import java.io.*; import java.util.*; public class Main { static InputReader in = new InputReader(System.in); static OutputWriter out = new OutputWriter(System.out); /* in.nextInt(); out.printLine(); */ /* use in for reading input use out for printing output */ public static void main(String[] args) throws IOException { // write your code here. out.close(); } private static class InputReader implements AutoCloseable { private static final int DEFAULT_BUFFER_SIZE = 1 << 16; private static final InputStream DEFAULT_STREAM = System.in; private static final int MAX_DECIMAL_PRECISION = 21; private int c; private final byte[] buf; private final int bufferSize; private int bufIndex; private int numBytesRead; private final InputStream stream; private static final byte EOF = -1; private static final byte NEW_LINE = 10; private static final byte SPACE = 32; private static final byte DASH = 45; private static final byte DOT = 46; private char[] charBuffer; private static final byte[] bytes = new byte[58]; private static final int[] ints = new int[58]; private static final char[] chars = new char[128]; static { char ch = '' ''; int value = 0; byte _byte = 0; for (int i = 48; i < 58; i++) bytes[i] = _byte++; for (int i = 48; i < 58; i++) ints[i] = value++; for (int i = 32; i < 128; i++) chars[i] = ch++; } private static final double[][] doubles = { { 0.0d, 0.00d, 0.000d, 0.0000d, 0.00000d, 0.000000d, 0.0000000d, 0.00000000d, 0.000000000d, 0.0000000000d, 0.00000000000d, 0.000000000000d, 0.0000000000000d, 0.00000000000000d, 0.000000000000000d, 0.0000000000000000d, 0.00000000000000000d, 0.000000000000000000d, 0.0000000000000000000d, 0.00000000000000000000d, 0.000000000000000000000d }, { 0.1d, 0.01d, 0.001d, 0.0001d, 0.00001d, 0.000001d, 0.0000001d, 0.00000001d, 0.000000001d, 0.0000000001d, 0.00000000001d, 0.000000000001d, 0.0000000000001d, 0.00000000000001d, 0.000000000000001d, 0.0000000000000001d, 0.00000000000000001d, 0.000000000000000001d, 0.0000000000000000001d, 0.00000000000000000001d, 0.000000000000000000001d }, { 0.2d, 0.02d, 0.002d, 0.0002d, 0.00002d, 0.000002d, 0.0000002d, 0.00000002d, 0.000000002d, 0.0000000002d, 0.00000000002d, 0.000000000002d, 0.0000000000002d, 0.00000000000002d, 0.000000000000002d, 0.0000000000000002d, 0.00000000000000002d, 0.000000000000000002d, 0.0000000000000000002d, 0.00000000000000000002d, 0.000000000000000000002d }, { 0.3d, 0.03d, 0.003d, 0.0003d, 0.00003d, 0.000003d, 0.0000003d, 0.00000003d, 0.000000003d, 0.0000000003d, 0.00000000003d, 0.000000000003d, 0.0000000000003d, 0.00000000000003d, 0.000000000000003d, 0.0000000000000003d, 0.00000000000000003d, 0.000000000000000003d, 0.0000000000000000003d, 0.00000000000000000003d, 0.000000000000000000003d }, { 0.4d, 0.04d, 0.004d, 0.0004d, 0.00004d, 0.000004d, 0.0000004d, 0.00000004d, 0.000000004d, 0.0000000004d, 0.00000000004d, 0.000000000004d, 0.0000000000004d, 0.00000000000004d, 0.000000000000004d, 0.0000000000000004d, 0.00000000000000004d, 0.000000000000000004d, 0.0000000000000000004d, 0.00000000000000000004d, 0.000000000000000000004d }, { 0.5d, 0.05d, 0.005d, 0.0005d, 0.00005d, 0.000005d, 0.0000005d, 0.00000005d, 0.000000005d, 0.0000000005d, 0.00000000005d, 0.000000000005d, 0.0000000000005d, 0.00000000000005d, 0.000000000000005d, 0.0000000000000005d, 0.00000000000000005d, 0.000000000000000005d, 0.0000000000000000005d, 0.00000000000000000005d, 0.000000000000000000005d }, { 0.6d, 0.06d, 0.006d, 0.0006d, 0.00006d, 0.000006d, 0.0000006d, 0.00000006d, 0.000000006d, 0.0000000006d, 0.00000000006d, 0.000000000006d, 0.0000000000006d, 0.00000000000006d, 0.000000000000006d, 0.0000000000000006d, 0.00000000000000006d, 