Problem: On the well-known testing system MathForces, a draw of n rating units is arranged. The rating will be distributed according to the following algorithm: if k participants take part in this event, then the n rating is evenly distributed between them and rounded to the nearest lower integer, At the end of the drawing, an unused rating may remain — it is not given to any of the participants.

For example, if n = 5 and k = 3, then each participant will recieve an 1 rating unit, and also 2 rating units will remain unused. If n = 5, and k = 6, then none of the participants will increase their rating.

Vasya participates in this rating draw but does not have information on the total number of participants in this event. Therefore, he wants to know what different values of the rating increment are possible to get as a result of this draw and asks you for help.

For example, if n=5, then the answer is equal to the sequence 0, 1, 2, 5. Each of the sequence values (and only them) can be obtained as ⌊ n/k ⌋ for some positive integer k (where ⌊ x ⌋ is the value of x rounded down): 0 = ⌊ 5/7 ⌋, 1 = ⌊ 5/5 ⌋, 2 = ⌊ 5/2 ⌋, 5 = ⌊ 5/1 ⌋.

Write a program that, for a given n, finds a sequence of all possible rating increments.

Input

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

Each line contains an integer n (1 ≤ n ≤ 10^9) — the total number of the rating units being drawn.

Output

Output the answers for each of t test cases. Each answer should be contained in two lines.

In the first line print a single integer m — the number of different rating increment values that Vasya can get.

In the following line print m integers in ascending order — the values of possible rating increments.

Example

Input


4
5
11
1
3


Output


4
0 1 2 5 
6
0 1 2 3 5 11 
2
0 1 
3
0 1 3 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class CodeForces extends Functions {

    private static void solve() {
        int n = sc.nextInt();
        boolean[] isTaken = new boolean[(int)Math.sqrt(n)+2];
        List<Integer> list = new ArrayList<>();
        list.add(0);
        for(int i=1;i*i<=n;i++) {
            int div1 = i;
            int div2 = n/i;
            if(div2<isTaken.length && isTaken[div2])continue;
            list.add(div1);
            if(div1!=div2)list.add(div2);
            isTaken[div1] = true;
        }
        sort(list,true);
        out.println(list.size());
        for(int ele : list)
            out.print(ele+" ");
        out.println();

    }



    public static void main(String[] args) {
        int testCase = 1;
        testCase= sc.nextInt();
        while (testCase-->0) solve();
        sc.close();
        out.flush();
        out.close();
    }

    static Scanner sc = new Scanner(); // Fast Input
            static  PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));  // Fast output
//    static PrintStream out = new PrintStream(System.out);   // output


    private static class Scanner {
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private StringTokenizer st = new StringTokenizer("");
        public String next(){
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                }catch (IOException e){
                    e.printStackTrace();
                }
            return st.nextToken();

        }
        public int nextInt(){return Integer.parseInt(next());}
        public long nextLong(){return Long.parseLong(next());}
        public double nextDouble(){return Double.parseDouble(next());}
        public int[] setintArray(int n){
            int[] arr =new int[n];
            for(int i=0;i<n;i++)arr[i] = nextInt();
            return arr;
        }
        public long[] setlongArray(int n){
            long[] arr =new long[n];
            for(int i=0;i<n;i++)arr[i] = nextLong();
            return arr;
        }
        public int[][] set2DintArray(int row, int col){
            int[][] arr = new int[row][col];
            for(int i=0;i<row;i++)
                for(int j= 0;j<col;j++)
                    arr[i][j] = nextInt();
            return arr;
        }
        public long[][] set2DlongArray(int row, int col){
            long[][] arr = new long[row][col];
            for(int i=0;i<row;i++)
                for(int j= 0;j<col;j++)
                    arr[i][j] = nextLong();
            return arr;
        }
        public void close(){
            try{
                br.close();
            }catch (IOException e){
                e.printStackTrace();
            }
        }
    }

}


class Functions {
    public static int mod = (int)1e9+7;
    public static final int INT_MAX = Integer.MAX_VALUE;
    public static final int INT_MIN = Integer.MIN_VALUE;
    public static final long LONG_MAX = Long.MAX_VALUE;
    public static final long LONG_MIN = Long.MIN_VALUE;
    public static final double DOUBLE_MAX = Double.MAX_VALUE;
    public static final double DOUBLE_MIN = Double.MIN_VALUE;
    public static final String YES = "YES";
    public static final String NO = "NO";

    public static void sort(int[] a,boolean isAscending){
        ArrayList<Integer> temp = new ArrayList<>();
        for (int j : a) temp.add(j);
        sort(temp,isAscending);
        for(int i=0;i<a.length;i++)a[i] = temp.get(i);
    }

    public static void sort(List list,boolean isAscending){
        if(isAscending)
            Collections.sort(list);
        else Collections.sort(list,Collections.reverseOrder());
    }
    // euclidean algorithm
    public static long gcd(long a, long b) {
        // time O(max (loga ,logb))
        long x = Math.min(a,b);
        long y = Math.max(a,b);
        if (y % x == 0) return x;
        return gcd(y%x,x);
    }
    public static long lcm(long a, long b) {
        // lcm(a,b) * gcd(a,b) = a * b
        return (a / gcd(a, b)) * b;
    }

    public static long factorial(long n){
        long fact = 1L;
        for(int i=2;i<=n;i++)fact = (fact*i)%mod;
        return fact;
    }
    public static long firstDivisor(long n){
        if(n==1)return n;
        for(long i=2;i*i<=n;i++)
            if(n%i==0)return i;
        return -1;
    }
    public static long power(long x,long n){
        // calculate x^n %mod using binary exponentiation
        // time : O(logn)
        long ans = 1;
        while(n>0){
            if(n%2!=0){
                ans *= x;
                n--;
            }else {
                x *= x;
                n/=2;
            }
            x %=mod;
            ans %=mod;
        }
        return ans;
    }
    public  static int ncr(int n, int r){
        // time O(n+r)
        if (r > n)
            return 0;
        long[] inv = new long[r + 1];
        inv[1] = 1;
        // Getting the modular inversion
        // for all the numbers
        // from 2 to r with respect to m
        for (int i = 2; i <= r; i++) {
            inv[i] = mod - (mod / i) * inv[mod % i] % mod;
        }
        int ans = 1;
        // for 1/(r!) part
        for (int i = 2; i <= r; i++) {
            ans = (int) (((ans % mod) * (inv[i] % mod)) % mod);
        }
        // for (n)*(n-1)*(n-2)*...*(n-r+1) part
        for (int i = n; i >= (n - r + 1); i--) {
            ans = (int) (((ans % mod) * (i % mod)) % mod);
        }
        return ans;
    }
    public static void reverseArray(int[] a){
        int left = 0;
        int right = a.length-1;
        while (left<right){
            int temp =a[left];
            a[left] = a[right];
            a[right] = temp;
            left++;
            right--;
        }
    }
}