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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

/*
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 */
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.*;
import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;

import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.pow;
import static java.lang.Math.abs;

import static java.lang.String.format;


public class Main {
    final static int INF = Integer.MAX_VALUE>>1;
    final static int MOD = 1_000_000_007;
    final static int[] dx4 = { 0, -1, 1, 0 };
    final static int[] dy4 = { -1, 0, 0, 1 };
    final static int[] dx8 = { -1, -1, -1, 0, 0, 1, 1, 1 };
    final static int[] dy8 = { -1, 0, 1, -1, 1, -1, 0, 1 };
    public static void main(String[] args) {
        Scanner sc=new Scanner();
        int bCount=0;
        int cCount=0;
        int dCount=0;
        int n=sc.nextInt();
        for(int i=0;i<n;i++){
            int a=sc.nextInt();
            if(a%4==0){
                dCount++;
            }else if(a%2==0){
                cCount++;
            }else{
                bCount++;
            }
        }
        putE("b,c,d=%d,%d,%d",bCount,cCount,dCount);
        if(cCount>0){
            if(bCount>dCount){
                put("No");
            }else{
                put("Yes");
            }
        }else{
            if(bCount-1>dCount){
                put("No");
            }else{
                put("Yes");
            }
        }


    }


    public static void print(Object object){
        System.out.print(object);
    }
    public static void put(Object object) {
        System.out.println(object);
    }
    public static void put(){
        System.out.println();
    }

    public static void printE(Object object){
        System.err.print("DEBUG:"+object);
    }
    public static void putE(Object object){
        System.err.println("DEBUG:"+object);
    }
    public static void putE(){
        System.err.println("DEBUG:");
    }

    public static void print(String format,Object... args){
        System.out.print(String.format(format,args));
    }
    public static void put(String format,Object... args) {
        System.out.println(String.format(format,args));
    }
    public static void printE(String format,Object... args){
        System.err.print("DEBUG:"+String.format(format,args));
    }
    public static void putE(String format,Object... args){
        System.err.println("DEBUG:"+String.format(format,args));
    }

    final static private class Scanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte())
                return buffer[ptr++];
            else
                return -1;
        }

        private boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr]))
                ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
                throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
    final static private class FixedLongPair {
        final public long x, y;
        final static public FixedLongPair ZEROS=new FixedLongPair(0,0);
        FixedLongPair(long x, long y) {
            this.x = x;
            this.y = y;
        }
        public static double distance(FixedLongPair flp1,FixedLongPair flp2){
            double x = (double) flp1.x - flp2.x;
            double y = (double) flp1.y - flp2.y;
            return Math.sqrt(x*x+y*y);
        }

        @Override
        public int hashCode() {
            return (int)x+(int)y;
        }

        @Override
        public boolean equals(Object obj) {
            boolean result=super.equals(obj);
            if(obj.getClass()!=this.getClass()){
                return false;
            }
            FixedLongPair pair=(FixedLongPair)obj;
            if(this.x==pair.x&&this.y==pair.y) return true;
            return false;
        }

        @Override
        public String toString() {
            return String.format(FixedLongPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class FixedIntPair {
        final public int x, y;
        final static public FixedIntPair ZEROS=new FixedIntPair(0,0);
        FixedIntPair(int x, int y) {
            this.x = x;
            this.y = y;
        }
        public static double distance(FixedIntPair fip1,FixedIntPair fip2){
            double x = (double) fip1.x - fip2.x;
            double y = (double) fip1.y - fip2.y;
            return Math.sqrt(x*x+y*y);
        }

        @Override
        public int hashCode() {
            return x+y;
        }

        @Override
        public boolean equals(Object obj) {
            boolean result=super.equals(obj);
            if(obj.getClass()!=this.getClass()){
                return false;
            }
            FixedIntPair pair=(FixedIntPair) obj;
            if(this.x==pair.x&&this.y==pair.y) return true;
            return false;
        }

        @Override
        public String toString() {
            return String.format(FixedIntPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class Tuple<T,V>{
        //immutabl1でないことに注意(T,Vがmutableの場合変更可能)
        final private T t;
        final private V v;
        Tuple(T t,V v){
            this.t=t;
            this.v=v;
        }

        public T getT() {
            return t;
        }

        public V getV() {
            return v;
        }

        @Override
        public int hashCode() {
            return (t.hashCode()+v.hashCode());
        }

        @Override
        @SuppressWarnings("unchecked")
        public boolean equals(Object obj) {
            if(obj.getClass()!=this.getClass()){
                return false;
            }
            Tuple<T,V> tuple=(Tuple<T, V>) obj;
            return tuple.t.equals(this.t)&&tuple.v.equals(this.v);
        }

        @Override
        public String toString() {
            return String.format("<Tuple>=<%s,%s>",t,v);
        }
    }
    final static private class Binary{
        public static String toZeroPadding(int i){
            return String.format("%"+Integer.toBinaryString(-1).length()+"s",Integer.toBinaryString(i)).replace(' ','0');
        }
        public static String toZeroPadding(long i){
            return String.format("%"+Long.toBinaryString(-1).length()+"s",Long.toBinaryString(i)).replace(' ','0');
        }
    }
    final static private class Util {
        static long gcd(long a,long b){
            //最大公約数　
            if(a%b==0)return b;
            return gcd(b,a%b);
        }
        static long lcm(long a,long b){
            //最小公倍数
            long gcd=gcd(a,b);
            long result=b/gcd;
            return a*result;
        }
        static <T extends Comparable<T>> Map<T,Integer> count(List<T> list){
            //副作用
            Collections.sort(list);
            Map<T,Integer> result=new HashMap<>();
            int l=0,r=0;
            while(l<list.size()){
                while(r<list.size()-1&&list.get(r).equals(r+1)){
                    r++;
                }
                result.put(list.get(r),r-l+1);
                r++;
                l=r;
            }
            return result;

        }
        static Map<Integer,Integer> count(int[] array){
            //副作用
            Arrays.sort(array);
            Map<Integer,Integer> result=new HashMap<>();
            int l=0,r=0;
            while(l<array.length){
                while(r<array.length-1&&array[r]==array[r+1]){
                    r++;
                }
                result.put(array[l],r-l+1);
                r++;
                l=r;
            }
            return result;
        }
        static <T> String toStringBWS(Iterable<T> iterable){
            Iterator<T> ite=iterable.iterator();
            return toStringBWS(ite);
        }
        static <T> String toStringBWS(Iterator<T> ite){
            StringBuilder sb=new StringBuilder();
            sb.append(ite.next());
            while(ite.hasNext()){
                sb.append(" ");
                sb.append(ite.next());
            }
            return sb.toString();
        }
        static int[] factoringInPrimeNumbers(long n,int size){
            //素因数分解
            //sizeがnに比べて小さい場合完全に素因数分解出来ていない可能性がある
            int[] result=new int[size];
            for(int i=2;n>1&&i< result.length;i++){
                while(n%i==0){
                    result[i]++;
                    n/=i;
                }
            }
            return result;

        }
    }
}