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.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.Runtime.CompilerServices;
using System.IO;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;
using static Ex;
class AC {
    /*------------------------------------------------------------------*/
    private int N;
    private int[] a;
    void Solve() {
        io.i(out N);
        io.ini(out a, N);
        var x4 = a.Count(x => x % 4 == 0);
        var x2 = a.Count(x => x % 4 != 0 && x % 2 == 0);
        var x1 = N - x4 - x2 + (x2 % 2);
        io.Yn(x4 + 1 >= x1);
    }
    /*------------------------------------------------------------------*/
    void Test() {
        //--- TEST ---//
    }
    public static void Main(string[] args) => new AC().Stream();
    IO io = new IO();
    private void Stream() {
        /*
        var exStdIn = new System.IO.StreamReader("stdin.txt");
        SetIn(exStdIn);
        Test();
        */
        Solve();
        io.Flush();
    }
}
class IO {
    #region INPUT
    #region FastRead    
    private const int Size = 1 << 12;
    private readonly Stream _stream = OpenStandardInput();
    private readonly byte[] _buffer = new byte[Size];
    private int _ptr = 0, _buffLen = 0;
    private bool HasNextByte() {
        if(_ptr < _buffLen) return true;
        _ptr = 0;
        _buffLen = _stream.Read(_buffer, 0, Size);
        return _buffLen > 0;
    }
    private byte ReadByte() {
        if(HasNextByte()) return _buffer[_ptr++];
        else
        //inputの末尾の改行がないとerror
            throw new EndOfStreamException();
    }
    private bool IsAscii(int c) => '!' <= c && c <= '~';
    private char NextChar() {
        var b = ReadByte();
        while(!IsAscii(b)) b = ReadByte();
        return (char)b;
    }
    private string Next() {
        var sb = new StringBuilder();
        for(var b = NextChar(); IsAscii(b); b = (char)ReadByte()) sb.Append(b);
        return sb.ToString();
    }
    public string String => Next();
    public char Char => NextChar();
    public int Int => int.Parse(Next());
    public long Long => long.Parse(Next());
    public double Double => double.Parse(Next());
    #endregion
    #region LazyRead        
    private void scan <T>(ref T x) {
        if(x is int) __refvalue(__makeref(x),int) = int.Parse(Next());
        else if(x is long) __refvalue(__makeref(x),long) = long.Parse(Next());
        else if(x is double) __refvalue(__makeref(x),double) = double.Parse(Next());
        else if(x is char) __refvalue(__makeref(x),char) = NextChar();
        else __refvalue(__makeref(x),string) = Next();
    }
    public void i <T>(out T t) {
        t = default(T);
        scan(ref t);
    }
    public void i <T, TU>(out T t, out TU u) {
        i(out t);
        i(out u);
    }
    public void i <T, TU, TV>(out T t, out TU u, out TV v) {
        i(out t, out u);
        i(out v);
    }
    public void i <T, TU, TV, TW>(out T t, out TU u, out TV v, out TW w) {
        i(out t, out u);
        i(out v, out w);
    }
    public void i <T, TU, TV, TW, TX>(out T t, out TU u, out TV v, out TW w, out TX x) {
        i(out t, out u, out v);
        i(out w, out x);
    }
    public void i <T, TU, TV, TW, TX, TY>(out T t, out TU u, out TV v, out TW w, out TX x, out TY y) {
        i(out t, out u, out v);
        i(out w, out x, out y);
    }
    public void ini <T>(out T[] a, int n) {
        a = new T[n];
        for(int i = 0; i < n; ++i) i <T>(out a[i]);
    }
    public void ini <T, TU>(out T[] a, out TU[] b, int n) {
        a = new T[n];
        b = new TU[n];
        for(int i = 0; i < n; ++i) i <T, TU>(out a[i], out b[i]);
    }
    public void ini <T, TU, TV>(out T[] a, out TU[] b, out TV[] c, int n) {
        a = new T[n];
        b = new TU[n];
        c = new TV[n];
        for(var i = 0; i < n; ++i) i <T, TU, TV>(out a[i], out b[i], out c[i]);
    }
    public void ini <T>(out T[,] a, int h, int w) {
        a = new T[h, w];
        for(int i = 0; i < h; ++i) for(int j = 0; j < w; ++j) i <T>(out a[i, j]);
    }
    #endregion
    #endregion
    #region OUTPUT
    private readonly StreamWriter _sw = new StreamWriter(OpenStandardOutput()) {
#if DEBUG
        AutoFlush = true
#else
        AutoFlush = false
#endif
    };
