Problem: You are given a sequence b_1, b_2, …, b_n. Find the lexicographically minimal permutation a_1, a_2, …, a_{2n} such that b_i = min(a_{2i-1}, a_{2i}), or determine that it is impossible.

Input

Each test contains one or more test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100).

The first line of each test case consists of one integer n — the number of elements in the sequence b (1 ≤ n ≤ 100).

The second line of each test case consists of n different integers b_1, …, b_n — elements of the sequence b (1 ≤ b_i ≤ 2n).

It is guaranteed that the sum of n by all test cases doesn't exceed 100.

Output

For each test case, if there is no appropriate permutation, print one number -1.

Otherwise, print 2n integers a_1, …, a_{2n} — required lexicographically minimal permutation of numbers from 1 to 2n.

Example

Input


5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8


Output


1 2 
-1
4 5 1 2 3 6 
-1
1 3 5 6 7 9 2 4 8 10 

Solution (in JAVA):

Solution:
//package learning;
import java.util.*;
import java.io.*;
import java.lang.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public class NitsLocal {
    static ArrayList<String> s1;
    static boolean[] prime;
    static int n = (int)1e7;
    
     static void sieve() {
Arrays.fill(prime	, true);
prime[0] = prime[1] = false;
for(int i = 2 ; i * i <= n ; ++i) {
if(prime[i]) {
for(int k = i * i; k<= n ; k+=i) {
prime[k] = false;
}
}
}
 
}
    public static void main(String[] args) {
        InputReader sc = new InputReader(System.in);
        n *= 2;
           prime  = new boolean[n + 1];
           //sieve();
                prime[1] = false;
              
                  
             /*    
        int n = sc.ni();
        int k = sc.ni();
        int []vis = new int[n+1];
        int []a = new int[k];
        for(int i=0;i<k;i++)
        {
            a[i] = i+1;
        }
        int j = k+1;
        int []b = new int[n+1];
        for(int i=1;i<=n;i++)
        {
            b[i] = -1;
        }
        int y = n - k +1;
        int tr = 0;
        int y1 = k+1;
        while(y-- > 0)
        {
        System.out.print("? ");
        for(int i=0;i<k;i++)
        {
            System.out.print(a[i] + " ");
        }
        
        System.out.flush();
        int pos = sc.ni();
        int a1 = sc.ni();
        b[pos] = a1;
        
        
        for(int i=0;i<k;i++)
        {
            if(a[i] == pos)
            {
                a[i] = y1;
                y1++;
            }
        }
        }
        ArrayList<Integer> a2 = new ArrayList<>();
        if(y >= k)
        {
            
        int c = 0;
        int k1 = 0;
            for(int i=1;i<=n;i++)
            {
                if(b[i] != -1)
                {
                    c++;
                    a[k1] = i;
                    a2.add(b[i]);
                    k1++;
                }
                if(c==k)
                    break;
            }
            
            Collections.sort(a2);
            System.out.print("? ");
        for(int i=0;i<k;i++)
        {
            System.out.print(a[i] + " ");
        }
        System.out.println();
        System.out.flush();
        int pos = sc.ni();
        int a1 = sc.ni();
        int ans = -1;
        for(int i=0;i<a2.size();i++)
        {
            if(a2.get(i) == a1)
            {
                ans = i+1;
                break;
            }
        }
        System.out.println("!" + " " + ans);
           System.out.flush();  
        }
        else
        {
            int k1 = 0;
            a = new int[k];
             for(int i=1;i<=n;i++)
            {
                if(b[i] != -1)
                {
                    
                    a[k1] = i;
                    a2.add(b[i]);
                    k1++;
                }
             
            }
              for(int i=1;i<=n;i++)
            {
                if(b[i] == -1)
                {
                    
                    a[k1] = i;
                    
                    k1++;
                    if(k1==k)
                        break;
                }
             
