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.awt.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class Abc{
    public static void main(String[] args) throws java.lang.Exception {
        InputReader sc = new InputReader(System.in);
        int n=sc.nextInt();
        int a[]=new int[n];
        int b[]=new int[n];
        for (int i=0;i<n;i++){
            a[i]=sc.nextInt();
            b[i]=a[i];
        }
        TreeSet<Integer> set =new TreeSet<>();
        for (int i=0;i<=n;i++){
            set.add(i);
        }
        int suf[]=new int[n];
        for (int i=n-1;i>=0;i--){
            if (set.contains(a[i]))set.remove(a[i]);
            if (set.ceiling(a[i])==null) {
                suf[i] = -1;
            }
        }
        set=new TreeSet<>();
        Map<Integer,Integer> map=new TreeMap<>();

        for (int i=0;i<=n;i++)set.add(i);
        for (int i=0;i<n;i++){
            if (suf[i]!=-1 && set.ceiling(0)!=null){
                if (set.ceiling(0)+1==a[i]){
                    a[i]=set.ceiling(0);
                }else a[i]=suf[i];
            }else if (set.ceiling(0)==null && suf[i]==-1){
                a[i]=a[i-1];
            }else if (set.ceiling(0)==null){
                a[i]=suf[i];
            }else if (suf[i]==-1){
                a[i]=set.ceiling(0);
            }
            map.put(a[i],map.getOrDefault(a[i],0)+1);
            if (set.contains(a[i]))set.remove(a[i]);
        }
        boolean ok = true;
//        for (int i=0;i<n;i++){
//            if (i>0) {
//                map.put(a[i],map.getOrDefault(a[i],0)-1);
//                if (map.get(a[i])<=0)map.remove(a[i]);
//                int x=((TreeMap<Integer, Integer>) map).ceilingKey(0);
//                if (x+1!=b[i]){
//                    ok=false;
//                    break;
//                }
//            }else if (i==0){
//
//            }
//
//        }
//        if (!ok) {
//            System.out.println(-1);
//            return;
//        }


        StringBuilder sb=new StringBuilder();
        for (int i=0;i<n;i++)sb.append(a[i]+" ");
        System.out.println(sb);
    }


    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9') throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            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);
        }
    }
}