    public void Flush() => Out.Flush();
    public void YN(bool f) => WriteLine(f ? "YES" : "NO");
    public void Yn(bool f) => WriteLine(f ? "Yes" : "No");
    public void yn(bool f) => WriteLine(f ? "yes" : "no");
    #endregion
    public IO() { SetOut(_sw); }
}
static class Ex {
    #region マクロもどき        
    public static void LOG <T>(T x, [CallerLineNumber] int line = 0) => Error.WriteLine($"LOG[{line}]: {x}");
    public static void FOR(int a, int b, Action <int> f) => FOR(a, b, 1, f);
    public static void FOR(int a, int b, int n, Action <int> f) {
        for(int i = a; i < b; i += n) f(i);
    }
    public static void REP(int a, Action <int> f) => FOR(0, a, f);
    public static void REPEQ(int a, Action <int> f) => FOR(0, a + 1, f);
    public static void FOREQ(int a, int b, Action <int> f) => FOR(a, b + 1, f);
    public static void FOREQ(int a, int b, int n, Action <int> f) => FOR(a, b + 1, n, f);
    public static T MIN <T>(params T[] xs) => xs.Min();
    public static T MAX <T>(params T[] xs) => xs.Max();
    public static IEnumerable <int> RANGE(int s, int e) => Enumerable.Range(s, e - s + 1);
    public static int LCM(int a, int b) => a * (b / GCD(a, b));
    public static int GCD(int a, int b) => (a < b) ? GCD(b, a) : b == 0 ? a : GCD(b, a % b);
    public static int LCM(params int[] xs) => xs.Aggregate(LCM);
    public static int GCD(params int[] xs) => xs.Aggregate(GCD);
    public static long LCM(long a, long b) => a * (b / GCD(a, b));
    public static long GCD(long a, long b) => (a < b) ? GCD(b, a) : b == 0L ? a : GCD(b, a % b);
    public static long LCM(params long[] xs) => xs.Aggregate(LCM);
    public static long GCD(params long[] xs) => xs.Aggregate(GCD);
    #endregion
    #region 拡張メソッド        
    public static void Rep(this int x, Action <int> f) => REP(x, f);
    public static void RepEq(this int x, Action <int> f) => REPEQ(x, f);
    public static void Do <T>(this T x, Action <T> f) => f(x);
    public static void Log <T>(this T x, [CallerLineNumber] int line = 0) => Error.WriteLine($"LOG[{line}]: {x}");
    public static void Fun <T>(this T[] xs, Action <int> f) => REP(xs.Length, f);
    public static void Fun <T>(this T[,] xxs, Action <int, int> f) => REP(xxs.GetLength(0), i => REP(xxs.GetLength(1), j => f(i, j)));
    public static bool IsIn <T>(this T[] xs, int i) => 0 <= i && i < xs.Length;
    public static bool IsIn <T>(this T[,] xxs, int i, int j) => 0 <= i && i < xxs.GetLength(0) && 0 <= j && j < xxs.GetLength(1);
    public static void Iter <T>(this IEnumerable <T> xs, Action <T> f) {
        foreach(var x in xs) f(x);
    }
    public class IndexedItem <T> {
        public int Idx;
        public T Val;
        public IndexedItem(int idx, T val) {
            Idx = idx;
            Val = val;
        }
    }
    public static IEnumerable <IndexedItem <T>> Indexed <T>(this IEnumerable <T> xs) => xs.Select((x, i) => new IndexedItem <T>(i, x));
    public static void Set <T>(this T[] xs, T v) => REP(xs.Length, i => xs[i] = v);
    public static void Set <T>(this T[,] xxs, T v) => REP(xxs.GetLength(0), i => REP(xxs.GetLength(1), j => xxs[i, j] = v));
    public static T[] Sort <T>(this T[] xs) {
        Array.Sort(xs);
        return xs;
    }
    public static T[] SortR <T>(this T[] xs) {
        Array.Reverse(xs.Sort());
        return xs;
    }
    public static string Pad0 <T>(this T s, int n) => s.ToString().PadLeft(n, '0');
    public static int RoundOff(this double v, int n) => (int)Round(v, n - 1, MidpointRounding.AwayFromZero);
    public static int RoundUp(this double v) => (int)Ceiling(v);
    public static int RoundDown(this double v) => (int)Floor(v);
    public static bool Odd(this int v) => (v & 1) != 0;
    public static bool Odd(this long v) => (v & 1) != 0;
    public static bool Eve(this int v) => !v.Odd();
    public static bool Eve(this long v) => !v.Odd();
    public static void Prt <T>(this T x) => WriteLine(x);
    public static void Prt <T>(this T[] xs) => xs.Iter(x => WriteLine(x));
    public static void Prt <T>(this List <T> xs) => xs.Iter(x => WriteLine(x));
    public static string Reversed(this string s) => string.Join("", s.Reverse());
    public static string Repeat(this string s, int n) => string.Concat(Enumerable.Repeat(s, n).ToArray());
    #endregion
}