Given an array a of length n, find another array, b, of length n such that:

  * for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i. 



The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.

If such array doesn't exist, determine this.

Input

The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.

Output

If there's no such array, print a single line containing -1.

Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)

If there are multiple answers, print any.

Examples

Input


3
1 2 3


Output


0 1 2 

Input


4
0 0 0 2


Output


1 3 4 0 

Input


3
1 1 3


Output


0 2 1 

Note

In the second test case, other answers like [1,1,1,0], for example, are valid.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.TreeSet;
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;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CEhabAndPrefixMEXs solver = new CEhabAndPrefixMEXs();
        solver.solve(1, in, out);
        out.close();
    }

    static class CEhabAndPrefixMEXs {
        public void solve(int testNumber, FastReader s, PrintWriter out) {
            int n = s.nextInt();
            int[] arr = s.nextIntArray(n);


            int[] ans = new int[n];
            Arrays.fill(ans, -1);
            int maxm = (int) (1e5 + 5);
            TreeSet<Integer> available = new TreeSet<>();
            for (int i = 0; i < maxm; i++) {
                available.add(i);
            }
            int prev = 0;

            for (int i = 0; i < n; i++) {
                if (arr[i] != prev) {
                    ans[i] = prev;
                    available.remove(prev);
                    prev = arr[i];
                }
            }
            for (int i = 0; i < n; i++) {
                available.remove(arr[i]);
            }

            int start = maxm + 1;
            for (int i = 0; i < n; i++) {
                if (ans[i] == -1) {
                    if (!available.isEmpty()) {
                        ans[i] = available.first();
                        available.remove(available.first());
                    } else {
                        ans[i] = start++;
                    }
                }
            }

            out.println(CEhabAndPrefixMEXs.arrays.printArr(ans));
        }

        private static class arrays {
            static String formatString(String str) {
                str = str.replace(",", "").replace("[", "").replace("]", "");
                return str;
            }

            static StringBuilder printArr(Object arr) {
                String str = null;
                if (arr instanceof int[]) {
                    str = Arrays.toString((int[]) arr);
                }

                if (arr instanceof long[]) {
                    str = Arrays.toString((long[]) arr);
                }

                if (arr instanceof char[]) {
                    str = Arrays.toString((char[]) arr);
                }

                if (arr instanceof boolean[]) {
                    str = Arrays.toString((boolean[]) arr);
                }

                if (arr instanceof byte[]) {
                    str = Arrays.toString((byte[]) arr);
                }

                if (arr instanceof double[]) {
                    str = Arrays.toString((double[]) arr);
                }

                if (arr instanceof float[]) {
                    str = Arrays.toString((float[]) arr);
                }

                if (arr instanceof short[]) {
                    str = Arrays.toString((short[]) arr);
                }

                if (str != null) {
                    return new StringBuilder(formatString(str));
                }

                return null;

            }

        }

    }

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

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

        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 nextInt() {
            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 int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = nextInt();
            return array;
        }

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

        }

    }
}

