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:
// @uthor -: puneet
// TimeStamp -: 9:03 PM - 29/11/19 

import javax.swing.*;
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Q33 implements Runnable {


    public void solve() {
        int t=in.ni();
        while(t-->0){
            int n=in.ni();
            TreeMap<Integer,Integer> map=new TreeMap<>();
            for(int i=1;i*i<=n;++i){
                int temp=n/i;
                int temp2=n/temp;
                map.put(temp,1);
                map.put(temp2,1);
            }
            map.put(0,1);
            out.println(map.size());
            for(int i:map.keySet()){
                out.print(i+" ");
            }
            out.println();
        }
    }

    /* -------------------- Templates and Input Classes -------------------------------*/

    @Override
    public void run() {
        try {
            init();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
        solve();
        out.flush();
    }

    private FastInput in;
    private PrintWriter out;

    public static void main(String[] args) throws Exception {
        new Thread(null, new Q33(), "Main", 1 << 27).start();
    }

    private void init() throws FileNotFoundException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        try {
            if (System.getProperty("user.name").equals("puneet")) {
                outputStream = new FileOutputStream("/home/puneet/Desktop/output.txt");
                inputStream = new FileInputStream("/home/puneet/Desktop/input.txt");
            }
        } catch (Exception ignored) {
        }
        out = new PrintWriter(outputStream);
        in = new FastInput(inputStream);
    }

    private void sort(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int object : arr) list.add(object);
        Collections.sort(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }

    private void sort(long[] arr) {
        List<Long> list = new ArrayList<>();
        for (long object : arr) list.add(object);
        Collections.sort(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }

    public long ModPow(long x, long y, long MOD) {
        long res = 1L;
        x = x % MOD;
        while (y >= 1) {
            if ((y & 1) > 0) res = (res * x) % MOD;
            x = (x * x) % MOD;
            y >>= 1;
        }
        return res;
    }

    public int gcd(int a, int b) {
        if (a == 0) return b;
        return gcd(b % a, a);
    }

    public long gcd(long a, long b) {
        if (a == 0) return b;
        return gcd(b % a, a);
    }

    static class FastInput {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public FastInput(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int peek() {
            if (numChars == -1) {
                return -1;
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String ns() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private String readLine0() {
            StringBuilder buf = new StringBuilder();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r') {
                    buf.appendCodePoint(c);
                }
                c = read();
            }
            return buf.toString();
        }

        public String readLine() {
            String s = readLine0();
            while (s.trim().length() == 0) {
                s = readLine0();
            }
            return s;
        }

        public String readLine(boolean ignoreEmptyLines) {
            if (ignoreEmptyLines) {
                return readLine();
            } else {
                return readLine0();
            }
        }

        public BigInteger readBigInteger() {
            try {
                return new BigInteger(ns());
            } catch (NumberFormatException e) {
                throw new InputMismatchException();
            }
        }

        public char nc() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            return (char) c;
        }

        public double nd() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, ni());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, ni());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }


        public String next() {
            return ns();
        }

        public SpaceCharFilter getFilter() {
            return filter;
        }

        public void setFilter(SpaceCharFilter filter) {
            this.filter = filter;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }

        public int[] intarr(int n) {
            int arr[] = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = ni();
            }
            return arr;
        }

        public double[] doublearr(int n) {
            double arr[] = new double[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nd();
            }
            return arr;
        }

        public double[][] doublearr(int n, int m) {
            double[][] arr = new double[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    arr[i][j] = nd();
                }
            }
            return arr;
        }

        public int[][] intarr(int n, int m) {
            int[][] arr = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    arr[i][j] = ni();
                }
            }
            return arr;
        }


        public long[][] longarr(int n, int m) {
            long[][] arr = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    arr[i][j] = nl();
                }
            }
            return arr;
        }

        public long[] longarr(int n) {
            long arr[] = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nl();
            }
            return arr;
        }

    }

}