Ivan has an array consisting of n elements. Each of the elements is an integer from 1 to n.

Recently Ivan learned about permutations and their lexicographical order. Now he wants to change (replace) minimum number of elements in his array in such a way that his array becomes a permutation (i.e. each of the integers from 1 to n was encountered in his array exactly once). If there are multiple ways to do it he wants to find the lexicographically minimal permutation among them.

Thus minimizing the number of changes has the first priority, lexicographical minimizing has the second priority.

In order to determine which of the two permutations is lexicographically smaller, we compare their first elements. If they are equal — compare the second, and so on. If we have two permutations x and y, then x is lexicographically smaller if xi < yi, where i is the first index in which the permutations x and y differ.

Determine the array Ivan will obtain after performing all the changes.

Input

The first line contains an single integer n (2 ≤ n ≤ 200 000) — the number of elements in Ivan's array.

The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ n) — the description of Ivan's array.

Output

In the first line print q — the minimum number of elements that need to be changed in Ivan's array in order to make his array a permutation. In the second line, print the lexicographically minimal permutation which can be obtained from array with q changes.

Examples

Input

4
3 2 2 3


Output

2
1 2 4 3 


Input

6
4 5 6 3 2 1


Output

0
4 5 6 3 2 1 


Input

10
6 8 4 6 7 1 6 3 4 5


Output

3
2 8 4 6 7 1 9 3 10 5 

Note

In the first example Ivan needs to replace number three in position 1 with number one, and number two in position 3 with number four. Then he will get a permutation [1, 2, 4, 3] with only two changed numbers — this permutation is lexicographically minimal among all suitable. 

In the second example Ivan does not need to change anything because his array already is a permutation.




    import java.io.*;
    import java.util.ArrayDeque;
    import java.util.Arrays;
    import java.util.InputMismatchException;
    import java.util.Queue;
    import java.io.*;
    import java.lang.reflect.Array;
    import java.math.BigInteger;
    import java.util.*;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.util.Collections;
    import java.io.InputStreamReader;
    import java.util.logging.SimpleFormatter;


        public class Main1 {







            public static void main(String[] args) {
                FastScanner in = new FastScanner();
                PrintWriter out = new PrintWriter(System.out) ;

                int n = in.nextInt() ;
                int a[] = new int[n] ;
                int dp[] = new int[n] ;
                boolean ff[] = new boolean[n] ;
                for (int i = 0; i <n ; i++) {
                    a[i] = in.nextInt() -1 ;
                    dp[a[i]]++ ;
                }
                ArrayList<Integer> list = new ArrayList<>() ;
                for (int i = 0; i <n ; i++) {
                    if (dp[i] == 0 )list.add(i);
                }
                int ptr = 0 ;
                int cnt = 0 ;
                for (int i = 0; i <n ; i++) {
                    if (ptr == list.size())break;
                    if (dp[a[i]] == 1)continue;
                    if (a[i] > list.get(ptr) || ff[a[i]]){
                        dp[a[i]]-- ;
                        a[i] = list.get(ptr) ;

                        cnt++ ;
                        ff[list.get(ptr)]= true ;
                        ptr++ ;
                    }
                    else ff[a[i]] = true ;

                }

                out.append(cnt + "\n") ;
                for (int i = 0; i <n ; i++)out.append((a[i]+1) + " ");














                out.flush(); out.close();
            }


            private static int countDigits(long l) {
                if (l >= 1000000000000000000L) return 19;
                if (l >= 100000000000000000L) return 18;
                if (l >= 10000000000000000L) return 17;
                if (l >= 1000000000000000L) return 16;
                if (l >= 100000000000000L) return 15;
                if (l >= 10000000000000L) return 14;
                if (l >= 1000000000000L) return 13;
                if (l >= 100000000000L) return 12;
                if (l >= 10000000000L) return 11;
                if (l >= 1000000000L) return 10;
                if (l >= 100000000L) return 9;
                if (l >= 10000000L) return 8;
                if (l >= 1000000L) return 7;
                if (l >= 100000L) return 6;
                if (l >= 10000L) return 5;
                if (l >= 1000L) return 4;
                if (l >= 100L) return 3;
                if (l >= 10L) return 2;
                return 1;
            }






            static void updateRangeLazy(int tree[] , int lazy[] , int ss ,int se , int l , int r , int increment , int index){

                if (lazy[index] != 0 ){
                    tree[index] += lazy[index];

                    if (ss != se){
                        lazy[2*index]  +=  lazy[index];
                        lazy[2*index + 1]  +=  lazy[index];
                    }
                    lazy[index ] = 0 ;
                }

                if (ss > r && se< l )
                    return;

                if (ss >= l && se <= r) {
                    tree[index] += increment;


                    if (ss != se) {
                        lazy[2 * index] += increment;
                        lazy[2 * index + 1] += increment;
                    }
                    return;
                }

                int mid = (ss + se)/2 ;


                tree[index] =  Math.min( tree[2*index], tree[2*index + 1] ) ;

            }




            static class FastOutput implements AutoCloseable, Closeable, Appendable {
                private static final int THRESHOLD = 32 << 10;
                private final Writer os;
                private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

                public FastOutput append(CharSequence csq) {
                    cache.append(csq);
                    return this;
                }

                public FastOutput append(CharSequence csq, int start, int end) {
                    cache.append(csq, start, end);
                    return this;
                }

                private void afterWrite() {
                    if (cache.length() < THRESHOLD) {
                        return;
                    }
                    flush();
                }

                public FastOutput(Writer os) {
                    this.os = os;
                }

                public FastOutput(OutputStream os) {
                    this(new OutputStreamWriter(os));
                }

                public FastOutput append(char c) {
                    cache.append(c);
                    afterWrite();
                    return this;
                }

                public FastOutput append(long c) {
                    cache.append(c);
                    afterWrite();
                    return this;
                }

                public FastOutput append(String c) {
                    cache.append(c);
                    afterWrite();
                    return this;
                }

                public FastOutput println() {
                    return append(System.lineSeparator());
                }

                public FastOutput flush() {
                    try {
    //            boolean success = false;
    //            if (stringBuilderValueField != null) {
    //                try {
    //                    char[] value = (char[]) stringBuilderValueField.get(cache);
    //                    os.write(value, 0, cache.length());
    //                    success = true;
    //                } catch (Exception e) {
    //                }
    //            }
    //            if (!success) {
                        os.append(cache);
    //            }
                        os.flush();
                        cache.setLength(0);
                    } catch (IOException e) {
                        throw new UncheckedIOException(e);
                    }
                    return this;
                }

                public void close() {
                    flush();
                    try {
                        os.close();
                    } catch (IOException e) {
                        throw new UncheckedIOException(e);
                    }
                }

                public String toString() {
                    return cache.toString();
                }

            }







            static class FastScanner {
                BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st = new StringTokenizer("");

                String next() {
                    while (!st.hasMoreTokens())
                        try {
                            st = new StringTokenizer(br.readLine());
                        } catch (IOException e) {
                            e.printStackTrace();
                        }
                    return st.nextToken();
                }

                int nextInt() {
                    return Integer.parseInt(next());
                }

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


                long nextLong() {
                    return Long.parseLong(next());
                }
            }


        }







