There are n positive integers a_1, a_2, ..., a_n. For the one move you can choose any even value c and divide by two all elements that equal c.

For example, if a=[6,8,12,6,3,12] and you choose c=6, and a is transformed into a=[3,8,12,3,3,12] after the move.

You need to find the minimal number of moves for transforming a to an array of only odd integers (each element shouldn't be divisible by 2).

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.

The first line of a test case contains n (1 ≤ n ≤ 2⋅10^5) — the number of integers in the sequence a. The second line contains positive integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).

The sum of n for all test cases in the input doesn't exceed 2⋅10^5.

Output

For t test cases print the answers in the order of test cases in the input. The answer for the test case is the minimal number of moves needed to make all numbers in the test case odd (i.e. not divisible by 2).

Example

Input


4
6
40 6 40 3 20 1
1
1024
4
2 4 8 16
3
3 1 7


Output


4
10
4
0

Note

In the first test case of the example, the optimal sequence of moves can be as follows:

  * before making moves a=[40, 6, 40, 3, 20, 1]; 
  * choose c=6; 
  * now a=[40, 3, 40, 3, 20, 1]; 
  * choose c=40; 
  * now a=[20, 3, 20, 3, 20, 1]; 
  * choose c=20; 
  * now a=[10, 3, 10, 3, 10, 1]; 
  * choose c=10; 
  * now a=[5, 3, 5, 3, 5, 1] — all numbers are odd. 



Thus, all numbers became odd after 4 moves. In 3 or fewer moves, you cannot make them all odd.
import java.io.*;
import java.util.*;

public class A {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		int tc = sc.nextInt();
		while (tc-- > 0) {
			int n = sc.nextInt();
			PriorityQueue<Integer> pq = new PriorityQueue<Integer>(Collections.reverseOrder());
			while (n-- > 0)
				pq.add(sc.nextInt());
			int ans = 0;
			int last = -1;
			while (!pq.isEmpty()) {
				int x = pq.poll();
				if (x % 2 == 1 || last == x)
					continue;
				last = x;
				pq.add(x / 2);
				ans++;
			}
			out.println(ans);

		}
		out.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		Scanner(String fileName) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(fileName));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}

		boolean ready() throws IOException {
			return br.ready();
		}

	}

	static void sort(int[] a) {
		shuffle(a);
		Arrays.sort(a);
	}

	static void shuffle(int[] a) {
		int n = a.length;
		Random rand = new Random();
		for (int i = 0; i < n; i++) {
			int tmpIdx = rand.nextInt(n);
			int tmp = a[i];
			a[i] = a[tmpIdx];
			a[tmpIdx] = tmp;
		}
	}

}