Problem: You are given an array [a_1, a_2, ..., a_n] such that 1 ≤ a_i ≤ 10^9. Let S be the sum of all elements of the array a.

Let's call an array b of n integers beautiful if:

  * 1 ≤ b_i ≤ 10^9 for each i from 1 to n; 
  * for every pair of adjacent integers from the array (b_i, b_{i + 1}), either b_i divides b_{i + 1}, or b_{i + 1} divides b_i (or both); 
  * 2 ∑ _{i = 1}^{n} |a_i - b_i| ≤ S. 



Your task is to find any beautiful array. It can be shown that at least one beautiful array always exists.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each test case consists of two lines. The first line contains one integer n (2 ≤ n ≤ 50).

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).

Output

For each test case, print the beautiful array b_1, b_2, ..., b_n (1 ≤ b_i ≤ 10^9) on a separate line. It can be shown that at least one beautiful array exists under these circumstances. If there are multiple answers, print any of them.

Example

Input


4
5
1 2 3 4 5
2
4 6
2
1 1000000000
6
3 4 8 1 2 3


Output


3 3 3 3 3
3 6
1 1000000000
4 4 8 1 3 3

Solution (in JAVA):

Solution:
/**
 *
 * @author Harshwardhan Yadav
 */
import java.math.*;
import java.io.*;
import java.util.*;
public class Codeforces {

    /**
     * @param args the command line arguments
     */
    //matrix eight directions conditions
    /*if(p.x>1 && p.y>1 && board[p.x-1][p.y-1]!=1)
                {
                    q.add(new pair(p.x-1,p.y-1));
                }
                if(p.x>1 && board[p.x-1][p.y]!=1){
                    q.add(new pair(p.x-1,p.y));
                }
                if(p.x>1 && p.y<n && board[p.x-1][p.y+1]!=1){
                    q.add(new pair(p.x-1,p.y+1));
                }
                if(p.y>1 && board[p.x][p.y-1]!=1){
                    q.add(new pair(p.x,p.y-1));
                }
                if(p.y<n && board[p.x][p.y+1]!=1){
                    q.add(new pair(p.x,p.y+1));
                }
                if(p.x<n && p.y>1 && board[p.x+1][p.y-1]!=1){
                    q.add(new pair(p.x+1,p.y-1));
                }
                if(p.x<n && board[p.x+1][p.y]!=1){
                    q.add(new pair(p.x+1,p.y));
                }
                if(p.x<n && p.y<n && board[p.x+1][p.y+1]!=1){
                    q.add(new pair(p.x+1,p.y+1));
                }
            }*/
    static class Valueable{
        char ch;
        int pos;
        Valueable(char ch,int pos)
        {
            this.ch=ch;
            this.pos=pos;
        }
    }

    static class Sortbyroll implements Comparator<Valueable> 
    { 
        // Used for sorting in ascending order of 
        // roll number 
        @Override
        public int compare(Valueable a,Valueable b)
        {
            return a.ch-b.ch;
        }
    } 

    static int findMaxElementIndex(int ar[])
    {
        int index=0;
        int max=0;
        int n=ar.length;
        for(int i=0;i<n;i++)
        {
            if(ar[i]>max)
            {
                max=ar[i];
                index=i;
            }
        }
        return index;
    }

    static int findMaxElement(int ar[])
    {
        int max=0;
        int n=ar.length;
        for(int i=0;i<n;i++)
        {
            if(ar[i]>max)
            {
                max=ar[i];
            }
        }
        return max;
    }

    static int binarySearch(String s,String q,int p[],int start,int end)
    {
        int mid=(start+end)/2;
        int result=-1;
        int n=s.length();
        if(start<=end)
        {
            int x=0;
            if(x==0)
            {
                return mid;
            }
            else if(x<0)
            {
                result=binarySearch(s, q, p,mid+1, end);
            }
            else{
                result=binarySearch(s, q, p,start, mid-1);
            }
        }
        else{
            return -1;
        }
        return result;
    }
    
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
 
        public FastReader() 
        { 
            br = new BufferedReader(new
                    InputStreamReader(System.in)); 
        } 
 
