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)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    private static final int MOD = (int) Math.pow(10, 9);
    private static final long EIGHT = (long) 1e18;
    private static final int[][] DIRS = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};

    public static void main(String[] args) {
        FastReader sc = new FastReader();
        long n = sc.nextLong();
        int x = 0; // 4的倍數
        int y = 0; // 不是4的倍數而是2的倍數

        for (int i = 0; i < n; i++) {
            long num = sc.nextLong();
            if (num % 4 == 0) {
                x++;
            } else if (num % 2 == 0) {
                y++;
            }
        }

        if (x  + (y/2) >= n/2) {
            print("Yes");
        } else {
            print("No");
        }
    }

    /*
     * Check if a * b is overflow or not
     */
    static Boolean isOverflowByMul(long a, long b) {
        if (a == 0 || b == 0) {
            return false;
        }

        long result = a * b;
        if (a == result / b) {
            return false;
        }
        return true;
    }

    static private void swap(int[] nums, int x, int y) {
        int tmp = nums[x];
        nums[x] = nums[y];
        nums[y] = tmp;
    }

    static  private void reverse(int[] nums, int left, int right) {
        while (left < right) {
            swap(nums, left, right);
            left++;
            right--;
        }
    }

    static private boolean findNextPermutation(int[] nums) {
        if (nums.length <= 1) {
            return false;
        }

        int last = nums.length - 2;

        while (last >= 0) {
            if (nums[last] < nums[last + 1]){
                break;
            }
            last--;
        }

        if (last < 0) { return false; }
        int nextGenerater = nums.length - 1;

        for (int i = nums.length - 1; i > last; i--) {
            if (nums[i] > nums[last]) {
                nextGenerater = i;
                break;
            }
        }

        swap(nums, nextGenerater, last);
        reverse(nums, last + 1, nums.length - 1);
        return true;
    }

    static private int[] generateNArray(int n) {
        int[] res = new int[n];

        for (int i = 0; i < n; i++) {
            res[i] = i + 1;
        }

        return res;
    }

    static  private void print(String s) {
        System.out.println(s);
    }

    static private void printArray(int[] e) {
        for (int s: e) {
            System.out.print(s + " ");
        }
        print("");
    }

    static private int log2(int x) {
        return (int)(Math.log(x) / Math.log(2));
    }

    static private long gcd(long m, long n) {
        if (m < n) { return gcd(n, m); }
        if (m % n == 0) { return n; }
        return gcd(n, m%n);
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException  e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try{
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}