Gregor is learning about RSA cryptography, and although he doesn't understand how RSA works, he is now fascinated with prime numbers and factoring them.

Gregor's favorite prime number is P. Gregor wants to find two bases of P. Formally, Gregor is looking for two integers a and b which satisfy both of the following properties.

  * P mod a = P mod b, where x mod y denotes the remainder when x is divided by y, and 
  * 2 ≤ a < b ≤ P. 



Help Gregor find two bases of his favorite prime number!

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 1000).

Each subsequent line contains the integer P (5 ≤ P ≤ {10}^9), with P guaranteed to be prime.

Output

Your output should consist of t lines. Each line should consist of two integers a and b (2 ≤ a < b ≤ P). If there are multiple possible solutions, print any.

Example

Input


2
17
5


Output


3 5
2 4

Note

The first query is P=17. a=3 and b=5 are valid bases in this case, because 17 mod 3 = 17 mod 5 = 2. There are other pairs which work as well.

In the second query, with P=5, the only solution is a=2 and b=4.
2
17
5
 1
55439
 5
5
7
11
13
19

2 16
2 4
 2 55438
 2 4
2 6
2 10
2 12
2 18

    import java.io.*;
    import java.util.*;
    import java.math.*;
    import java.lang.*;
     



     //@Manan Parmar
    public class Solution2 implements Runnable {
        public void run() {
            
        InputReader sc = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        
        
        //code
        int t1=sc.nextInt();
        while(t1--!=0)
        {
            int n=sc.nextInt();
            int x=(n-1)/2;
            if(n==5)
                out.println(2+" "+4);
            else
            out.println(2+" "+x);
        }


        out.close();
        }
    /*
    class pairComparator implements Comparator<Pair>
        {
            public int compare(Pair p1,Pair p2)
            {
                return p1.a-p2.a;
            }
        }
            class Pair{
            int id;
            int a;

            public Pair(int id,int a)
            {
                this.id=id;
                this.a=a;
            }   
        }
    */  
     

    //========================================================================
        boolean isPrime(int n) 
        { 
            // Corner case 
            if (n <= 1) 
                return false; 
      
            // Check from 2 to n-1 
            for (int i = 2; i < n; i++) 
                if (n % i == 0) 
                    return false; 
      
            return true; 
        } 
        int lcm(int number1, int number2) {
            if (number1 == 0 || number2 == 0) {
                return 0;
            }
            int absNumber1 = Math.abs(number1);
            int absNumber2 = Math.abs(number2);
            int absHigherNumber = Math.max(absNumber1, absNumber2);
            int absLowerNumber = Math.min(absNumber1, absNumber2);
            int lcm = absHigherNumber;
            while (lcm % absLowerNumber != 0) {
                lcm += absHigherNumber;
            }
            return lcm;
        }
        void quickSort(int a[],int l,int r)
        {
            if(l<r)
            {
                int pindex=partition(a,l,r);
                quickSort(a,l,pindex-1);
                quickSort(a,pindex+1,r);
            }

        }
        int partition(int a[],int l,int r)
        {
            int pivot = a[r],pindex=l;
            for(int i=l;i<r;i++)
            {
                if(a[i]<pivot)
                {
                    int temp=a[i];
                    a[i]=a[pindex];
                    a[pindex]=temp;
                    pindex++;
                }
            }
            int temp1=a[r];
            a[r]=a[pindex];
            a[pindex]=temp1;
            return pindex;
        }
        int binarySearch(int arr[], int x) 
        { 
            int l = 0, r = arr.length - 1; 
            while (l <= r) { 
                int m = l + (r - l) / 2; 
      
                // Check if x is present at mid 
                if (arr[m] >= x)
                    if(m!=0&&arr[m-1]<x) 
                        return m;
                    else if(m==0)
                        return m; 
      
                // If x greater, ignore left half 
                if (arr[m] < x) 
                    l = m + 1; 
      
                // If x is smaller, ignore right half 
                else
                    r = m - 1; 
            } 
      
            // if we reach here, then element was 
            // not present 
            return -1; 
        } 
        boolean check(char a,char b)
        {
            if(a==b)
                return true;
            else
                return false;
        }
        long binarySearch(long arr[], long x) 
        { 
            int l = 0, r = arr.length - 1,q=0; 
            while (l<=r) { 
                int m = l + (r - l) / 2; 
                if (arr[l] >=x) 
                {
                    q=1;
                    return l; 
                }
                if (arr[m] < x) 
                    l=m+1; 
                else
                    r=m;
            } 
            return -1;
        }

        static class InputReader {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;
            private SpaceCharFilter filter;
            private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
     
            public InputReader(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 String nextLine() {
                String str = "";
                try {
                    str = br.readLine();
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
                return str;
            }
            public int nextInt() {
                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 nextLong() {
                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 double nextDouble() {
                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, nextInt());
                    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, nextInt());
                        if (c < '0' || c > '9')
                            throw new InputMismatchException();
                        m /= 10;
                        res += (c - '0') * m;
                        c = read();
                    }
                }
                return res * sgn;
            }
           
            public String readString() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = read();
                }
                while (!isSpaceChar(c));
               
                return res.toString();
            }
         
            public boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }
         
            public String next() {
                return readString();
            }
           
            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }

        public static void main(String args[]) throws Exception {
            new Thread(null, new Solution2(),"Main",1<<27).start();
        }
    }
