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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.ComponentModel;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using static System.Console;
using static System.Math;
class Simple
{
    int N;
    int[] a;
    void Solve() {
        //input
        N = io.Int;
        a = new int[N];
        for (int i = 0; i < N; ++i)
            a[i] = io.Int;
        //cal
        Func<int, bool> isMulOf4 = (n) => n % 4 == 0;
        var mulOf4Num = a.Count(a => isMulOf4(a));
        var twoNum = a.Count(a => a == 2);
        var ans = 3 * mulOf4Num >= N || 3 * mulOf4Num - 1 + twoNum >= N;
        //ret
        WriteLine(ans ? "Yes" : "No");
    }
    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) => new Simple().Stream();
    private void Stream() {
        //var exStdIn = new System.IO.StreamReader("stdin.txt");
        //SetIn(exStdIn);
        Solve();
        io.Flush();
    }
}
class SimpleIO
{
    string[] _nextBuffer;
    int _bufferCnt;
    char[] cs = new char[] { ' ', '"', ',' };
    StreamWriter sw = new StreamWriter(OpenStandardOutput()) {
        AutoFlush = false
    };
    public SimpleIO() {
        _nextBuffer = new string[0];
        _bufferCnt = 0;
        SetOut(sw);
    }
    string Next() {
        if (_bufferCnt < _nextBuffer.Length)
            return _nextBuffer[_bufferCnt++];
        var st = ReadLine();
        while (st == "")
            st = ReadLine();
        if (st != null)
            _nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        else
            st = "";
        _bufferCnt = 0;
        return _nextBuffer[_bufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void Flush() => Out.Flush();
}