Problem: We know that lucky digits are digits 4 and 7, however Vasya's got another favorite digit 0 and he assumes it also is lucky! Lucky numbers are such non-negative integers whose decimal record only contains lucky digits. For example, numbers 0, 47, 7074 are lucky, but 1, 7377, 895,  -7 are not.

Vasya has t important positive integers he needs to remember. Vasya is quite superstitious and he wants to remember lucky numbers only, so he is asking you for each important number to represent it as a sum of exactly six lucky numbers (Vasya just can't remember more numbers). Then Vasya can just remember these six numbers and calculate the important number at any moment.

For each of t important integers represent it as the sum of six lucky numbers or state that this is impossible.

Input

The first line contains a single integer t (1 ≤ t ≤ 5000).

Next t lines contain a single positive integer ni (1 ≤ ni ≤ 1018) — the list of important numbers.

Please, do not use the %lld to read or write 64-bit integers С++. It is preferred to read the cin, cout streams or the %I64d specifier.

Output

Print t lines. The i-th line must contain the answer for the i-th important number: if the solution exists, the line must contain exactly six lucky numbers the sum of which equals ni, if the solution doesn't exist the string must contain a single integer -1.

If there are multiple answers print any of them.

Examples

Input

5
42
17
444
7
51


Output

7 7 7 7 7 7
-1
400 0 40 0 4 0
7 0 0 0 0 0
47 4 0 0 0 0

Solution (in JAVA):

Solution:

import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.*;

public class E {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();

	int[] cnt = new int[10];
	int[] len = new int[10];
	int[][] pos = new int[10][];
	int[] map = new int[8*8];
	long[] ans = new long[6];
	
	boolean dfs(long v, long idx) {
		if(v == 0) return true;
		if(v < 0 || idx * 4 > v) return false;
		int k = (int)(v / idx % 10);
		
		for(int x : pos[k]) {
			if(dfs(v - map[x] * idx, idx * 10)) {
				final int i4 = x / 8;
				final int i7 = x % 8;
				for(int i = 0; i < i4; i++) { ans[i] += idx * 4; }
				for(int i = 0; i < i7; i++) { ans[i+i4] += idx * 7; }
				return true;
			}
		}
		return false;
	}
	
	public void run() throws IOException {
		for(int i = 0; i <= 6; i++){
			for(int j = 0; i + j <= 6; j++) {
				int v = 0;
				for(int k = 0; k < i; k++) v += 4;
				for(int k = 0; k < j; k++) v += 7;
				cnt[v%10]++;
			}
		}
		for(int i = 0; i < 10; i++) pos[i] = new int[cnt[i]];
		for(int i = 0; i <= 6; i++){
			for(int j = 0; i + j <= 6; j++) {
				int v = 0;
				for(int k = 0; k < i; k++) v += 4;
				for(int k = 0; k < j; k++) v += 7;
				pos[v%10][len[v%10]++] = i * 8 + j;
				map[i*8+j] = v;
			}
		}
		
		int t = io.nextInt();
		for(int i = 0; i < t; i++) {
			long v = io.nextLong();
			Arrays.fill(ans, 0);
			if(dfs(v, 1)) {
				for(int j = 0; j < 6; j++) {
					io.out.print(ans[j] + (j==5?"\n":" "));
				}
			}
			else {
				io.out.println(-1);
			}
		}
	}

	static void arrayIntSort(int[][] x, int key) {
		Arrays.sort(x, new IntArrayComparator(key));
	}
	
	static class IntArrayComparator implements Comparator<int[]> {
		final int KEY;
		
		public IntArrayComparator(int key) {
			KEY = key;
		}
		
		@Override
		public int compare(int[] o1, int[] o2) {
			return o1[KEY] - o2[KEY];
		}
	}
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try {
			run();
		}
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}

	public static void main(String[] args) throws IOException {
		new E().main();
	}
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIO(String ins, String outs) throws IOException {
			in = new BufferedReader(new FileReader(ins));
			out = new PrintWriter(new FileWriter(outs));
		}

		//		private static final int BUFFER_SIZE = 50 * 200000;
		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static final char[] str = new char[500000*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static {
			for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; }
			isDigit['-'] = true;
			isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
			isLineSep['\r'] = isLineSep['\n'] = true;
		}

		public int read() throws IOException {
			if(pos >= readLen) {
				pos = 0;
				readLen = in.read(buffer);
				if(readLen <= 0) { throw new EndOfFileRuntimeException(); }
			}
			return buffer[pos++];
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(nextString());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(nextString());
		}

		public char nextChar() throws IOException {
			while(true) {
				final int c = read();
				if(!isSpace[c]) { return (char)c; }
			}
		}
		
		int reads(char[] cs, int len, boolean[] accept) throws IOException {
			try {
				while(true) {
					final int c = read();
					if(accept[c]) { break; }
					cs[len++] = (char)c;
				}
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return len;
		}

		public char[] nextLine() throws IOException {
			int len = 0;
			str[len++] = nextChar();
			len = reads(str, len, isLineSep);
			
			try {
				if(str[len-1] == '\r') { len--; read(); }
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return Arrays.copyOf(str, len);
		}

		public String nextString() throws IOException {
			return new String(next());
		}

		public char[] next() throws IOException {
			int len = 0;
			str[len++] = nextChar();
			len = reads(str, len, isSpace);
			return Arrays.copyOf(str, len);
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(nextString());
		}

		public long[] nextLongArray(final int n) throws IOException {
			final long[] res = new long[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public int[] nextIntArray(final int n) throws IOException {
			final int[] res = new int[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public int[][] nextIntArray2D(final int n, final int k) throws IOException {
			final int[][] res = new int[n][];
			for(int i = 0; i < n; i++) {
				res[i] = nextIntArray(k);
			}
			return res;
		}

		public double[] nextDoubleArray(final int n) throws IOException {
			final double[] res = new double[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextDouble();
			}
			return res;
		}

	}

}