Problem:
Score : 800 points

Problem Statement

Niwango has N cards, numbered 1,2,\ldots,N.
He will now arrange these cards in a row.

Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below.
To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.

To the immediate right of Card 1 (if any) is NOT Card a_1.

To the immediate right of Card 2 (if any) is NOT Card a_2.

\vdots

To the immediate right of Card N (if any) is NOT Card a_N.

Constraints

2 \leq N \leq 10^{5}

1 \leq a_i \leq N

a_i \neq i

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N

Output

If no arrangements satisfy the conditions, print -1. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:

b_1 b_2 \ldots b_N

Here, b_i represents the i-th card from the left.

Sample Input 1

4
2 3 4 1

Sample Output 1

1 3 2 4

The arrangement (1,2,3,4) is lexicographically smaller than (1,3,2,4), but is invalid, since it violates the condition "to the immediate right of Card 1 is not Card 2."

Sample Input 2

2
2 1

Sample Output 2

-1

If no arrangements satisfy the conditions, print -1.

Sample Input 3

13
2 3 4 5 6 7 8 9 10 11 12 13 12

Sample Output 3

1 3 2 4 6 5 7 9 8 10 12 11 13

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DArrangement solver = new DArrangement();
        solver.solve(1, in, out);
        out.close();
    }

    static class DArrangement {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int[] a = in.readIntArray(n);
            MiscUtils.decreaseByOne(a);

            if (n == 2) {
                out.printLine(-1);
                return;
            }

            if (n <= 5) {
                int[] b = ArrayUtils.createOrder(n);
                do {
                    boolean flg = true;
                    for (int i = 0; i < n - 1; i++) {
                        if (a[b[i]] == b[i + 1]) flg = false;
                    }
                    if (flg) {
                        for (int i = 0; i < n; i++) {
                            if (i > 0) out.print(" ");
                            out.print(b[i] + 1);
                        }
                        out.printLine();
                        return;
                    }
                } while (ArrayUtils.nextPermutation(b));
            }

            int[] b = ArrayUtils.createOrder(n);
            for (int i = 0; i < n - 4; i++) {
                if (a[b[i]] == b[i + 1]) {
                    int tmp = b[i + 1];
                    b[i + 1] = b[i + 2];
                    b[i + 2] = tmp;
                }
            }
            int[] c = ArrayUtils.createOrder(4);
            do {
                boolean flg = true;
                if (a[b[n - 5]] == b[n - 4 + c[0]]) flg = false;
                for (int i = 0; i < 3; i++) {
                    if (a[b[n - 4 + c[i]]] == b[n - 4 + c[i + 1]]) flg = false;
                }
                if (flg) {
                    int[] tmp = new int[4];
                    for (int i = 0; i < 4; i++) {
                        tmp[i] = b[n - 4 + i];
                    }
                    for (int i = 0; i < 4; i++) {
                        b[n - 4 + c[i]] = tmp[i];
                    }
                    break;
                }
            } while (ArrayUtils.nextPermutation(c));
            for (int i = 0; i < n; i++) {
                if (i > 0) out.print(" ");
                out.print(b[i] + 1);
            }
            out.printLine();
        }

    }

    static class IntArray extends IntAbstractStream implements IntList {
        private int[] data;

        public IntArray(int[] arr) {
            data = arr;
        }

        public int size() {
            return data.length;
        }

        public int get(int at) {
            return data[at];
        }

        public void addAt(int index, int value) {
            throw new UnsupportedOperationException();
        }

        public void removeAt(int index) {
            throw new UnsupportedOperationException();
        }

        public void set(int index, int value) {
            data[index] = value;
        }

    }

    static class OutputWriter {
        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() {
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void print(int i) {
            writer.print(i);
        }

        public void printLine(int i) {
            writer.println(i);
        }

    }

    static interface IntList extends IntReversableCollection {
        public abstract int get(int index);

        public abstract void set(int index, int value);

        public abstract void addAt(int index, int value);

        public abstract void removeAt(int index);

        default public void swap(int first, int second) {
            if (first == second) {
                return;
            }
            int temp = get(first);
            set(first, get(second));
            set(second, temp);
        }

        default public IntIterator intIterator() {
            return new IntIterator() {
                private int at;
                private boolean removed;

                public int value() {
                    if (removed) {
                        throw new IllegalStateException();
                    }
                    return get(at);
                }

                public boolean advance() {
                    at++;
                    removed = false;
                    return isValid();
                }

                public boolean isValid() {
                    return !removed && at < size();
                }

                public void remove() {
                    removeAt(at);
                    at--;
                    removed = true;
                }
            };
        }

        default public void add(int value) {
            addAt(size(), value);
        }

        default public boolean nextPermutation() {
            return nextPermutation(IntComparator.DEFAULT);
        }

        default public boolean nextPermutation(IntComparator comparator) {
            int size = size();
            int last = get(size - 1);
            for (int i = size - 2; i >= 0; i--) {
                int current = get(i);
                if (comparator.compare(last, current) > 0) {
                    for (int j = size - 1; j > i; j--) {
                        if (comparator.compare(get(j), current) > 0) {
                            swap(i, j);
                            subList(i + 1, size).inPlaceReverse();
                            return true;
                        }
                    }
                }
                last = current;
            }
            return false;
        }

        default public void inPlaceReverse() {
            for (int i = 0, j = size() - 1; i < j; i++, j--) {
                swap(i, j);
            }
        }

        default public IntList subList(final int from, final int to) {
            return new IntList() {
                private final int shift;
                private final int size;

