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: Wrong Answer)

#include <bits/stdc++.h>
#include<iostream>
#include<string>
#include<queue>
#include<vector>
#define FOR(i,a,b) for(int i=(a);i<(b);i++)//初期値a,i<bの範囲でループ
#define REP(i,n) FOR(i,0,n)//初期値0,i<nの範囲でループ
using namespace std;
typedef long long ll;//int64
typedef unsigned long long ull;

int n;
ll a[100010];
int c[5];

int main(){
    cin>>n;
    REP(i,n){
        cin>>a[i];
        if(a[i]%4==0){
            a[i]=4;
        }else if(a[i]%2==0){
            a[i]=2;
        }else{
            a[i]=1;
        }
        c[a[i]]++;
    }
    
    int f2=0;
    if(c[2])f2==1;
    if(c[4]==0){
        if(c[2]==n)cout<<"Yes";
        else cout<<"No";
    }
    else if(f2){
        if(c[4]>=c[1])cout<<"Yes";
        cout<<"No";

    }else{
        if(c[4]>=c[1]-1)cout<<"Yes";
        else cout<<"No";
    }


    
    

    return 0;
}