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.io.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Test{

        static FastReader scan;

        static void solve(){
            int n=scan.nextInt();
            n--;
            int a=2,b=n-2;
            while(a<b){
                if(gcd(a,b)==1){
                    System.out.println(a+" "+b+" "+1);
                    break;
                }
                a++;
                b--;
            }
            
        }

        public static void main (String[] args) throws java.lang.Exception{
            scan=new FastReader();
            int t=scan.nextInt();
            while(t-->0){
                solve();
            }
        }

        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;
            }
        }

        static class Pair implements Comparable<Pair>{
            int e;
            int wt;
            Pair(int x,int y){
                this.e=x;
                this.wt=y;
            }
            @Override
            public int compareTo(Pair x){
                return (int)(x.wt-this.wt);
            }
        }        

        static void printLong(long []arr){
            for(long x:arr)System.out.print(x+" ");
        }

        static void printInt(int []arr){
            for(int x:arr)System.out.print(x+" ");
        }

        static void scanInt(int []arr){
            for(int i=0;i<arr.length;i++){
                arr[i]=scan.nextInt();
            }
        }

        static void scanLong(long []arr){
            for(int i=0;i<arr.length;i++){
                arr[i]=scan.nextLong();
            }
        }

        static long gcd(long a, long b){
            if (b == 0)
                return a;
            
            return gcd(b, a % b);
        }   

        static long power(long x, long y, long mod){
            long res = 1; 
        
            x = x % mod; 
         
            if (x == 0)
              return 0; 
         
            while (y > 0){              
                if ((y & 1) != 0)
                res = (res * x) % mod;
              
                y = y >> 1; 
                x = (x * x) % mod;
            }
                return res;
        }

        static long add(long a,long b,long mod){
            a = a % mod; 
            b = b % mod; 
            return (((a + b) % mod) + mod) % mod;
        }

        static long sub(long a, long b,long mod){
            a = a % mod; 
            b = b % mod; 
            return (((a - b) % mod) + mod) % mod;
        }

        static long mul(long a, long b,long mod){
            a = a % mod; 
            b = b % mod; 
            return (((a * b) % mod) + mod) % mod;
        }
        

        static long mminvprime(long a, long b,long mod) {
            return power(a, b - 2,mod);
        }
}
