import java.math.*;
import java.util.concurrent.atomic.*;

public class Solution {
    public String largestNumber(int[] nums) {
        if (nums == null || nums.length == 0) {
            return "0";
        }

        List<Integer> sortedNums = new ArrayList<Integer>(nums.length);
        for (int i = 0; i < nums.length; i++) sortedNums.add(nums[i]);
        Collections.sort(sortedNums);
        Collections.reverse(sortedNums);

        Function<List<Integer>, List<Integer>> idx2nums = indexes -> indexes.stream()
                    .map(i -> sortedNums.get(i))
                    .collect(Collectors.toList());

        Function<List<Integer>, BigInteger> nums2bi = indexes -> new BigInteger(indexes.stream()
                    .map(n -> Integer.toString(n))
                    .collect(Collectors.joining()));

        final AtomicReference<BigInteger> refMax = new AtomicReference<>();
        final AtomicReference<List<Integer>> refMaxNums = new AtomicReference<List<Integer>>();

        permutateIndexes(nums.length, indexes -> {
            List<Integer> thisNums = idx2nums.apply(indexes);
            BigInteger thisNum = nums2bi.apply(thisNums);
            if (refMax.get() == null || thisNum.compareTo(refMax.get()) > 0) {
                refMax.set(thisNum);
                refMaxNums.set(thisNums);
            }

        }, indexes -> {
            if (refMaxNums.get() == null) {
                return true;
            }

            List<Integer> thisNums = idx2nums.apply(indexes);
            List<Integer> maxNums = refMaxNums.get().subList(0, thisNums.size());
            if (thisNums.equals(maxNums)) {
                return false;
            }

            String thisNum = nums2bi.apply(thisNums).toString();
            String maxNum = nums2bi.apply(maxNums).toString();
            if (thisNum.length() == maxNum.length()) {
                return thisNum.compareTo(maxNum) > 0;
            }

            int minLen = Math.min(thisNum.length(), maxNum.length());
            return thisNum.substring(0, minLen).compareTo(maxNum.substring(0, minLen)) >= 0;
        });

        return refMax.get().toString();
    }

    public static void permutateIndexes(int length, Consumer<List<Integer>> consumer,
            Predicate<List<Integer>> continueCheck) {
        permutateIndexes(length, consumer, continueCheck, new LinkedList<Integer>());
    }

    private static void permutateIndexes(int length, Consumer<List<Integer>> consumer,
            Predicate<List<Integer>> continueCheck,
            LinkedList<Integer> indexes) {

        if (indexes == null) {
            indexes = new LinkedList<Integer>();

        } else if (!indexes.isEmpty() && indexes.size() < length) {
            if (continueCheck != null && !continueCheck.test(indexes)) {
                return;
            }

        } else if (indexes.size() == length) {
            consumer.accept(indexes);
            return;
        }

        for (int i = 0; i < length; i++) {
            if (indexes.contains(i)) {
                continue;
            }

            indexes.add(i);
            permutateIndexes(length, consumer, continueCheck, indexes);
            indexes.removeLast();
        }
    }

}