import java.io.*; import java.util.*; public class Main { static InputReader in = new InputReader(System.in); static PrintWriter out = new PrintWriter(System.out); public static void main(String[] args) throws Exception { 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++; } 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(); } } }

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