Problem: Brothers Fred and George Weasley once got into the sporting goods store and opened a box of Quidditch balls. After long and painful experiments they found out that the Golden Snitch is not enchanted at all. It is simply a programmed device. It always moves along the same trajectory, which is a polyline with vertices at the points (x0, y0, z0), (x1, y1, z1), ..., (xn, yn, zn). At the beginning of the game the snitch is positioned at the point (x0, y0, z0), and then moves along the polyline at the constant speed vs. The twins have not yet found out how the snitch behaves then. Nevertheless, they hope that the retrieved information will help Harry Potter and his team in the upcoming match against Slytherin. Harry Potter learned that at the beginning the game he will be at the point (Px, Py, Pz) and his super fast Nimbus 2011 broom allows him to move at the constant speed vp in any direction or remain idle. vp is not less than the speed of the snitch vs. Harry Potter, of course, wants to catch the snitch as soon as possible. Or, if catching the snitch while it is moving along the polyline is impossible, he wants to hurry the Weasley brothers with their experiments. Harry Potter catches the snitch at the time when they are at the same point. Help Harry.

Input

The first line contains a single integer n (1 ≤ n ≤ 10000). The following n + 1 lines contain the coordinates xi, yi, zi, separated by single spaces. The coordinates of any two consecutive points do not coincide. The next line contains the velocities vp and vs, the last line contains Px, Py, Pz, separated by single spaces. All the numbers in the input are integers, their absolute value does not exceed 104. The speeds are strictly positive. It is guaranteed that vs ≤ vp.

Output

If Harry Potter can catch the snitch while it is moving along the polyline (including the end (xn, yn, zn)), print "YES" in the first line (without the quotes). Print in the second line t, which is the earliest moment of time, when Harry will be able to catch the snitch. On the third line print three numbers X, Y, Z, the coordinates of the point at which this happens. The absolute or relative error in the answer should not exceed 10 - 6. If Harry is not able to catch the snitch during its moving along the described polyline, print "NO".

Examples

Input

4
0 0 0
0 10 0
10 10 0
10 0 0
0 0 0
1 1
5 5 25


Output

YES
25.5000000000
10.0000000000 4.5000000000 0.0000000000


Input

4
0 0 0
0 10 0
10 10 0
10 0 0
0 0 0
1 1
5 5 50


Output

NO


Input

1
1 2 3
4 5 6
20 10
1 2 3


Output

YES
0.0000000000
1.0000000000 2.0000000000 3.0000000000

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.List;

/**
 * @author Egor Kulikov (egor@egork.net)
 */
public class TaskC {
	@SuppressWarnings({"FieldCanBeLocal", "UnusedDeclaration"})
	private final InputReader in;
	private final PrintWriter out;
	private final boolean testMode;
	private static final double EPS = 1e-11;

	private void solve() {
		int pointCount = in.readInt();
		int[] x = new int[pointCount + 1];
		int[] y = new int[pointCount + 1];
		int[] z = new int[pointCount + 1];
		in.readIntArrays(x, y, z);
		int potterSpeed = in.readInt();
		int snitchSpeed = in.readInt();
		int potterX = in.readInt();
		int potterY = in.readInt();
		int potterZ = in.readInt();
		double snitchDistance = 0;
		for (int i = 1; i <= pointCount; i++) {
			double oldSnitchDistance = snitchDistance;
			final double edgeLength = Math.hypot(x[i] - x[i - 1], Math.hypot(y[i] - y[i - 1], z[i] - z[i - 1]));
			snitchDistance += edgeLength;
			double potterDistance = Math.hypot(potterX - x[i], Math.hypot(potterY - y[i], potterZ - z[i]));
			if (snitchDistance / snitchSpeed > potterDistance / potterSpeed - EPS) {
				out.println("YES");
				double addTime = oldSnitchDistance / snitchSpeed;
				double leftTime = 0;
				double edgeTime = edgeLength / snitchSpeed;
				double rightTime = edgeTime;
				while (leftTime + EPS < rightTime) {
					double currentTime = (leftTime + rightTime) / 2;
					double snitchX = x[i - 1] + currentTime / edgeTime * (x[i] - x[i - 1]);
					double snitchY = y[i - 1] + currentTime / edgeTime * (y[i] - y[i - 1]);
					double snitchZ = z[i - 1] + currentTime / edgeTime * (z[i] - z[i - 1]);
					double distance = Math.hypot(potterX - snitchX, Math.hypot(potterY - snitchY, potterZ - snitchZ));
					if (currentTime + addTime > distance / potterSpeed - EPS)
						rightTime = currentTime;
					else
						leftTime = currentTime;
				}
				double currentTime = (leftTime + rightTime) / 2;
				out.printf("%.10f\n", currentTime + addTime);
				double snitchX = x[i - 1] + currentTime / edgeTime * (x[i] - x[i - 1]);
				double snitchY = y[i - 1] + currentTime / edgeTime * (y[i] - y[i - 1]);
				double snitchZ = z[i - 1] + currentTime / edgeTime * (z[i] - z[i - 1]);
				out.printf("%.10f %.10f %.10f\n", snitchX, snitchY, snitchZ);
				return;
			}
		}
		out.println("NO");
	}

