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"
	"math"
)

var N, cnt int

func main() {
	fmt.Scan(&N)
	a := make([]int, N)

	for i := 0; i < N; i++ {
		fmt.Scan(&a[i])
	}

	c := make([]int, 3)

	for i := 0; i < N; i++ {
		var cnt int
		for j := 0; j < 2; j++ {
			if a[i]%2 == 0 {
				cnt++
				a[i] /= 2
			}
		}
		c[cnt]++
	}
	if c[0]+c[1] <= c[2]+1 || c[2] == c[0] {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}

}

/*  ----------------------------------------  */

func gcd(x, y uint64) uint64 {
	if x%y == 0 {
		return y
	} else {
		r := x % y
		return gcd(y, r)
	}
}

func combination(x, y int) int {
	return permutation(x, y) / permutation(y, y)
}

func permutation(x, y int) int {
	var ans int = 1
	for i := x - y; 0 < i; i-- {
		ans *= i
	}
	return ans
}

func max(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Max(float64(x[i]), float64(res)))
	}
	return res
}

func min(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Min(float64(x[i]), float64(res)))
	}
	return res
}

func pow(x, y int) uint64 { return uint64(math.Pow(float64(x), float64(y))) }
func abs(x int) int       { return int(math.Abs(float64(x))) }
func floor(x int) int     { return int(math.Floor(float64(x))) }

type XY struct {
	x int
	y int
}

type SortBy [][]int

func (a SortBy) Len() int      { return len(a) }
func (a SortBy) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
func (a SortBy) Less(i, j int) bool {
	if a[i][0] == a[j][0] {
		return a[i][1] > a[j][1]
	}
	return a[i][0] > a[j][0]
}