++)
#define FOE(i,s,e) for (int i=s;i<=e;i++)
#define FOD(i,s,e) for (int i=s;i>=e;i--)
#define SET(a,e) memset(a,e,sizeof(a))
#define LL long long
#define LD long double
#define pb push_back
#define x first
#define y second
#define PII pair<int,int>
#define PLI pair<LL,int>
#define PIL pair<int,LL>
#define PLL pair<LL,LL>
#define eps 1e-9
#define mp make_pair

int n,a[100005],c[3];

int main () {
	scanf("%d",&n);
	FOE(i,1,n) {
		scanf("%d",&a[i]);
		if (a[i]%4==0) ++c[2];
		else if (a[i]%2==0) ++c[1];
		else ++c[0];
	}
	if (c[1]==n) {
		printf("Yes\n");
		return 0;
	}
	if (c[2]!=0)
	c[2]=c[2]+1;
	c[2]-=c[0];
	if (c[2]<0) {
		printf("No\n");
		return 0;	
	}
	if (c[1]==1 && c[2]==0) {
		printf("No\n");
		return 0;	
	}
	if (c[1]>=1 && c[2]==0 && n>c[1]) {
		printf("No\n");
		return 0;	
	}
	printf("Yes\n");
	return 0;
}