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 <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <limits>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <functional>
#include <iomanip>

using namespace std;

#ifdef LOCAL
#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
#define eprintf(...) 42
#endif
using ll = long long;
using vll = std::vector<ll>;
using vvll = std::vector<vll>;
using vvvll = std::vector<vvll>;
#define reps(i, S, E) for (ll i = (S); i <= (E); i++)
#define rep(i, N) reps(i, 0, N-1)
#define deps(i, E, S) for (ll i = (E); i >= (S); i--)
#define dep(i, N) deps(i, N-1, 0)
const ll INF = 1LL << 60;
const int INF_INT = 1 << 30;

template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }
struct mll {
	static ll MOD;
	ll val;
	mll(ll v = 0) : val(v % MOD) { if (val < 0) val += MOD; }
	mll operator - () const { return -val; }
	mll operator + (const mll &b) const { return val + b.val; }
	mll operator - (const mll &b) const { return val - b.val; }
	mll operator * (const mll &b) const { return val * b.val; }
	mll operator / (const mll &b) const { return mll(*this) /= b; }
	mll operator + (ll b) const { return *this + mll(b); }
	mll operator - (ll b) const { return *this - mll(b); }
	mll operator * (ll b) const { return *this * mll(b); }
	friend mll operator + (ll a, const mll &b) { return b + a; }
	friend mll operator - (ll a, const mll &b) { return -b + a; }
	friend mll operator * (ll a, const mll &b) { return b * a; }
	mll &operator += (const mll &b) { val = (val + b.val) % MOD; return *this; }
	mll &operator -= (const mll &b) { val = (val + MOD - b.val) % MOD; return *this; }
	mll &operator *= (const mll &b) { val = (val*b.val) % MOD; return *this; }
	mll &operator /= (const mll &b) {
		ll c = b.val, d = MOD, u = 1, v = 0;
		while (d) {
			ll t = c / d;
			c -= t * d; swap(c, d);
			u -= t * v; swap(u, v);
		}
		val = val * u % MOD;
		if (val < 0) val += MOD;
		return *this;
	}
	mll &operator += (ll b) { return *this += mll(b); }
	mll &operator -= (ll b) { return *this -= mll(b); }
	mll &operator *= (ll b) { return *this *= mll(b); }
	mll &operator /= (ll b) { return *this /= mll(b); }
	bool operator == (const mll &b) { return val == b.val; }
	bool operator != (const mll &b) { return val != b.val; }
	bool operator == (ll b) { return *this == mll(b); }
	bool operator != (ll b) { return *this != mll(b); }
	friend bool operator == (ll a, const mll &b) { return mll(a) == b.val; }
	friend bool operator != (ll a, const mll &b) { return mll(a) != b.val; }
	friend ostream &operator << (ostream &os, const mll &a) { return os << a.val; }
	friend istream &operator >> (istream &is, mll &a) { return is >> a.val; }
	static mll Combination(ll a, ll b) {
		chmin(b, a - b);
		if (b < 0) return mll(0);
		mll c = 1;
		rep(i, b) c *= a - i;
		rep(i, b) c /= i + 1;
		return c;
	}
};
using vmll = std::vector<mll>;
using vvmll = std::vector<vmll>;
using vvvmll = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;

struct Fast {
	Fast() {
		cin.tie(0);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(std::numeric_limits<double>::max_digits10);
	}
} fast; //cin,cout高速化のおまじない＋桁数指定

ll mll::MOD = (ll)(1e9 + 7);// 998244353ll;

//素因数分解
void DecompositPrime(ll n, map<ll, ll> &result) {
	result.clear();
	ll a = 2;
	while (n >= a * a) {
		if (n % a == 0) {
			result[a]++;
			n /= a;
		}
		else {
			a++;
		}
	}
	if (n > 1) {
		result[n]++;
	}
}

int main() {
	ll N;
	cin >> N;
	vector<ll> A(N);
	rep(i, N) {
		cin >> A[i];
	}

	map<ll, ll> mp;
	vll count(3, 0); //2が0個、1個、2個以上のカウント
	rep(i, N) {
		if (A[i] % 4 == 0) {
			count[2]++;
		}
		else if (A[i] % 2 == 0) {
			count[1]++;
		}
		else {
			count[0]++;
		}
	}
	
	bool result = true;

	//0 2 0 2 ...とする。0が1個につき2が1個なければならない
	if (count[0] > count[2]) {
		//[0 2 0 2 0]の場合は、特例でOK
		if (count[0] + count[2] == N && count[0] - 1 == count[2]) {
			
		}
		else {
			result = false;
		}
	}

	if (result == true) {
		cout << "Yes" << endl;
	}
	else {
		cout << "No" << endl;
	}

	return 0;
}