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: Accepted)

#include <bits/stdc++.h>
#define SORT(a) sort(a.begin(), a.end())
#define RSORT(a) sort(a.rbegin(), a.rend())
#define REP(i, n) for (long long i = 0; i < n; i++)
#define RREP(i, n) for (long long i = n - 1; 0 <= i; i--)
#define FOR(i, start, end) for (long long i = start; i < end; i++)
#define RFOR(i, start, end) for (long long i = start - 1; 0 <= i; i--)
#define ALL(a) a.begin(), a.end()
#define MOD(a) a %= 1'000'000'007
using ll = long long;
using namespace std;
const int INF32       = 1'050'000'000;
const long long INF64 = 4'000'000'000'000'000'000;
const int MOD7        = 1'000'000'007;
const int MOD9        = 1'000'000'009;
template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
void print() { std::cout << '\n'; }
template <class H, class... T> void print(H &&head, T &&... args) {
    std::cout << head;
    sizeof...(args) == 0 ? std::cout << "" : std::cout << ' ';
    print(std::forward<T>(args)...);
}
template <class T> void print(std::vector<T> &v) {
    for (int i = 0; i < v.size(); i++) {
        std::cout << v[i];
        i == v.size() - 1 ? std::cout << '\n' : std::cout << ' ';
    }
}
template <class T> void print(std::vector<std::vector<T>> &v) {
    for (int i = 0; i < v.size(); i++) {
        for (int j = 0; j < v[i].size(); j++) {
            std::cout << v[i][j];
            j == v[i].size() - 1 ? std::cout << '\n' : std::cout << ' ';
        }
    }
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    cin >> N;
    vector<int> v(N);
    for (auto &&i : v) {
        cin >> i;
    }

    int two = 0, four = 0;
    for (auto &&i : v) {
        if (i % 4 == 0)
            four++;
        else if (i % 2 == 0)
            two++;
    }

    int cnt = N - (2 * four + 1) - 2 * (two / 2);
    if (cnt <= 0) {
        print("Yes");
    } else {
        print("No");
    }

    return 0;
}