Problem: Peter had a cube with non-zero length of a side. He put the cube into three-dimensional space in such a way that its vertices lay at integer points (it is possible that the cube's sides are not parallel to the coordinate axes). Then he took a piece of paper and wrote down eight lines, each containing three integers — coordinates of cube's vertex (a single line contains coordinates of a single vertex, each vertex is written exactly once), put the paper on the table and left. While Peter was away, his little brother Nick decided to play with the numbers on the paper. In one operation Nick could swap some numbers inside a single line (Nick didn't swap numbers from distinct lines). Nick could have performed any number of such operations.

When Peter returned and found out about Nick's mischief, he started recollecting the original coordinates. Help Peter restore the original position of the points or else state that this is impossible and the numbers were initially recorded incorrectly.

Input

Each of the eight lines contains three space-separated integers — the numbers written on the piece of paper after Nick's mischief. All numbers do not exceed 106 in their absolute value.

Output

If there is a way to restore the cube, then print in the first line "YES". In each of the next eight lines print three integers — the restored coordinates of the points. The numbers in the i-th output line must be a permutation of the numbers in i-th input line. The numbers should represent the vertices of a cube with non-zero length of a side. If there are multiple possible ways, print any of them.

If there is no valid way, print "NO" (without the quotes) in the first line. Do not print anything else.

Examples

Input

0 0 0
0 0 1
0 0 1
0 0 1
0 1 1
0 1 1
0 1 1
1 1 1


Output

YES
0 0 0
0 0 1
0 1 0
1 0 0
0 1 1
1 0 1
1 1 0
1 1 1


Input

0 0 0
0 0 0
0 0 0
0 0 0
1 1 1
1 1 1
1 1 1
1 1 1


Output

NO

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Scanner;

public class Main {

	static ArrayList<P3D> G_ANS;

	static int G_ITERS = 0;

	private static class P3D {
		public long x, y, z;

		public P3D(long xx, long yy, long zz) {
			x = xx;
			y = yy;
			z = zz;
		}

		public long sqDistTo(P3D p) {
			// possible overflow?
			return (x - p.x) * (x - p.x) + (y - p.y) * (y - p.y) + (z - p.z)
					* (z - p.z);
		}

		public String toString() {
			return x + " " + y + " " + z;
		}

		public boolean equals(P3D p) {
			return x == p.x && y == p.y && z == p.z;
		}
	}

	public static boolean isCube(ArrayList<P3D> placedLines, boolean fullCheck) {
		long edgeSqd = Long.MAX_VALUE;

		ArrayList<Long> dists = new ArrayList<Long>();

		for (int i = 0; i < placedLines.size(); i++) {
			P3D p1 = placedLines.get(i);
			for (int j = i + 1; j < placedLines.size(); j++) {
				P3D p2 = placedLines.get(j);
				long d = p1.sqDistTo(p2);

				if (d == 0) {
					return false;
				}

				if (d < edgeSqd) {
					edgeSqd = d;
				}

				dists.add(d);
			}
		}

		// final checks
		long sqDiag = 2L * edgeSqd;
		long cbDiag = 3L * edgeSqd;

		int numSq = 0;
		int numCb = 0;
		int numE = 0;

		for (Long d : dists) {

			if (d == edgeSqd) {
				numE++;
			} else if (d == sqDiag) {
				numSq++;
			} else if (d == cbDiag) {
				numCb++;
			} else {
				return false;
			}
		}

		if (fullCheck) {
			return numE == 12 && numSq == 12 && numCb == 4;
		}

		return true;
	}

	public static boolean solve(ArrayList<P3D> origLines,
			ArrayList<P3D> placedLines, int currLine) {

		if (currLine >= origLines.size()) {

			// G_ITERS++;
			// is it a cube
			if (isCube(placedLines, true)) {
				// System.out.println(placedLines);
				G_ANS = placedLines;
				return true;
			} else {
				return false;
			}
		}

		// Try each permutation of x, y, z
		P3D p = origLines.get(currLine);

		ArrayList<P3D> perms = new ArrayList<P3D>();
		perms.add(new P3D(p.x, p.y, p.z));
		perms.add(new P3D(p.x, p.z, p.y));
		perms.add(new P3D(p.y, p.x, p.z));
		perms.add(new P3D(p.y, p.z, p.x));
		perms.add(new P3D(p.z, p.x, p.y));
		perms.add(new P3D(p.z, p.y, p.x));

		for (P3D pp : perms) {
			placedLines.add(pp);
			if (isCube(placedLines, false)) {
				if (solve(origLines, placedLines, currLine + 1)) {
					return true;
				}
			}
			placedLines.remove(pp);
		}

		return false;
	}

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		ArrayList<P3D> origLines = new ArrayList<P3D>();

		for (int i = 0; i < 8; i++) {

			long x = sc.nextLong();
			long y = sc.nextLong();
			long z = sc.nextLong();

			origLines.add(new P3D(x, y, z));
		}

		if (solve(origLines, new ArrayList<P3D>(), 0)) {
			System.out.println("YES");
			for (P3D p : G_ANS) {
				System.out.println(p.x + " " + p.y + " " + p.z);
			}
		} else {
			System.out.println("NO");
		}

		sc.close();

	}
}