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.text.DecimalFormat;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public class B {
    static long mod = (long) 1e9 + 7;
    static long mod1 = 998244353;
    static InputStream inputStream = System.in;
    static OutputStream outputStream = System.out;
    static InputReader in = new InputReader(inputStream);
    static PrintWriter out = new PrintWriter(outputStream);

    public static void main(String[] args) throws IOException {
        int t = in.nextInt();
        while(t-->0) {
            long n = in.nextLong();
            for(long i = 2;i<=Math.sqrt(n);i++){
                long second = n - i - 1;
                if(gcd(i,second) == 1) {
                    out.println(i + " " + second + " " + 1);
                    break;
                }
            }
        }
        out.close();
    }


    static final Random random = new Random();

    static void ruffleSort(int[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    static long gcd(long x, long y) {
        if (x == 0)
            return y;
        if (y == 0)
            return x;
        long r = 0, a, b;
        a = Math.max(x, y);
        b = Math.min(x, y);
        r = b;
        while (a % b != 0) {
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }

    static long modulo(long a, long b, long c) {
        long x = 1, y = a % c;
        while (b > 0) {
            if (b % 2 == 1)
                x = (x * y) % c;
            y = (y * y) % c;
            b = b >> 1;
        }
        return x % c;
    }

    public static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    static int upper_bound(int[] arr, int n, int x) {
        int mid;
        int low = 0;
        int high = n;
        while (low < high) {
            mid = low + (high - low) / 2;
            if (x >= arr[mid])
                low = mid + 1;
            else
                high = mid;
        }
        return low;
    }

    static int lower_bound(int[] arr, int n, int x) {
        int mid;
        int low = 0;
        int high = n;
        while (low < high) {
            mid = low + (high - low) / 2;
            if (x <= arr[mid])
                high = mid;
            else
                low = mid + 1;
        }
        return low;
    }

    static String printPrecision(double d) {
        DecimalFormat ft = new DecimalFormat("0.00000000000");
        return String.valueOf(ft.format(d));
    }

    static int countBit(long mask) {
        int ans = 0;
        while (mask != 0) {
            mask &= (mask - 1);
            ans++;
        }
        return ans;
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] readArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) arr[i] = nextInt();
            return arr;
        }
    }
}