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.util.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.Arrays;
import java.util.Map.Entry;

import javafx.scene.shape.Line;
 
public class codeforces {
	public static void main(String[] args) throws Exception {
		int t=sc.nextInt();
		while(t-->0) {
			int p=sc.nextInt();
			int a=2;
			int b=(p-1)/2;
			if(a==b)b*=2;
			pw.println(a+" "+b);
		}
		
		pw.close();
	}
	
	
	
	public static long eval(String s) {
		long p=1;
		long res=0;
		for (int i = 0; i < s.length(); i++) {
			res+=p*(s.charAt(s.length()-1-i)=='1'?1:0);
			p*=2;
		}
		return res;
	}
	
	public static String binary(long x) {
		String s="";
		while(x!=0) {
			s=(x%2)+s;
			x/=2;
		}
		return s;
	}
	
	public static boolean allSame(String s) {
		char x=s.charAt(0);
		for (int i = 0; i < s.length(); i++) {
			if(s.charAt(i)!=x)return false;
		}
		return true;
	}
	
	public static boolean isPalindrom(String s) {
		int l=0;
		int r=s.length()-1;
		while(l<r) {
			if(s.charAt(r--)!=s.charAt(l++))return false;
			
		}
		return true;
	}
	 
	public static String putAtFront(String s,char c) {
		if(s.length()==0)return s;
		if(s.charAt(s.length()-1)==c) {
			return s.charAt(s.length()-1)+putAtFront(s.substring(0,s.length()-1), c);
		}else {
			return putAtFront(s.substring(0,s.length()-1), c)+s.charAt(s.length()-1);
		}
	}
	
	public static boolean isSubString(String s,String t) {
		int ls=s.length();
		int lt=t.length();
		boolean res=false;
		for (int i = 0; i <=lt-ls; i++) {
			if(t.substring(i, i+ls).equals(s)) {
				res=true;
				break;
			}
		}
		return res;
	}
	
	public static boolean isSorted(int[]a) {
		for (int i = 0; i < a.length-1; i++) {
			if(a[i]>a[i+1])return false;
		}
		return true;
	}
	
	public static boolean isPrime(int n)
    {
 
        // Check if number is less than
        // equal to 1
        if (n <= 1)
            return false;
 
        // Check if number is 2
        else if (n == 2)
            return true;
 
        // Check if n is a multiple of 2
        else if (n % 2 == 0)
            return false;
 
        // If not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2)
        {
            if (n % i == 0)
                return false;
        }
        return true;
    }
	public static long power(long x,long k) {
		long res=1;
		long mod=((int)1e9)+7;
		for (int i = 0; i < k; i++) {
			res*=x;
			res=res%mod;
		}
		return res;
	}
	public static int whichPower(int x) {
		int res=0;
		for (int j = 0; j < 31; j++) {
			if((1<<j&x)!=0) {
				res=j;
				break;
			}
		}
		return res;
	}
 
	public static long evaln(String x,int n) {
		long res=0;
		for (int i = 0; i < x.length(); i++) {
			res+=Long.parseLong(x.charAt(x.length()-1-i)+"")*Math.pow(n, i);
		}
		return res;
	}
	static void merge(int[] arr,int b,int m,int e) {
		int len1=m-b+1,len2=e-m;
		int[] l=new int[len1];
		int[] r=new int[len2];
		for(int i=0;i<len1;i++)l[i]=arr[b+i];
		for(int i=0;i<len2;i++)r[i]=arr[m+1+i];
		int i=0,j=0,k=b;
		while(i<len1 && j<len2) {
			if(l[i]<r[j])arr[k++]=l[i++];
			else arr[k++]=r[j++];
		}
		while(i<len1)arr[k++]=l[i++];
		while(j<len2)arr[k++]=r[j++];
		return;
	}
	static void mergesortidx(long[] arr,long[]idx,int b,int e) {
		if(b<e) {
			int m=b+(e-b)/2;
			mergesortidx(arr,idx,b,m);
			mergesortidx(arr,idx,m+1,e);
			mergeidx(arr,idx,b,m,e);
		}
		return;
		
