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 <bits/stdc++.h>
using namespace std;

#define REP(i, n) for (int (i) = 0 ; (i) < (int)(n) ; ++(i))
#define REPN(i, m, n) for (int (i) = m ; (i) < (int)(n) ; ++(i))
#define REP_REV(i, n) for (int (i) = (int)(n) - 1 ; (i) >= 0 ; --(i))
#define REPN_REV(i, m, n) for (int (i) = (int)(n) - 1 ; (i) >= m ; --(i))

#define INF 2e9
#define INF_LL 1LL<<60
#define ll long long
#define MAX_V
const double PI=3.14159265358979323846;

#define print2D(h, w, arr) REP(i, h) { REP(j, w) cout << arr[i][j] << " "; cout << endl; }
#define print_line(vec, n) {for(int i=0;i<(n-1);i++) cout << (vec)[i] << " "; cout << (vec)[(n)-1] << endl;}
template<class T> void print(const T& x){cout << x << endl;}
template<class T, class... A> void print(const T& first, const A&... rest) { cout << first << " "; print(rest...); }
struct PreMain {PreMain(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(20);}} premain; 

ll gcd(ll a, ll b){
    ll tmp;
    if(a<b){
        tmp = a;
        a = b;
        b = tmp;
    }

    ll r = a%b;
    while(r!=0){
        a = b;
        b = r;
        r = a % b;
    }

    return b;
}

int main() {
    int n;
    cin >> n;
    vector<ll> t(n);

    int ni = 0;
    int yon = 0;
    int sonota = 0;

    REP(i, n) {
        int k;
        cin >> k;
        if(k % 4 == 0) yon++;
        else if(k % 2 == 0) ni++;
        else sonota++;
    }
    
    int ans = 0;
    
    if(ni == 0) {
        if(yon + 1 < sonota) {
            cout << "No" << endl;
        } else {
            cout << "Yes" << endl;
        }
    } else {
        if(yon < sonota) {
            cout << "No" << endl;
        } else {
            cout << "Yes" << endl;
        }
    }
}