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
 
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
 
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
 
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
 
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        }
        
        int[] nextIntArray(int n)
        {
            int arr[]=new int[n];
            for(int i=0;i<n;i++)
            {
                arr[i]=Integer.parseInt(next());
            }
            return arr;
        }

        Integer[] nextIntegerArray(int n)
        {
            Integer arr[]=new Integer[n];
            for(Integer i=0;i<n;i++)
            {
                arr[i]=Integer.parseInt(next());
            }
            return arr;
        }

        long[] nextLongArray(int n)
        {
            long arr[]=new long[n];
            for(int i=0;i<n;i++)
            {
                arr[i]=Long.parseLong(next());
            }
            return arr;
        }

    } 
 
    static int gcd(Integer a,Integer b)
    {
        if(b==0)
            return a;
        else
            return gcd(b,a%b);
    }
 
    static boolean checkForPrime(long inputNumber)
    {
        boolean isItPrime = true;
        if(inputNumber <= 1) 
        {
            isItPrime = false;
            return isItPrime;
        }
        else
        {
            if(inputNumber%2==0 && inputNumber==2)
            {
                return true;
            }
            else if(inputNumber%2==0)
            {
                return false;
            }
            else{
                int check=(int)Math.sqrt(inputNumber);
                for (int i = 3; i<= check; i+=2) 
                {
                    if ((inputNumber % i) == 0)
                    {
                        isItPrime = false;
                        break;
                    }
                }
            }
        }
 
        return isItPrime;
    } 
    
    /*static SortedSet<Valueable> ts=new TreeSet<Valueable>(new Comparator<Valueable>(){
        @Override
        public int compare(Valueable a,Valueable b)
        {
            if(a.r-a.l==b.r-b.l)
            {
                return a.l-b.l;
            }
            else{
                return (-1)*((a.r-a.l)-(b.r-b.l));
            }
        }
    }
    );*/
    
    static int getMax(int arr[], int n) 
    { 
        int mx = arr[0]; 
        for (int i = 1; i < n; i++) 
            if (arr[i] > mx) 
                mx = arr[i]; 
        return mx; 
    }
    static void countSort(int p[], int n, int exp,int[] c) 
    { 
        int output[] = new int[n]; 
        int i; 
        int count[] = new int[10]; 
        Arrays.fill(count, 0);  
        for (i = 0; i < n; i++) 
            count[(c[p[i]] / exp) % 10]++;
        for (i = 1; i < 10; i++) 
            count[i] += count[i - 1]; 
        for (i = n - 1; i >= 0; i--) { 
            output[count[(c[p[i]] / exp) % 10] - 1] = p[i]; 
            count[(c[p[i]] / exp) % 10]--; 
        } 
        for (i = 0; i < n; i++) 
            p[i] = output[i]; 
    } 
  
    static void radixsort(int p[], int[] c) 
    { 
        int m = getMax(p,p.length); 
        for (int exp = 1; m / exp > 0; exp *= 10) 
            countSort(p, p.length, exp,c); 
    }
    
    static class pair{
        int x,y;
        boolean b=false;
        pair(int i,int j)
        {
            x=i;
            y=j;
        }
    }
    
    public static void main(String[] args) throws UnsupportedEncodingException, IOException {
        // TODO code application logic here
        FastReader sc=new FastReader();
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);
        int t=sc.nextInt();
        for(int test=0;test<t;test++)
        {
            int n=sc.nextInt();
            int a[]=sc.nextIntArray(n);
            int[] b=new int[n];
            long s=0;
            long s1=0;
            for(int i=0;i<n;i++)
            {
                if(i%2==0)
                    b[i]=1;
                else
                    b[i]=a[i];
                s+=a[i];
                s1+=(int)Math.abs(b[i]-a[i]);
            }
            if(2*s1>s)
            {
                for(int i=0;i<n;i++)
                {
                    if(i%2!=0)
                        b[i]=1;
                    else
                        b[i]=a[i];
                }
            }
            for(int i=0;i<n;i++)
                out.write(b[i]+" ");
            out.write("\n");
            out.flush();
        }    
        out.close();
    }
    
}