0.000000000000000006d, 0.0000000000000000006d, 0.00000000000000000006d, 0.000000000000000000006d }, { 0.7d, 0.07d, 0.007d, 0.0007d, 0.00007d, 0.000007d, 0.0000007d, 0.00000007d, 0.000000007d, 0.0000000007d, 0.00000000007d, 0.000000000007d, 0.0000000000007d, 0.00000000000007d, 0.000000000000007d, 0.0000000000000007d, 0.00000000000000007d, 0.000000000000000007d, 0.0000000000000000007d, 0.00000000000000000007d, 0.000000000000000000007d }, { 0.8d, 0.08d, 0.008d, 0.0008d, 0.00008d, 0.000008d, 0.0000008d, 0.00000008d, 0.000000008d, 0.0000000008d, 0.00000000008d, 0.000000000008d, 0.0000000000008d, 0.00000000000008d, 0.000000000000008d, 0.0000000000000008d, 0.00000000000000008d, 0.000000000000000008d, 0.0000000000000000008d, 0.00000000000000000008d, 0.000000000000000000008d }, { 0.9d, 0.09d, 0.009d, 0.0009d, 0.00009d, 0.000009d, 0.0000009d, 0.00000009d, 0.000000009d, 0.0000000009d, 0.00000000009d, 0.000000000009d, 0.0000000000009d, 0.00000000000009d, 0.000000000000009d, 0.0000000000000009d, 0.00000000000000009d, 0.000000000000000009d, 0.0000000000000000009d, 0.00000000000000000009d, 0.000000000000000000009d } }; public InputReader() { this(DEFAULT_STREAM, DEFAULT_BUFFER_SIZE); } public InputReader(int bufferSize) { this(DEFAULT_STREAM, bufferSize); } public InputReader(InputStream stream) { this(stream, DEFAULT_BUFFER_SIZE); } public InputReader(InputStream stream, int bufferSize) { if (stream == null || bufferSize <= 0) throw new IllegalArgumentException(); buf = new byte[bufferSize]; charBuffer = new char[128]; this.bufferSize = bufferSize; this.stream = stream; } private byte read() throws IOException { if (numBytesRead == EOF) throw new IOException(); if (bufIndex >= numBytesRead) { bufIndex = 0; numBytesRead = stream.read(buf); if (numBytesRead == EOF) return EOF; } return buf[bufIndex++]; } private int readJunk(int token) throws IOException { if (numBytesRead == EOF) return EOF; do { while (bufIndex < numBytesRead) { if (buf[bufIndex] > token) return 0; bufIndex++; } numBytesRead = stream.read(buf); if (numBytesRead == EOF) return EOF; bufIndex = 0; } while (true); } public byte nextByte() throws IOException { return (byte) nextInt(); } public int nextInt() throws IOException { if (readJunk(DASH - 1) == EOF) throw new IOException(); int sgn = 1, res = 0; c = buf[bufIndex]; if (c == DASH) { sgn = -1; bufIndex++; } do { while (bufIndex < numBytesRead) { if (buf[bufIndex] > SPACE) { res = (res << 3) + (res << 1); res += ints[buf[bufIndex++]]; } else { bufIndex++; return res * sgn; } } numBytesRead = stream.read(buf); if (numBytesRead == EOF) return res * sgn; bufIndex = 0; } while (true); } public int[] nextIntArray(int n) throws IOException { int[] ar = new int[n]; for (int i = 0; i < n; i++) ar[i] = nextInt(); return ar; } public int[] nextIntArray1(int n) throws IOException { int[] ar = new int[n + 1]; for (int i = 1; i <= n; i++) ar[i] = nextInt(); return ar; } public void close() throws IOException { stream.close(); } } private static class OutputWriter implements AutoCloseable { private final PrintWriter writer; public OutputWriter(OutputStream outputStream) { writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream))); } public OutputWriter(Writer writer) { this.writer = new PrintWriter(writer); } public void print(Object... objects) { for (int i = 0; i < objects.length; i++) { if (i != 0) writer.print('' ''); writer.print(objects[i]); } } public void printLine(Object... objects) { print(objects); writer.println(); } public void close() { writer.close(); } public void flush() { writer.flush(); } } }

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