	}
	static void mergeidx(long[] arr,long[]idx,int b,int m,int e) {
		int len1=m-b+1,len2=e-m;
		long[] l=new long[len1];
		long[] lidx=new long[len1];
		long[] r=new long[len2];
		long[] ridx=new long[len2];
		for(int i=0;i<len1;i++) {
			l[i]=arr[b+i];
			lidx[i]=idx[b+i];
		}
		for(int i=0;i<len2;i++) {
			r[i]=arr[m+1+i];
			ridx[i]=idx[m+1+i];
		}
		int i=0,j=0,k=b;
		while(i<len1 && j<len2) {
			if(l[i]<r[j]) {
				arr[k++]=l[i++];
				idx[k-1]=lidx[i-1];
			}
			else {
				arr[k++]=r[j++];
				idx[k-1]=ridx[j-1];
			}
		}
		while(i<len1) {
			idx[k]=lidx[i];
			arr[k++]=l[i++];
		}
		while(j<len2) {
			idx[k]=ridx[j];
			arr[k++]=r[j++];
		}
		return;
	}
	static void mergesort(int[] arr,int b,int e) {
		if(b<e) {
			int m=b+(e-b)/2;
			mergesort(arr,b,m);
			mergesort(arr,m+1,e);
			merge(arr,b,m,e);
		}
		return;
		
	}
	
	static long mergen(int[] arr,int b,int m,int e) {
		int len1=m-b+1,len2=e-m;
		int[] l=new int[len1];
		int[] r=new int[len2];
		for(int i=0;i<len1;i++)l[i]=arr[b+i];
		for(int i=0;i<len2;i++)r[i]=arr[m+1+i];
		int i=0,j=0,k=b;
		long c=0;
		while(i<len1 && j<len2) {
			if(l[i]<r[j])arr[k++]=l[i++];
			else {
				arr[k++]=r[j++];
				c=c+(long)(len1-i);
			}
		}
		while(i<len1)arr[k++]=l[i++];
		while(j<len2)arr[k++]=r[j++];
		return c;
	}
	static long mergesortn(int[] arr,int b,int e) {
		long c=0;
		if(b<e) {
			int m=b+(e-b)/2;
			c=c+(long)mergesortn(arr,b,m);
			c=c+(long)mergesortn(arr,m+1,e);
			c=c+(long)mergen(arr,b,m,e);
		}
		return c;
		
	}
	public static long fac(int n) {
		if(n==0)return 1;
		return n*fac(n-1);
	}
	public static long gcd(long a, long b)
    {
      if (b == 0)
        return a;
      return gcd(b, a % b);
    }
     
	public static long summ(long x) {
		long sum=0;
		while(x!=0) {
			sum+=x%10;
			x=x/10;
		}
		return sum;
				
	}
	
	public static void sort2darray(Integer[][]a){
		Arrays.sort(a,Comparator.<Integer[]>comparingInt(x -> x[0]).thenComparingInt(x -> x[1]));
 
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
		public Scanner(String file) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		public boolean ready() throws IOException {
			return br.ready();
		}
		public int[] nextArrint(int size) throws IOException {
			int[] a=new int[size];
			for (int i = 0; i < a.length; i++) {
				a[i]=sc.nextInt();
			}
			return a;
		}
		public long[] nextArrlong(int size) throws IOException {
			long[] a=new long[size];
			for (int i = 0; i < a.length; i++) {
				a[i]=sc.nextLong();
			}
			return a;
		}
		public int[][] next2dArrint(int rows,int columns) throws IOException{
			int[][]a=new int[rows][columns];
			for (int i = 0; i < rows; i++) {
				for (int j = 0; j < columns; j++) {
					a[i][j]=sc.nextInt();
				}
			}
			return a;
		}
		public long[][] next2dArrlong(int rows,int columns) throws IOException{
			long[][]a=new long[rows][columns];
			for (int i = 0; i < rows; i++) {
				for (int j = 0; j < columns; j++) {
					a[i][j]=sc.nextLong();
				}
			}
			return a;
		}
	}
	static class Side{
		Point a;
		Point b;
		public Side(Point a,Point b) {
			this.a=a;
			this.b=b;
		}
		@Override
		public boolean equals(Object obj) {
			Side s=(Side)obj;
			return (s.a.equals(a)&&s.b.equals(b))||(s.b.equals(a)&&s.a.equals(b));
		}
		@Override
		public String toString() {
			
			return "("+a.toString()+","+b.toString()+")";
		}
	}
	static class Point{
		int x;
		int y;
		int z;
		public Point(int x,int y,int z) {
			this.x=x;
			this.y=y;
			this.z=z;
		}
		@Override
		public boolean equals(Object obj) {
			Point p=(Point)obj;
			return x==p.x&&y==p.y&&z==p.z;
		}
		@Override
		public String toString() {
			return "("+x+","+y+","+z+")";
		}
	}
	static class Pair{
		long x;
		long y;
		public Pair(long x,long y) {
			this.x=x;
			this.y=y;
		}
	}
	static Scanner sc=new Scanner(System.in);
	static PrintWriter pw=new PrintWriter(System.out);
}