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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 * @author rainweep
 * @data 2021/12/16 21:43
 */
public class Main {
    static class FastReader{
        StringTokenizer st;
        BufferedReader br;
        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 PrintWriter out = new PrintWriter(System.out);
    static FastReader in = new FastReader();
    static void solve(){
        int n=in.nextInt();
        if((n&1)==0){
            out.printf("%d %d %d\n",n/2-1,n/2,1);
            return;
        }
        for(int i=2;i*i<=n-1;i++){
            if(gcd(i,n-1-i)==1){
                out.printf("%d %d %d\n",i,n-1-i,1);
            }
        }
    }
    static int gcd(int a,int b){
        return b!=0?gcd(b,a%b):a;
    }
    public static void main(String[] args) {
        int t=in.nextInt();
        while (t-->0){
            solve();
        }
        out.flush();

    }
}
