Given a positive integer n. Find three distinct positive integers a, b, c such that a + b + c = n and \operatorname{gcd}(a, b) = c, where \operatorname{gcd}(x, y) denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers x and y.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Description of the test cases follows.

The first and only line of each test case contains a single integer n (10 ≤ n ≤ 10^9).

Output

For each test case, output three distinct positive integers a, b, c satisfying the requirements. If there are multiple solutions, you can print any. We can show that an answer always exists.

Example

Input


6
18
63
73
91
438
122690412


Output


6 9 3
21 39 3
29 43 1
49 35 7
146 219 73
28622 122661788 2

Note

In the first test case, 6 + 9 + 3 = 18 and \operatorname{gcd}(6, 9) = 3.

In the second test case, 21 + 39 + 3 = 63 and \operatorname{gcd}(21, 39) = 3.

In the third test case, 29 + 43 + 1 = 73 and \operatorname{gcd}(29, 43) = 1.
1
669278611
 10
10
52
91
23
44
99
28
54
99
51

334639303 334639307 1
 4 5 1
25 26 1
43 47 1
9 13 1
21 22 1
47 51 1
13 14 1
26 27 1
47 51 1
23 27 1

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

public class Main
{
    static long mod = (int)1e9+7;
    // static PrintWriter out=new PrintWriter(new BufferedOutputStream(System.out));
    public static void main (String[] args) throws java.lang.Exception
    {
        FastReader sc =new FastReader();

        int t=sc.nextInt();
   
    //   int t=1;
   
        while(t-->0)
        {
            int n=sc.nextInt();
            int m=n-1;
		    if(n%2==0)
		    {
			    System.out.println(2+" "+(n-3)+" "+1);
		    }
		    else if(((n-1)/2)%2==0)
		    {
			    System.out.println((m/2-1)+" "+(m/2+1)+" "+1);
		    }
		    else
		    {
			    System.out.println((m/2-2)+" "+(m/2+2)+" "+1);
		    }
        }
        // out.flush();
    }

static int findfrequencies(int a[],int n)
{
    int count=0;
    for(int i=0;i<a.length;i++)
    {
        if(a[i]==n)
        {
            count++;
        }
    }
    return count;
}

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());
        }
       
        float nextFloat()
        {
            return Float.parseFloat(next());
        }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
       
        int[] readArray(int n) {
int[] a=new int[n];
for (int i=0; i<n; i++) a[i]=nextInt();
return a;
}

long[] readArrayLong(int n) {
long[] a=new long[n];
for (int i=0; i<n; i++) a[i]=nextLong();
return a;
}

    }
   
    public static int[] radixSort2(int[] a)
{
int n = a.length;
int[] c0 = new int[0x101];
int[] c1 = new int[0x101];
int[] c2 = new int[0x101];
int[] c3 = new int[0x101];
for(int v : a) {
c0[(v&0xff)+1]++;
c1[(v>>>8&0xff)+1]++;
c2[(v>>>16&0xff)+1]++;
c3[(v>>>24^0x80)+1]++;
}
for(int i = 0;i < 0xff;i++) {
c0[i+1] += c0[i];
c1[i+1] += c1[i];
c2[i+1] += c2[i];
c3[i+1] += c3[i];
}
int[] t = new int[n];
for(int v : a)t[c0[v&0xff]++] = v;
for(int v : t)a[c1[v>>>8&0xff]++] = v;
for(int v : a)t[c2[v>>>16&0xff]++] = v;
for(int v : t)a[c3[v>>>24^0x80]++] = v;
return a;
}

static int[] EvenOddArragement(int a[])
{
    ArrayList<Integer> list=new ArrayList<>();
    for(int i=0;i<a.length;i++)
    {
        if(a[i]%2==0)
        {
            list.add(a[i]);
        }
    }
    for(int i=0;i<a.length;i++)
    {
        if(a[i]%2!=0)
        {
            list.add(a[i]);
        }
    }
    for(int i=0;i<a.length;i++)
    {
        a[i]=list.get(i);
    }
    return a;
}
static int gcd(int a, int b) {
    while (b != 0) {
        int t = a;
        a = b;
        b = t % b;
    }
    return a;
}
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }
   
    public static HashMap<Integer, Integer> sortByValue(HashMap<Integer, Integer> hm)
    {
        // Create a list from elements of HashMap
        List<Map.Entry<Integer, Integer> > list =
               new LinkedList<Map.Entry<Integer, Integer> >(hm.entrySet());
 
        // Sort the list
        Collections.sort(list, new Comparator<Map.Entry<Integer, Integer> >() {
            public int compare(Map.Entry<Integer, Integer> o1,
                               Map.Entry<Integer, Integer> o2)
            {
                return (o1.getValue()).compareTo(o2.getValue());
            }
        });
         
        // put data from sorted list to hashmap
        HashMap<Integer, Integer> temp = new LinkedHashMap<Integer, Integer>();
        for (Map.Entry<Integer, Integer> aa : list) {
            temp.put(aa.getKey(), aa.getValue());
        }
        return temp;
    }
    static int DigitSum(int n)
    {
        int r=0,sum=0;
        while(n>=0)
        {
            r=n%10;
            sum=sum+r;
            n=n/10;
        }
        return sum;
    }
    static boolean checkPerfectSquare(int number)    
    {   
        double sqrt=Math.sqrt(number);   
        return ((sqrt - Math.floor(sqrt)) == 0);   
    }  
    static boolean isPowerOfTwo(int n)
    {
        if(n==0)
        return false;
 
        return (int)(Math.ceil((Math.log(n) / Math.log(2)))) == (int)(Math.floor(((Math.log(n) / Math.log(2)))));
    }
    static boolean isPrime2(int n) 
    {
        if (n <= 1) 
        {
            return false;
        }
        if (n == 2) 
        {
            return true;
        }
        if (n % 2 == 0) 
        {
            return false;
        }
        for (int i = 3; i <= Math.sqrt(n) + 1; i = i + 2) 
        {
            if (n % i == 0)
            {
                return false;
            }
        }
        return true;
    }
    static String minLexRotation(String str)
    {
        int n = str.length();
        String arr[] = new String[n];
        String concat = str + str;
        for(int i=0;i<n;i++)
        {
            arr[i] = concat.substring(i, i + n);
        }
        Arrays.sort(arr);
        return arr[0];
    }
 
static String maxLexRotation(String str)
    {
        int n = str.length();
        String arr[] = new String[n];
        String concat = str + str;
        for (int i = 0; i < n; i++)
        {
            arr[i] = concat.substring(i, i + n);
        }
        Arrays.sort(arr);
        return arr[arr.length-1];
    }
    static class P implements Comparable<P> {
		int i, j;
		public P(int i, int j) {
			this.i=i;
			this.j=j;
		}
		public int compareTo(P o) {
			return Integer.compare(i, o.i);
		}
	}
}