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.*;
import java.lang.*;

public class c2 {
    public static MyScanner scan;
    public static PrintWriter out;
    public static void main(String[] args) {
        scan=new MyScanner();
        out=new PrintWriter(new BufferedOutputStream(System.out));

//        int t=1;
        int t=scan.nextInt();
        while(t-->0) {

            int n=scan.nextInt();
            int[] a=new int[n];
            HashSet<Integer> even=new HashSet<>();
            int max=0,moves=0;
            for(int c=0;c<n;c++) {
                a[c]=scan.nextInt();
                if(a[c]%2==0) {
                    int temp=pow2(a[c]);
                    if(temp!=-1&&temp>max) max=temp;
                    else if(temp==-1) {
                        while(a[c]%2==0&&!even.contains(a[c])) {
                            even.add(a[c]);
                            moves++;
                            a[c]/=2;
                        }
                        even.add(a[c]);
                    }
                }
            }
            moves+=max;
            out.println(moves);
        }
        out.close();
    }

    //-----------------------------------------------------COMP-SPACE-----------------------------------------------------

    public static int pow2(int n) {
        int pow=1;
        while(Math.pow(2,pow)<=n) {
            if(Math.pow(2,pow)==n) return pow;
            pow++;
        } return -1;
    }

    //--------------------------------------------------------------------------------------------------------------------

    //node
    static class Node implements Comparable<Node> {
        public int x,y;
        public Node(int x,int y) {
            this.x=x;
            this.y=y;
        }

        public int compareTo(Node other) {
            if(this.x==other.x) return 0;
            else if(this.x>other.x) return 1;
            else return -1;
        }

        public boolean equals(Node other) {
            return this.x==other.x;
        }

//        public int compareTo(Node other) {
//            if(this.y==other.y) return 0;
//            else if(this.y>other.y) return 1;
//            else return -1;
//        }
//
//        public boolean equals(Node other) {
//            return this.y==other.y;
//        }
    }
    //edge
    static class Edge implements Comparable<Edge> {
        public Node a,b;
        public int weight;

        public Edge(Node a,Node b,int weight) {
            this.a=a;
            this.b=b;
            this.weight=weight;
        }

        public int compareTo(Edge other) {
            if(this.weight==other.weight) return 0;
            else if(this.weight>other.weight) return 1;
            else return -1;
        }
    }

    //util
    public static int gcd(int a, int b) {
        if (b == 0)
            return a;
        if (a == 0)
            return b;
        return (a > b) ? gcd(a % b, b) : gcd(a, b % a);
    }

    public static int lcm(int a, int b) {
        return a * b / gcd(a, b);
    }

    public static int min(int a,int b) {
        if(a<=b) return a;
        else return b;
    }

    public static int max(int a,int b) {
        if(a>=b) return a;
        else return b;
    }

    public static int abs(int a) {
        if(a<0) return a*-1;
        else return a;
    }

    public static ArrayList<Integer> getPrimes(int n) {
        boolean prime[]=new boolean[n+1];
        Arrays.fill(prime,true);
        for (int p=2;p*p<=n;p++) {
            if (prime[p]) {
                for (int i=p*2;i<=n;i+=p) {
                    prime[i]=false;
                }
            }
        }
        ArrayList<Integer> primeNumbers=new ArrayList<Integer>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                primeNumbers.add(i);
            }
        }
        return primeNumbers;
    }

    public static boolean isPrime(int a) {
        if (a == 0 || a == 1) {
            return false;
        }
        if (a == 2) {
            return true;
        }
        for (int i = 2; i < Math.sqrt(a) + 1; i++) {
            if (a % i == 0) {
                return false;
            }
        }
        return true;
    }

    public static ArrayList<Integer> getDivisors(int n) {
        ArrayList<Integer> div = new ArrayList<Integer>();
        for (int i=1;i*i<=n;i++) {
            if (n%i==0) {
                div.add(i);
                if (n/i!=i)
                    div.add(n/i);
            }
        }
        return div;
    }

    //scanner
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static int[] nextIntArray(int n) {
        int[] a=new int[n];
        for(int c=0;c<n;c++) a[c]=scan.nextInt();
        return a;
    }

    public static Integer[] nextIntegerArray(int n) {
        Integer[] a=new Integer[n];
        for(int c=0;c<n;c++) a[c]=scan.nextInt();
        return a;
    }

    public static int[][] nextIntMatrix(int n,int m) {
        int[][] a=new int[n][m];
        for(int i=0;i<n;i++) for(int j=0;j<m;j++) a[i][j]=scan.nextInt();
        return a;
    }

    public static Integer[][] nextIntegerMatrix(int n,int m) {
        Integer[][] a=new Integer[n][m];
        for(int i=0;i<n;i++) for(int j=0;j<m;j++) a[i][j]=scan.nextInt();
        return a;
    }

    //print
    public static void printIntArray(int[] a) {
        for(int c:a) out.print(c+" ");
        out.println();
    }

    public static void printIntegerArray(Integer[] a) {
        for(int c:a) out.print(c+" ");
        out.println();
    }

    public static void printIntMatrix(int[][] a) {
        for(int[] i:a) {
            for(int j:i) out.print(j+" ");
            out.println();
        }
    }

    public static void printIntegerMatrix(Integer[][] a) {
        for(Integer[] i:a) {
            for(Integer j:i) out.print(j+" ");
            out.println();
        }
    }

    public static void help(int t,int n) { out.println("Test Case: "+(t+1)+" | Variable Output: "+n); }
    public static void help(int t,String n) { out.println("Test Case: "+(t+1)+" | Variable Output: "+n); }
    public static void help(int t,char[] n) { out.print("Test Case: "+(t+1)+" | Variable Output: "); for(char c:n) out.print(c+" "); out.println(); }
}