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.InputMismatchException;
import java.util.*;

import static sun.swing.MenuItemLayoutHelper.*;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Manan Patel
 */
public class Main{
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter w = new PrintWriter(outputStream);
        Solution solver = new Solution();
        //int testCount = Integer.parseInt(in.next());
        //for (int i = 1; i <= testCount; i++)
            solver.solve(1 , in, w);
        w.close();
    }

    static class Solution {
        public void solve(int tc, InputReader sc, PrintWriter w) {
            int n = sc.nextInt();
            int a[] = new int[n + 1];
            boolean vis[] = new boolean[n + 1];
            for (int i = 1 ; i <= n ; i++){
                a[i] = sc.nextInt();
                vis[a[i]] = true;
            }
            ArrayList<Integer> remaining = new ArrayList<>();
            for (int i = 1 ; i <= n ; i++){
                if (!vis[i])
                    remaining.add(i);
            }
            int res[] = new int[n + 1] , idx = 0;
            for (int i = 1 ; i <= n ; i++){
                if (a[i] == a[i - 1]){
                    res[i] = remaining.get(idx++);
                }
                else
                    res[i] = a[i - 1];
            }
            for (int i = 1 ; i <= n ; i++)
                w.print(res[i] + " ");
            w.println();
        }
    }
    static class f{
        public static long max(long a[]){
            long ans = Long.MIN_VALUE;
            for (long i : a)
                ans = Math.max(ans , i);
            return ans;
        }
        public static long power(long x, int y){
            long res = 1;
            while (y > 0)
            {
                if ((y & 1) == 1)
                    res = (res*x);
                y = y >> 1;
                x = x * x;
            }
            return res;
        }
        public static long powerm(long x, long y, long p) {
            long res = 1;
            x %= p;
            while (y > 0) {
                if ((y & 1) == 1) {
                    res *= x;
                    res %= p;
                }
                y >>= 1;
                x *= x;
                x %= p;
            }
            return res;
        }
        public static void sort(int[] arr) {
            int n = arr.length, mid, h, s, l, i, j, k;
            int[] res = new int[n];
            for (s = 1; s < n; s <<= 1) {
                for (l = 0; l < n - 1; l += (s << 1)) {
                    h = Math.min(l + (s << 1) - 1, n - 1);
                    mid = Math.min(l + s - 1, n - 1);
                    i = l;
                    j = mid + 1;
                    k = l;
                    while (i <= mid && j <= h)
                        res[k++] = (arr[i] <= arr[j] ? arr[i++] : arr[j++]);
                    while (i <= mid)
                        res[k++] = arr[i++];
                    while (j <= h)
                        res[k++] = arr[j++];
                    for (k = l; k <= h; k++)
                        arr[k] = res[k];
                }
            }
        }
        public static long gcd(long a, long b)
        {
            if (a == 0)
                return b;
            return gcd(b % a, a);
        }

        public static long findGCD(long arr[], int n)
        {
            long result = arr[0];
            for (int i = 1; i < n; i++)
                result = gcd(arr[i], result);
            return result;
        }

    }

    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 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 long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long 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 String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

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

        }

    }

}