            }
              int ans = -1;
              while(true)
              {
                   System.out.print("? ");
                     for(int i=0;i<k;i++)
                   {
                         System.out.print(a[i] + " ");
                  }
                   System.out.println();
                   System.out.flush();
                   int pos = sc.ni();
                   int a1 = sc.ni();
                   int f = 0;
                   
                   if(b[pos] != -1)
                   {
                       Collections.sort(a2);
                       for(int i=0;i<a2.size();i++)
                       {
                           if(a2.get(i) == a1)
                           {
                               ans = i+1;
                               f = 1;
                               System.out.println("!" + " " + ans);
                               System.out.flush();
                               break;
                           }
                       }
                       if(f==1)
                           break;
                   }
                   else
                   {
                       b[pos] = a1;
                        a = new int[k];
                        a2.add(a1);
             for(int i=1;i<=n;i++)
            {
                if(b[i] != -1)
                {
                    
                    a[k1] = i;
                    a2.add(b[i]);
                    k1++;
                }
             
            }
              for(int i=1;i<=n;i++)
            {
                if(b[i] == -1)
                {
                    
                    a[k1] = i;
                    
                    k1++;
                    if(k1==k)
                        break;
                }
             
            }
                       
                   }
              }
        }  
          */
             
                 
     int t = sc.ni();
     while(t-- > 0)
     {
         int n = sc.ni();
         boolean []vis = new boolean[2*n+1];
         ArrayList<Integer> []a1 = new ArrayList[n];
         for(int i=0;i<n;i++)
         {
             a1[i] = new ArrayList<>();
             int p = sc.ni();
             a1[i].add(p);
             vis[p] = true;
         }
         int f = 0;
         for(int i=0;i<n;i++)
         {
             int temp = a1[i].get(0);
             for(int j=temp+1;j<=2*n;j++)
             {
                 if(!vis[j])
                 {
                     a1[i].add(j);
                     vis[j] = true;
                     break;
                 }
             }
             
         }
         for(int i=0;i<n;i++)
         {
             if(a1[i].size() != 2)
             {
                 f=1;
                 break;
             }
         }
         if(f==1)
             w.println("-1");
         else
         {
             for(int i=0;i<n;i++)
             {
                 w.print(a1[i].get(0) + " " + a1[i].get(1) + " ");
             }
             w.println();
         }
        
     }
           
             
         
        
      
      
       w.close();
       
        
    }
 static class Student{
     int time;
     int l;
     int h;
     Student(int time,int l,int h)
     {
         this.time = time;
         this.l = l;
         this.h = h;
     }
 }
   
   
   
 
     static int upperBound(ArrayList<Integer> a, int low, int high, int element){
    while(low < high){
        int middle = low + (high - low)/2;
        if(a.get(middle) >= element)
            high = middle;
        else 
            low = middle + 1;
    }
    return low;
}
   static long func(long t,long e,long h,long a, long b)
   {
       if(e*a >= t)
           return t/a;
       else
       {
           return e + Math.min(h,(t-e*a)/b);
       }
   }
         
      
    public static int upperBound(int []arr,int n,int num)
    {
        int l = 0;
        int r = n;
        while(l < r)
        {
            int mid = (l+r)/2;
            if(num >= arr[mid])
            {
                l = mid +1;
            }
            else
                r = mid;
        }
        return l;
    }
    public static int countSetBits(int number){
        int count = 0;
        while(number>0){
            ++count;
            number &= number-1;
        }
        return count;
    }
    
     
      
 
    
    static HashSet<Integer> fac;
    public static void primeFactors(int n) 
    { 
        // Print the number of 2s that divide n 
        int t = 0;
        while (n%2==0) 
        { 
            fac.add(2);
            n /= 2; 
        } 
  
        // n must be odd at this point.  So we can 
        // skip one element (Note i = i +2) 
        for (int i = 3; i*i <= n; i+= 2) 
        { 
            // While i divides n, print i and divide n 
            while (n%i == 0) 
            { 
                fac.add(i);
                n /= i; 
            } 
        } 
  