	private static List<Test> createTests() {
		List<Test> tests = new ArrayList<Test>();
		tests.add(new Test("4\n" +
			"0 0 0\n" +
			"0 10 0\n" +
			"10 10 0\n" +
			"10 0 0\n" +
			"0 0 0\n" +
			"1 1\n" +
			"5 5 25", "YES\n" +
			"25.5000000000\n" +
			"10.0000000000 4.5000000000 0.0000000000"));
		tests.add(new Test("4\n" +
			"0 0 0\n" +
			"0 10 0\n" +
			"10 10 0\n" +
			"10 0 0\n" +
			"0 0 0\n" +
			"1 1\n" +
			"5 5 50", "NO"));
		tests.add(new Test("1\n" +
			"1 2 3\n" +
			"4 5 6\n" +
			"20 10\n" +
			"1 2 3", "YES\n" +
			"0.0000000000\n" +
			"1.0000000000 2.0000000000 3.0000000000"));
//		tests.add(new Test("", ""));
//		tests.add(new Test("", ""));
//		tests.add(new Test("", ""));
//		tests.add(new Test("", ""));
//		tests.add(new Test("", ""));
//		tests.add(new Test("", ""));
//		tests.add(new Test("", ""));
		return tests;
	}

	private void run() {
		//noinspection InfiniteLoopStatement
//		while (true)
//		int testCount = in.readInt();
//		for (int i = 0; i < testCount; i++)
		solve();
		exit();
	}

	private TaskC() {
		@SuppressWarnings({"UnusedDeclaration"})
		String id = getClass().getName().toLowerCase();
		//noinspection EmptyTryBlock
		try {
//			System.setIn(new FileInputStream(id + ".in"));
//			System.setOut(new PrintStream(new FileOutputStream(id + ".out")));
//			System.setIn(new FileInputStream("input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream("output.txt")));
		} catch (Exception e) {
			throw new RuntimeException(e);
		}
		in = new StreamInputReader(System.in);
		out = new PrintWriter(System.out);
		testMode = false;
	}

	@SuppressWarnings({"UnusedParameters"})
	private static String check(String input, String result, String output) {
		return strictCheck(result, output);
//		return tokenCheck(result, output);
	}

	public static void main(String[] args) {
		if (args.length != 0 && args[0].equals("42"))
			test();
		else
			new TaskC().run();
	}

	private static void test() {
		List<Test> tests = createTests();
		int testCase = 0;
		for (Test test : tests) {
			System.out.print("Test #" + testCase + ": ");
			InputReader in = new StringInputReader(test.getInput());
			StringWriter out = new StringWriter(test.getOutput().length());
			long time = System.currentTimeMillis();
			try {
				new TaskC(in, new PrintWriter(out)).run();
			} catch (TestException e) {
				time = System.currentTimeMillis() - time;
				String checkResult = check(test.getInput(), out.getBuffer().toString(), test.getOutput());
				if (checkResult == null)
					System.out.print("OK");
				else
					System.out.print("WA (" + checkResult + ")");
				System.out.printf(" in %.3f s.\n", time / 1000.);
			} catch (Throwable e) {
				System.out.println("Exception thrown:");
				e.printStackTrace(System.out);
			}
			testCase++;
		}
	}

