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.*;

import static java.lang.Math.*;
import static java.lang.Math.ceil;
import static java.util.Arrays.sort;

public class C {
    static int mod = 1000000007;

    public static void main(String[] args) throws Exception {
        int t = ri();
        while (t-- > 0) {
            long n = rl();
            for (int target=2; true; target++) {
                if (gcd(n-1-target, target)!=1)
                    continue;
               prln(n-1-target+" "+target+" "+1);
                if (n-1-target<=1) throw null;
                    break;
            }



        }
        close();
    }


    static class Nodes {
        int a;
        int b;
        int i;

        Nodes(int a, int b, int i) {
            this.a = a;
            this.b = b;
            this.i = i;
        }
    }

    static class DisjointSetUnion {
        int p[];
        int count[];

        public DisjointSetUnion(int n) {
            p = new int[n];
            count = new int[n];
            for (int i = 0; i < n; i++) {
                count[i] = 1;
            }
            clear(n);
        }

        public void clear(int n) {
            for (int i = 0; i < n; i++) {
                p[i] = i;
            }
        }

        public int get(int x) {
            return x != p[x] ? p[x] = get(p[x]) : x;
        }

        public int getCount(int x) {
            return count[x];
        }

        public boolean union(int a, int b) {
            a = get(a);
            b = get(b);
            p[a] = b;
            if (a != b) {
                count[b] += count[a];
                count[a] = 0;
            }
            return a != b;
        }
    }

    static BufferedReader __i = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __o = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static boolean[] isPrime;
    static Random __r = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e9
    // LMAX ~= 9e18

    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final long LMAX = 9223372036854775807L;

    // math util
    static int minof(int a, int b, int c) {
        return min(a, min(b, c));
    }

    static int minof(int... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return min(x[0], x[1]);
        if (x.length == 3) return min(x[0], min(x[1], x[2]));
        int min = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
        return min;
    }

    static long minof(long a, long b, long c) {
        return min(a, min(b, c));
    }

    static long minof(long... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return min(x[0], x[1]);
        if (x.length == 3) return min(x[0], min(x[1], x[2]));
        long min = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
        return min;
    }

    static int maxof(int a, int b, int c) {
        return max(a, max(b, c));
    }

    static int maxof(int... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return max(x[0], x[1]);
        if (x.length == 3) return max(x[0], max(x[1], x[2]));
        int max = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
        return max;
    }

    static long maxof(long a, long b, long c) {
        return max(a, max(b, c));
    }

    static long maxof(long... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return max(x[0], x[1]);
        if (x.length == 3) return max(x[0], max(x[1], x[2]));
        long max = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
        return max;
    }

    static int powi(int a, int b) {
        if (a == 0) return 0;
        int ans = 1;
        while (b > 0) {
            if ((b & 1) > 0) ans *= a;
            a *= a;
            b >>= 1;
        }
        return ans;
    }

    static long powl(long a, int b) {
        if (a == 0) return 0;
        long ans = 1;
        while (b > 0) {
            if ((b & 1) > 0) ans *= a;
            a *= a;
            b >>= 1;
        }
        return ans;
    }

    static int fli(double d) {
        return (int) d;
    }

    static int cei(double d) {
        return (int) ceil(d);
    }

    static long fll(double d) {
        return (long) d;
    }

    static long cel(double d) {
        return (long) ceil(d);
    }

    static int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

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

    static int[] exgcd(int a, int b) {
        if (b == 0) return new int[]{1, 0};
        int[] y = exgcd(b, a % b);
        return new int[]{y[1], y[0] - y[1] * (a / b)};
    }

    static long[] exgcd(long a, long b) {
        if (b == 0) return new long[]{1, 0};
        long[] y = exgcd(b, a % b);
        return new long[]{y[1], y[0] - y[1] * (a / b)};
    }

    static int randInt(int min, int max) {
        return __r.nextInt(max - min + 1) + min;
    }

    static long mix(long x) {
        x += 0x9e3779b97f4a7c15L;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L;
        x = (x ^ (x >> 27)) * 0x94d049bb133111ebL;
        return x ^ (x >> 31);
    }

    static void setTrue(int n) {
        for (int i = 0; i < n; i++) {
            isPrime[i] = true;
        }
    }

    static void prime(int n) {
        for (int i = 2; i * i < n; i++) {
            if (isPrime[i]) {
                for (int j = i * i; j < n; j += i) isPrime[j] = false;
            }
        }
    }

    public static long lcm(long number1, long number2) {
        if (number1 == 0 || number2 == 0) {
            return 0;
        }
        long absNumber1 = Math.abs(number1);
        long absNumber2 = Math.abs(number2);
        long absHigherNumber = Math.max(absNumber1, absNumber2);
        long absLowerNumber = Math.min(absNumber1, absNumber2);
        long lcm = absHigherNumber;
        while (lcm % absLowerNumber != 0) {
            lcm += absHigherNumber;
        }
        return lcm;
    }

