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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Numerics;
using static System.Console;

class Solver {
    Scanner sc = new Scanner();

    public void Solve() {
        int N = sc.nextInt();
        var a = sc.ArrayInt(N);

        if (N / 2 <= a.Count(i => i % 4 == 0) + (a.Count(i => i % 4 != 0 && i % 2 == 0)) / 2) {
            WriteLine("Yes");
        } else {
            WriteLine("No");
        }
    }
}



class Scanner {
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner() {
        s = new string[0];
        i = 0;
    }

    public string next() {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt() {


        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0) {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++) {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong() {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0) {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++) {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble() {
        return double.Parse(next());
    }

    public double[] ArrayDouble(int N, double add = 0) {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++) {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}

class Program {
    static void Main(string[] args) {
        Solver s = new Solver();
        s.Solve();
    }
}