	private static String tokenCheck(String result, String output) {
		StringInputReader resultStream = new StringInputReader(result);
		StringInputReader outputStream = new StringInputReader(output);
		int index = 0;
		boolean readingResult = false;
		try {
			while (true) {
				readingResult = true;
				String resultToken = resultStream.readString();
				readingResult = false;
				String outputToken = outputStream.readString();
				if (!resultToken.equals(outputToken))
					return "'" + outputToken + "' expected at " + index + " but '" + resultToken + "' received";
				index++;
			}
		} catch (InputMismatchException e) {
			if (readingResult) {
				try {
					outputStream.readString();
					return "only " + index + " tokens received";
				} catch (InputMismatchException e1) {
					return null;
				}
			} else
				return "only " + index + " tokens expected";
		}
	}

	@SuppressWarnings({"UnusedDeclaration"})
	private static String strictCheck(String result, String output) {
		if (result.equals(output))
			return null;
		return "'" + output + "' expected but '" + result + "' received";
	}

	@SuppressWarnings({"UnusedDeclaration"})
	private static boolean isDoubleEquals(double expected, double result, double certainty) {
		return Math.abs(expected - result) < certainty || Math.abs(expected - result) < certainty * expected;
	}

	private TaskC(InputReader in, PrintWriter out) {
		this.in = in;
		this.out = out;
		testMode = true;
	}

	@SuppressWarnings({"UnusedDeclaration"})
	private void exit() {
		out.close();
		if (testMode)
			throw new TestException();
		System.exit(0);
	}

	private static class Test {
		private final String input;
		private final String output;

		private Test(String input, String output) {
			this.input = input;
			this.output = output;
		}

		public String getInput() {
			return input;
		}

		public String getOutput() {
			return output;
		}
	}

	@SuppressWarnings({"UnusedDeclaration"})
	private abstract static class InputReader {
		public abstract int read();

		public int readInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long readLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private String readLine0() {
			StringBuffer buf = new StringBuffer();
			int c = read();
			while (c != '\n' && c != -1) {
				if (c != '\r')
					buf.appendCodePoint(c);
				c = read();
			}
			return buf.toString();
		}

		public String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0)
				s = readLine0();
			return s;
		}

		public String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines)
				return readLine();
			else
				return readLine0();
		}

		public BigInteger readBigInteger() {
			try {
				return new BigInteger(readString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		public char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

		public double readDouble() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, readInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}

		public int[] readIntArray(int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++)
				array[i] = readInt();
			return array;
		}

		public long[] readLongArray(int size) {
			long[] array = new long[size];
			for (int i = 0; i < size; i++)
				array[i] = readLong();
			return array;
		}

		public double[] readDoubleArray(int size) {
			double[] array = new double[size];
			for (int i = 0; i < size; i++)
				array[i] = readDouble();
			return array;
		}

		public String[] readStringArray(int size) {
			String[] array = new String[size];
			for (int i = 0; i < size; i++)
				array[i] = readString();
			return array;
		}

		public char[][] readTable(int rowCount, int columnCount) {
			char[][] table = new char[rowCount][columnCount];
			for (int i = 0; i < rowCount; i++) {
				for (int j = 0; j < columnCount; j++)
					table[i][j] = readCharacter();
			}
			return table;
		}

		public void readIntArrays(int[]... arrays) {
			for (int i = 0; i < arrays[0].length; i++) {
				for (int j = 0; j < arrays.length; j++)
					arrays[j][i] = readInt();
			}
		}
	}

	private static class StreamInputReader extends InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar, numChars;

		public StreamInputReader(InputStream stream) {
			this.stream = stream;
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
	}

	private static class StringInputReader extends InputReader {
		private Reader stream;
		private char[] buf = new char[1024];
		private int curChar, numChars;

		public StringInputReader(String stream) {
			this.stream = new StringReader(stream);
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
	}

	private static class TestException extends RuntimeException {}
}