    // array util
    static void reverse(int[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            int swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void reverse(long[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            long swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void reverse(double[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            double swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void reverse(char[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            char swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void shuffle(int[] a) {
        int n = a.length - 1;
        for (int i = 0; i < n; ++i) {
            int ind = randInt(i, n);
            int swap = a[i];
            a[i] = a[ind];
            a[ind] = swap;
        }
    }

    static void shuffle(long[] a) {
        int n = a.length - 1;
        for (int i = 0; i < n; ++i) {
            int ind = randInt(i, n);
            long swap = a[i];
            a[i] = a[ind];
            a[ind] = swap;
        }
    }

    static void shuffle(double[] a) {
        int n = a.length - 1;
        for (int i = 0; i < n; ++i) {
            int ind = randInt(i, n);
            double swap = a[i];
            a[i] = a[ind];
            a[ind] = swap;
        }
    }

    static void rsort(int[] a) {
        shuffle(a);
        sort(a);
    }

    static void rsort(long[] a) {
        shuffle(a);
        sort(a);
    }

    static void rsort(double[] a) {
        shuffle(a);
        sort(a);
    }

    static int[] copy(int[] a) {
        int[] ans = new int[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static long[] copy(long[] a) {
        long[] ans = new long[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static double[] copy(double[] a) {
        double[] ans = new double[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static char[] copy(char[] a) {
        char[] ans = new char[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static void resetBoolean(boolean[] vis, int n) {
        for (int i = 0; i < n; i++) {
            vis[i] = false;
        }
    }

    static void setMinusOne(int[][] matrix) {
        int row = matrix.length;
        int col = matrix[0].length;

        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                matrix[i][j] = -1;
            }
        }

    }

    // input
    static void r() throws IOException {
        input = new StringTokenizer(rline());
    }

    static int ri() throws IOException {
        return Integer.parseInt(rline().split(" ")[0]);
    }

    static long rl() throws IOException {
        return Long.parseLong(rline());
    }

    static double rd() throws IOException {
        return Double.parseDouble(rline());
    }

    static int[] ria(int n) throws IOException {
        int[] a = new int[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = ni();
        return a;
    }

    static void ria(int[] a) throws IOException {
        int n = a.length;
        r();
        for (int i = 0; i < n; ++i) a[i] = ni();
    }

    static int[] riam1(int n) throws IOException {
        int[] a = new int[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = ni() - 1;
        return a;
    }

    static void riam1(int[] a) throws IOException {
        int n = a.length;
        r();
        for (int i = 0; i < n; ++i) a[i] = ni() - 1;
    }

    static long[] rla(int n) throws IOException {
        long[] a = new long[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = nl();
        return a;
    }

    static void rla(long[] a) throws IOException {
        int n = a.length;
        r();
        for (int i = 0; i < n; ++i) a[i] = nl();
    }

    static double[] rda(int n) throws IOException {
        double[] a = new double[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = nd();
        return a;
    }

    static void rda(double[] a) throws IOException {
        int n = a.length;
        r();
        for (int i = 0; i < n; ++i) a[i] = nd();
    }

    static char[] rcha() throws IOException {
        return rline().toCharArray();
    }

    static void rcha(char[] a) throws IOException {
        int n = a.length, i = 0;
        for (char c : rline().toCharArray()) a[i++] = c;
    }

    static String rline() throws IOException {
        return __i.readLine();
    }

    static String n() {
        return input.nextToken();
    }

    static int rni() throws IOException {
        r();
        return ni();
    }

    static int ni() {
        return Integer.parseInt(n());
    }

    static long rnl() throws IOException {
        r();
        return nl();
    }

    static long nl() {
        return Long.parseLong(n());
    }

    static double rnd() throws IOException {
        r();
        return nd();
    }

    static double nd() {
        return Double.parseDouble(n());
    }

    // output
    static void pr(int i) {
        __o.print(i);
    }

    static void prln(int i) {
        __o.println(i);
    }

    static void pr(long l) {
        __o.print(l);
    }

    static void prln(long l) {
        __o.println(l);
    }

    static void pr(double d) {
        __o.print(d);
    }

    static void prln(double d) {
        __o.println(d);
    }

    static void pr(char c) {
        __o.print(c);
    }

    static void prln(char c) {
        __o.println(c);
    }

    static void pr(char[] s) {
        __o.print(new String(s));
    }

    static void prln(char[] s) {
        __o.println(new String(s));
    }

    static void pr(String s) {
        __o.print(s);
    }

    static void prln(String s) {
        __o.println(s);
    }

    static void pr(Object o) {
        __o.print(o);
    }

    static void prln(Object o) {
        __o.println(o);
    }

    static void prln() {
        __o.println();
    }

    static void pryes() {
        prln("yes");
    }

    static void pry() {
        prln("Yes");
    }

    static void prY() {
        prln("YES");
    }

    static void prno() {
        prln("no");
    }

    static void prn() {
        prln("No");
    }

    static void prN() {
        prln("NO");
    }

    static boolean pryesno(boolean b) {
        prln(b ? "yes" : "no");
        return b;
    }

    ;

    static boolean pryn(boolean b) {
        prln(b ? "Yes" : "No");
        return b;
    }

    static boolean prYN(boolean b) {
        prln(b ? "YES" : "NO");
        return b;
    }

    static void prln(int... a) {
        for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
        if (a.length > 0) prln(a[a.length - 1]);
        else prln();
    }

    static void prln(long... a) {
        for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
        if (a.length > 0) prln(a[a.length - 1]);
        else prln();
    }

    static void prln(double... a) {
        for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
        if (a.length > 0) prln(a[a.length - 1]);
        else prln();
    }

    static <T> void prln(Collection<T> c) {
        int n = c.size() - 1;
        Iterator<T> iter = c.iterator();
        for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i) ;
        if (n >= 0) prln(iter.next());
        else prln();
    }

    static void h() {
        prln("hlfd");
        flush();
    }

    static void flush() {
        __o.flush();
    }

    static void close() {
        __o.close();
    }

}
