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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <string>
#include <vector>

using IV = std::vector<int>;
IV ToFixedIntArray(std::istream& is, int n) {
	IV ret(n);
	auto* dst = ret.data();
	while(n > 0) {
		--n;
		is >> *dst++;
	}
	return ret;
}

void DisableIOSync() {
	std::cin.tie(0);
	std::cout.tie(0);
	std::ios::sync_with_stdio(false);
}
int main() {
	DisableIOSync();

	int N = ToFixedIntArray(std::cin, 1)[0];
	const auto input = ToFixedIntArray(std::cin, N);
	int count_4 = 0,
		count_2 = 0;
	for(auto& i : input) {
		int flag = i & 0x03;
		if(flag == 0)
			++count_4;
		else if(flag == 2)
			++count_2;
	}
	N -= count_2/2;
	const int remain = N - count_4 - count_2/2;
	if((N+1)/2 >= remain)
		std::cout << "Yes";
	else
		std::cout << "No";
	std::cout << std::endl;

	return 0;
}