                {
                    if (from < 0 || from > to || to > IntList.this.size()) {
                        throw new IndexOutOfBoundsException("from = " + from + ", to = " + to + ", size = " + size());
                    }
                    shift = from;
                    size = to - from;
                }

                public int size() {
                    return size;
                }

                public int get(int at) {
                    if (at < 0 || at >= size) {
                        throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
                    }
                    return IntList.this.get(at + shift);
                }

                public void addAt(int index, int value) {
                    throw new UnsupportedOperationException();
                }

                public void removeAt(int index) {
                    throw new UnsupportedOperationException();
                }

                public void set(int at, int value) {
                    if (at < 0 || at >= size) {
                        throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
                    }
                    IntList.this.set(at + shift, value);
                }

                public IntList compute() {
                    return new IntArrayList(this);
                }
            };
        }

    }

    static class IntArrayList extends IntAbstractStream implements IntList {
        private int size;
        private int[] data;

        public IntArrayList() {
            this(3);
        }

        public IntArrayList(int capacity) {
            data = new int[capacity];
        }

        public IntArrayList(IntCollection c) {
            this(c.size());
            addAll(c);
        }

        public IntArrayList(IntStream c) {
            this();
            if (c instanceof IntCollection) {
                ensureCapacity(((IntCollection) c).size());
            }
            addAll(c);
        }

        public IntArrayList(IntArrayList c) {
            size = c.size();
            data = c.data.clone();
        }

        public IntArrayList(int[] arr) {
            size = arr.length;
            data = arr.clone();
        }

        public int size() {
            return size;
        }

        public int get(int at) {
            if (at >= size) {
                throw new IndexOutOfBoundsException("at = " + at + ", size = " + size);
            }
            return data[at];
        }

        private void ensureCapacity(int capacity) {
            if (data.length >= capacity) {
                return;
            }
            capacity = Math.max(2 * data.length, capacity);
            data = Arrays.copyOf(data, capacity);
        }

        public void addAt(int index, int value) {
            ensureCapacity(size + 1);
            if (index > size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size) {
                System.arraycopy(data, index, data, index + 1, size - index);
            }
            data[index] = value;
            size++;
        }

        public void removeAt(int index) {
            if (index >= size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size - 1) {
                System.arraycopy(data, index + 1, data, index, size - index - 1);
            }
            size--;
        }

        public void set(int index, int value) {
            if (index >= size) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            data[index] = value;
        }

        public int[] toArray() {
            return Arrays.copyOf(data, size);
        }

    }

    static class ArrayUtils {
        public static int[] range(int from, int to) {
            return Range.range(from, to).toArray();
        }

        public static int[] createOrder(int size) {
            return range(0, size);
        }

        public static boolean nextPermutation(int[] array) {
            return new IntArray(array).nextPermutation();
        }

    }

    static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
        public IntIterator intIterator();

        default public Iterator<Integer> iterator() {
            return new Iterator<Integer>() {
                private IntIterator it = intIterator();

                public boolean hasNext() {
                    return it.isValid();
                }

                public Integer next() {
                    int result = it.value();
                    it.advance();
                    return result;
                }
            };
        }

        default public int compareTo(IntStream c) {
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                int i = it.value();
                int j = jt.value();
                if (i < j) {
                    return -1;
                } else if (i > j) {
                    return 1;
                }
                it.advance();
                jt.advance();
            }
            if (it.isValid()) {
                return 1;
            }
            if (jt.isValid()) {
                return -1;
            }
            return 0;
        }

    }

    static interface IntCollection extends IntStream {
        public int size();

        default public void add(int value) {
            throw new UnsupportedOperationException();
        }

        default public int[] toArray() {
            int size = size();
            int[] array = new int[size];
            int i = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                array[i++] = it.value();
            }
            return array;
        }

        default public IntCollection addAll(IntStream values) {
            for (IntIterator it = values.intIterator(); it.isValid(); it.advance()) {
                add(it.value());
            }
            return this;
        }

    }

    static interface IntComparator {
        IntComparator DEFAULT = (first, second) -> {
            if (first < second) {
                return -1;
            }
            if (first > second) {
                return 1;
            }
            return 0;
        };

        public int compare(int first, int second);

    }

    static interface IntReversableCollection extends IntCollection {
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

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

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

        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++];
        }

        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 boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class Range {
        public static IntList range(int from, int to) {
            int[] result = new int[Math.abs(from - to)];
            int current = from;
            if (from <= to) {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current++;
                }
            } else {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current--;
                }
            }
            return new IntArray(result);
        }

    }

    static class MiscUtils {
        public static void decreaseByOne(int[]... arrays) {
            for (int[] array : arrays) {
                for (int i = 0; i < array.length; i++) {
                    array[i]--;
                }
            }
        }

    }

    static interface IntIterator {
        public int value() throws NoSuchElementException;

        public boolean advance();

        public boolean isValid();

    }

    static abstract class IntAbstractStream implements IntStream {
        public String toString() {
            StringBuilder builder = new StringBuilder();
            boolean first = true;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                if (first) {
                    first = false;
                } else {
                    builder.append(' ');
                }
                builder.append(it.value());
            }
            return builder.toString();
        }

        public boolean equals(Object o) {
            if (!(o instanceof IntStream)) {
                return false;
            }
            IntStream c = (IntStream) o;
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                if (it.value() != jt.value()) {
                    return false;
                }
                it.advance();
                jt.advance();
            }
            return !it.isValid() && !jt.isValid();
        }

        public int hashCode() {
            int result = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                result *= 31;
                result += it.value();
            }
            return result;
        }

    }
}