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 <map>
#include <cmath>
#include <stack>
#include <queue>
#include <vector>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#define L 100010
#define LL long long
using namespace std;

inline int gi() {
  char cj = getchar();
  int ans = 0, f = 1;
  while (cj < '0' || cj > '9') { if (cj == '-') f = -1; cj = getchar();}
  while (cj >= '0' && cj <= '9') ans = ans * 10 + cj - '0', cj = getchar();
  return f * ans;
}

int n, a, s4, s2;

int main() {
  //freopen("4-adjacent.in", "r", stdin);
  //freopen("4-adjacent.out", "w", stdout);
  n = gi();
  for (int i = 1; i <= n; ++i) {
    a = gi();
    if (a % 4 == 0) s4++;
    else if (a % 2 == 0) s2++;
  }
  //cout << n << " " << s4 << " " << s2 << endl;
  n -= (s2 / 2 + s4 + s4 + 1);
  if (n <= 0) puts("Yes");
  else puts("No");
  return 0;
}