import java.util.Arrays; import java.util.Scanner; public class Main { private long[] coef = new long[] { 1L, 1L << 6, 1L << 12, 1L << 18, 1L << 24, 1L << 30, }; private int[] dice_mask = new int[36]; private long[] dice_count = new long[36]; private int score = (int) -1e9; private int[] table = new int[36]; private int bestScore = (int) -1e9; private int[] bestTable = new int[36]; private int[] part_score_row = new int[6]; private long[] counts_row = new long[6]; private int[] part_score_column = new int[6]; private long[] counts_column = new long[6]; private SAState sa = new SAState(); public static void main(String[] args) throws Exception { new Main().run(); } private void run() { read(); solve(); write(); } private void read() { try (final Scanner in = new Scanner(System.in)) { for (int i = 0; i < 36; i++) { for (int j = 0; j < 6; j++) { int dice = in.nextInt() - 1; dice_mask[i] |= (1 << dice); dice_count[i] += coef[dice]; if (i == 0 && j == 0) { Constants.watch.init(); } } } } catch (Exception e) { e.printStackTrace(); } } private void solve() { greedy(); multiSA(); Utils.debug(bestScore, sa.numIterations); } private void greedy() { for (int r = 0; r < 6; r++) { for (int c = 0; c < 6; c++) { final int i = r * 6 + c; table[i] = i; counts_row[r] += dice_count[table[i]]; counts_column[c] += dice_count[table[i]]; } } score = calculateScore(); saveBest(); } private void saveBest() { if (score > bestScore) { bestScore = score; System.arraycopy(table, 0, bestTable, 0, table.length); } } private void restoreBest() { for (int i = 0; i < 6; i++) { counts_row[i] = 0; counts_column[i] = 0; } System.arraycopy(bestTable, 0, table, 0, table.length); for (int r = 0; r < 6; r++) { for (int c = 0; c < 6; c++) { final int i = r * 6 + c; counts_row[r] += dice_count[table[i]]; counts_column[c] += dice_count[table[i]]; } } score = calculateScore(); } private void multiSA() { int numRestart = 100; double startTime = Constants.watch.getSecond(); double endTime = 1.8; double remainTime = endTime - startTime; double startStartTemperature = 1.0 / 2; double endStartTemperature = 1.0 / 0.5; for (double restart = 0; restart < numRestart; restart++) { sa.startTime = startTime + remainTime * restart / numRestart; sa.endTime = startTime + remainTime * (restart + 1) / numRestart; sa.startTemperature = endStartTemperature + (startStartTemperature - endStartTemperature) * ((numRestart - restart) / numRestart); sa.endTemperature = 1.0 / 0.5; SA(); restoreBest(); } } private void SA() { sa.init(); for (;; ++sa.numIterations) { if ((sa.numIterations & ((1 << 10) - 1)) == 0) { sa.update(); if (sa.isTLE()) { break; } } mutate(); } } private void mutate() { change(); } private void change() { int v1 = sa.numIterations % 36; final int r1 = v1 / 6; final int c1 = v1 % 6; int v2 = Constants.RNG.nextInt(35); if (v2 >= v1) { v2++; } final int r2 = v2 / 6; final int c2 = v2 % 6; final int i1 = r1 * 6 + c1; final int current1 = table[i1]; final int i2 = r2 * 6 + c2; final int current2 = table[i2]; table[i1] = current2; table[i2] = current1; int before = 0; int after = 0; int after_r1 = 0; int after_r2 = 0; int after_c1 = 0; int after_c2 = 0; if (r2 != r1) { before += part_score_row[r1]; before += part_score_row[r2]; counts_row[r1] -= dice_count[current1]; counts_row[r2] -= dice_count[current2]; counts_row[r1] += dice_count[current2]; counts_row[r2] += dice_count[current1]; after_r1 = partScoreRow(r1); after_r2 = partScoreRow(r2); after += after_r1; after += after_r2; } if (c2 != c1) { before += part_score_column[c1]; before += part_score_column[c2]; counts_column[c1] -= dice_count[current1]; counts_column[c2] -= dice_count[current2]; counts_column[c1] += dice_count[current2]; counts_column[c2] += dice_count[current1]; after_c1 = partScoreColumn(c1); after_c2 = partScoreColumn(c2); after += after_c1; after += after_c2; } int deltaScore = after - before; if (sa.accept(deltaScore)) { score += deltaScore; if (r2 != r1) { part_score_row[r1] = after_r1; part_score_row[r2] = after_r2; } if (c2 != c1) { part_score_column[c1] = after_c1; part_score_column[c2] = after_c2; } saveBest(); } else { table[i1] = current1; table[i2] = current2; if (r2 != r1) { counts_row[r1] -= dice_count[current2]; counts_row[r2] -= dice_count[current1]; counts_row[r1] += dice_count[current1]; counts_row[r2] += dice_count[current2]; } if (c2 != c1) { counts_column[c1] -= dice_count[current2]; counts_column[c2] -= dice_count[current1]; counts_column[c1] += dice_count[current1]; counts_column[c2] += dice_count[current2]; } } } private int calculateScore() { int score = 0; for (int r = 0; r < 6; r++) { final int partScoreRow = partScoreRow(r); part_score_row[r] = partScoreRow; score += partScoreRow; } for (int c = 0; c < 6; c++) { final int partScoreColumn = partScoreColumn(c); part_score_column[c] = partScoreColumn; score += partScoreColumn; } return score; } private int partScoreRow(int r) { int mask = dice_mask[table[r * 6 + 0]] & dice_mask[table[r * 6 + 1]] & dice_mask[table[r * 6 + 2]] & dice_mask[table[r * 6 + 3]] & dice_mask[table[r * 6 + 4]] & dice_mask[table[r * 6 + 5]]; final long v = counts_row[r]; int part_score = (int) (((mask & (1 << 0)) == 0 ? 0 : -3 + (v & 63)) + ((mask & (1 << 1)) == 0 ? 0 : -3 + ((v >>> 6) & 63)) + ((mask & (1 << 2)) == 0 ? 0 : -3 + ((v >>> 12) & 63)) + ((mask & (1 << 3)) == 0 ? 0 : -3 + ((v >>> 18) & 63)) + ((mask & (1 << 4)) == 0 ? 0 : -3 + ((v >>> 24) & 63)) + ((mask & (1 << 5)) == 0 ? 0 : -3 + ((v >>> 30) & 63))); return part_score; } private int partScoreColumn(int c) { int mask = dice_mask[table[0 * 6 + c]] & dice_mask[table[1 * 6 + c]] & dice_mask[table[2 * 6 + c]] & dice_mask[table[3 * 6 + c]] & dice_mask[table[4 * 6 + c]] & dice_mask[table[5 * 6 + c]]; final long v = counts_column[c]; int part_score = (int) (((mask & (1 << 0)) == 0 ? 0 : -3 + (v & 63)) + ((mask & (1 << 1)) == 0 ? 0 : -3 + ((v >>> 6) & 63)) + ((mask & (1 << 2)) == 0 ? 0 : -3 + ((v >>> 12) & 63)) + ((mask & (1 << 3)) == 0 ? 0 : -3 + ((v >>> 18) & 63)) + ((mask & (1 << 4)) == 0 ? 0 : -3 + ((v >>> 24) & 63)) + ((mask & (1 << 5)) == 0 ? 0 : -3 + ((v >>> 30) & 63))); return part_score; } private void write() { String[] s = new String[36]; for (int i = 0; i < s.length; i++) { s[i] = ""; } for (int r = 0; r < 6; r++) { for (int c = 0; c < 6; c++) { s[bestTable[r * 6 + c]] = (r + 1) + " " + (c + 1); } } StringBuilder sb = new StringBuilder(); for (int i = 0; i < 36; i++) { sb.append(s[i]).append('\n'); } System.out.print(sb.toString()); System.out.flush(); } } class SAState { public static final boolean useTime = true; public double startTime; public double endTime; public double time; public double startTemperature; public double endTemperature; public double inverseTemperature; public double lastAcceptTemperature; public double startRange; public double endRange; public double range; public int numIterations; public int validIterations; public int acceptIterations; private double[] log = new double[32768]; public SAState() { for (int i = 0; i < log.length; i++) { log[i] = Math.log((i + 0.5) / log.length); } } public void init() { numIterations = 0; validIterations = 0; acceptIterations = 0; // startTime = useTime ? Constants.watch.getSecond() : numIterations; update(); lastAcceptTemperature = inverseTemperature; } public void update() { updateTime(); updateTemperature(); } // public boolean useExp = !true; public void updateTemperature() { // if (useExp) { // double time0to1 = elapsedPercentage(startTime, endTime, time); // double startY = startTemperature; // double endY = endTemperature; // double startX = Math.log(startY); // double endX = Math.log(endY); // double xStartToEnd = interpolate(startX, endX, time0to1); // double temperature = Math.exp(xStartToEnd); // inverseTemperature = 1.0 / temperature; // } else { inverseTemperature = interpolate(startTemperature, endTemperature, elapsedPercentage(startTime, endTime, time)); // inverseTemperature = 1.0 / temperature; // } } private double elapsedPercentage(double min, double max, double v) { return (v - min) / (max - min); } private double interpolate(double v0, double v1, double d0to1) { return v0 + (v1 - v0) * d0to1; } public void updateRange() { range = endRange + (startRange - endRange) * Math.pow((endTime - time) / (endTime - startTime), 1.0); } public void updateTime() { time = useTime ? Constants.watch.getSecond() : numIterations; } public boolean isTLE() { return time >= endTime; } public boolean accept(double deltaScore) { return acceptB(deltaScore); } public boolean acceptB(double deltaScore) { validIterations++; if (deltaScore > -1e-9) { acceptIterations++; return true; } double d = deltaScore * inverseTemperature; if (d < -10) { return false; } if (log[Constants.RNG.nextInt() & 32767] < d) { acceptIterations++; lastAcceptTemperature = inverseTemperature; return true; } return false; } public boolean acceptS(double deltaScore) { validIterations++; if (deltaScore < 1e-9) { acceptIterations++; return true; } double d = -deltaScore * inverseTemperature; if (d < -10) { return false; } if (log[Constants.RNG.nextInt() & 32767] < d) { acceptIterations++; lastAcceptTemperature = inverseTemperature; return true; } return false; } } final class Utils { private Utils() { } public static final void debug(Object... o) { System.err.println(toString(o)); System.err.flush(); } public static final String toString(Object... o) { return Arrays.deepToString(o); } public static boolean isValid(int v, int min, int minUpper) { return v >= min && v < minUpper; } } class Watch { private long start; public Watch() { init(); } public double getSecond() { return (System.nanoTime() - start) * 1e-9; } public void init() { init(System.nanoTime()); } private void init(long start) { this.start = start; } public String getSecondString() { return toString(getSecond()); } public static final String toString(double second) { if (second < 60) { return String.format("%5.2fs", second); } else if (second < 60 * 60) { int minute = (int) (second / 60); return String.format("%2dm%2ds", minute, (int) (second % 60)); } else { int hour = (int) (second / (60 * 60)); int minute = (int) (second / 60); return String.format("%2dh%2dm%2ds", hour, minute % (60), (int) (second % 60)); } } } interface Constants { Watch watch = new Watch(); PCG_XSH_RR RNG = new PCG_XSH_RR(System.nanoTime()); } final class PCG_XSH_RR { private long state = 5342; public PCG_XSH_RR(final long state) { this.state = state; } public int nextInt() { final long oldstate = state; state = oldstate * 6364136223846793005L + 521L; final int xorshift = (int) (((oldstate >>> 18) ^ oldstate) >>> 27); final int rotation = (int) (oldstate >>> 59); return (xorshift >>> rotation) | (xorshift << (-rotation & 31)); } public int nextInt(int n) { return (int) (n * nextDouble()); } public double nextDouble() { return (nextInt() >>> 1) * 4.6566128730773926E-10; } }