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.*;
import java.util.*;

public class Main {
    class Joinset{
        int father[];
        Joinset(int n){
            father = new int[n];
            for(int i = 0;i < n;i++) father[i] = i;
        }
        int find(int x){
            int old = x;
            while(x != father[x]){
                x = father[x];
            }
            while(old != x){
                int oldfather = father[old];
                father[old] = x;
                old = oldfather;
            }
            return x;
        }
        void join(int x, int y){
            int rx = find(x);
            int ry = find(y);
            if(rx != ry){
                father[rx] = ry;
            }
        }
    }
    static BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
    static int mod = (int)1e9+7;
    static boolean[] isprime=new boolean[1];
    static {
        for(int i=2;i<isprime.length;i++) isprime[i]=true;
        for(int i=2;i<isprime.length;i++) {
            if(isprime[i]) {
                for(int k = 2; i*k<isprime.length; k++) {
                    isprime[i*k] = false;
                }
            }
        }
    }
    public static long gcd(long a, long b){
        return b == 0 ? a : gcd(b,a%b);
    }
    public static long lcm(long a, long b){
        return a*b / gcd(a,b);
    }
    public static int get() throws Exception{
        String ss = bf.readLine();
        if (ss.contains(" ")) ss = ss.substring(0, ss.indexOf(" "));
        return Integer.parseInt(ss);
    }
    public static int[] getMore() throws Exception{
        String s[] = bf.readLine().split(" ");
        int[] a = new int[s.length];
        for(int i = 0;i < a.length;i++){
            a[i] = Integer.parseInt(s[i]);
        }
        return a;
    }
    public static int[] getInt() throws Exception {
        String s[] = bf.readLine().split(" ");
        int[] a = new int[s.length];
        for(int i = 0;i < a.length;i++){
            a[i] = Integer.parseInt(s[i]);
        }
        return a;
    }
    public static long[] getLong() throws Exception {
        String s[] = bf.readLine().split(" ");
        long[] a = new long[s.length];
        for(int i = 0;i < a.length;i++){
            a[i] = Long.parseLong(s[i]);
        }
        return a;
    }
    public static void print(int[] a) throws Exception {
        for(int i : a){
            bw.write(i + " ");
        }
        println();
    }
    public static void print(long[] a) throws Exception {
        for(long i : a){
            bw.write(i + " ");
        }
        println();
    }
    public static void println() throws Exception{
        bw.write("\n");
    }
    public static long pow(long a, long b){
        long ans = 1;
        while(b > 0){
            if((b&1) == 1){
                ans *= a;
            }
            a*=a;
            b>>=1;
        }
        return ans;
    }
    public static int powmod(long a, long b, int mod){
        long ans = 1;
        while(b > 0){
            if((b&1) == 1){
                ans = ans * a % mod;
            }
            a = a * a % mod;
            b>>=1;
        }
        return (int)ans;
    }
    public static void sort(int[] a){
        int n = a.length;
        Integer[] b = new Integer[n];
        for(int i = 0;i < n;i++) b[i] = a[i];
        Arrays.sort(b);
        for(int i = 0;i < n;i++) a[i] = b[i];
    }

    public static void main(String[] args) throws Exception {
        int t = get();
        while (t-- > 0) {
            int n = get();
            int a[] = new int[3];
            if(n % 2 == 0){
                a[2] = 1;
                a[1] = n/2;
                a[0] = n/2-1;
            }else{
                a[2] = 1;
                a[1] = (n-1)/2-1;
                a[0] = (n-1)/2+1;
            }
            print(a);
        }
        bw.flush();
    }
}