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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var n int
	fmt.Scan(&n)

	ctMultipleOf2 := 0
	ctMultipleOf4 := 0
	for i := 0; i < n; i++ {
		var a int
		fmt.Scan(&a)
		if a%4 == 0 {
			ctMultipleOf4++
		} else if a%2 == 0 {
			ctMultipleOf2++
		}
	}

	ok := false
	if ctMultipleOf4*2+1 >= n {
		ok = true
	} else if n-ctMultipleOf4*2 <= ctMultipleOf2 {
		ok = true
	}

	if ok {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}
}