        // This condition is to handle the case whien 
        // n is a prime number greater than 2 
        if (n > 2) 
            fac.add(n);
    } 
     static long modexp(long x,long n,long M)
{
    long power = n;
    long result=1;
    x = x%M;
    while(power>0)
    {
        if(power % 2 ==1)
            result=(result * x)%M;
        x=(x*x)%M;
        power = power/2;
    }
    return result;
}
      static long modInverse(long A,long M)
{
    return modexp(A,M-2,M);
}
    static long gcd(long a,long b)
    {
        if(a==0)
            return b;
        else
            return gcd(b%a,a);
    }
    static class Temp{
        int a;
        int b;
        int c;
        int d;
      
        Temp(int a,int b,int c,int d)
        {
            this.a = a;
            this.b = b;
            this.c  =c;
            this.d = d;
            //this.d = d;
        }
    }
   
    
    
   static long sum1(int t1,int t2,int x,int []t)
   {
       int mid = (t2-t1+1)/2;
  if(t1==t2)
      return 0;
    
   else
   return sum1(t1,mid-1,x,t) + sum1(mid,t2,x,t);
    
     
   }
  
   
    static String replace(String s,int a,int n)
    {
        char []c = s.toCharArray();
        for(int i=1;i<n;i+=2)
        {
            int num = (int) (c[i] - 48);
            num += a;
            num%=10;
            c[i] = (char) (num+48);
        }
        return new String(c);
    }
    static String move(String s,int h,int n)
    {
        h%=n;
        char []c = s.toCharArray();
        char []temp = new char[n];
        for(int i=0;i<n;i++)
        {
            temp[(i+h)%n] = c[i];
        }
        return new String(temp);
    }
    
     public static int ip(String s){
return Integer.parseInt(s);
}
     static class multipliers implements Comparator<Long>{
  
         
  public int compare(Long a,Long b) {
   if(a<b)
    return 1;
   else if(b<a)
    return -1;
   else
    return 0;
  }
 }
     
     static class multipliers1 implements Comparator<Student>{
  
  public int compare(Student a,Student b) {
   if(a.time<b.time)
    return -1;
   else if(b.time<a.time)
    return 1;
   else
   {
       if(a.l < b.l)
           return -1;
       else if(b.l<a.l)
           return 1;
       else
       {
           if(a.h < b.h)
           return -1;
       else if(b.h<a.h)
           return 1;
           else
           return 0;
       }
           
    //return 0;
   }
  }

 }

    // Java program to generate power set in 
// lexicographic order. 
 
    
    
    
      static class InputReader {
 
private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
 
public InputReader(InputStream st) {
this.stream = st;
}
 
public int read() {
if (snumChars == -1)
throw new InputMismatchException();
if (curChar >= snumChars) {
curChar = 0;
try {
snumChars = stream.read(buf);
} catch (IOException e) {
throw new InputMismatchException();
}
if (snumChars <= 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 {
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 {
res *= 10;
res += c - '0';
c = read();
} while (!isSpaceChar(c));
return res * sgn;
}
 
public int[] nia(int n) {
int a[] = new int[n];
for (int i = 0; i < n; i++) {
a[i] = ni();
}
return a;
}
 
public String rs() {
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 String nextLine() {
int c = read();
while (isSpaceChar(c))
c = read();
StringBuilder res = new StringBuilder();
do {
res.appendCodePoint(c);
c = read();
} while (!isEndOfLine(c));
return res.toString();
}
 
public boolean isSpaceChar(int c) {
return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
}
 
private boolean isEndOfLine(int c) {
return c == '\n' || c == '\r' || c == -1;
}
 
}
 
 
 
 
 
   
static PrintWriter w = new PrintWriter(System.out);
                  static class Student1
    {
        int id;
        //int x;
       
       int b;
      
        //long z;
        
        Student1(int id,int b)
        {
            this.id = id;
            //this.x = x;
            //this.s = s;
            this.b = b;
          
           // this.z = z;
            
            
            
           
        }
        
    }
}