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 javax.print.DocFlavor;
    import java.beans.IntrospectionException;
    import java.io.*;
    import java.lang.reflect.Array;
    import java.util.*;
    import java.lang.*;
    import static java.lang.Math.*;
    public class main implements Runnable {

        static ArrayList<Integer> adj[];

        static void Check2(int n) {
            adj = new ArrayList[n + 1];
            for (int i = 0; i <= n; i++) {
                adj[i] = new ArrayList<>();
            }

        }
        static void add(int i, int j){
            adj[i].add(j);
            adj[j].add(i);
        }
        public static void main(String[] args) {
            new Thread(null, new main(), "Check2", 1 << 28).start();// to increse stack size in java
        }
        static long mod = (long) (1e9 + 7);
        public void run() {
            InputReader in = new InputReader(System.in);
            PrintWriter w = new PrintWriter(System.out);
            int n=in.nextInt();
            int f[]=new int[n+1];
            int a[]=new int[n];
            for(int i=0;i<n;i++){
                a[i]=in.nextInt();
                f[a[i]]++;
            }
        Queue <Integer> q=new LinkedList<>();
            for(int i=1;i<=n;i++){
                if(f[i]==0){
                    q.add(i);
                }
            }
        int v[]=new int[n+1];
            int ans=0;
            for(int i=0;i<n;i++){

                if(!q.isEmpty()){

                    if(f[a[i]]>1){


                        if(q.peek()<a[i]){
                            f[a[i]]--;
                            a[i]=q.poll();
                            ans++;
                            f[a[i]]++;
                        }
                        else if(v[a[i]]==1){
                            f[a[i]]--;
                            a[i]=q.poll();
                            ans++;
                            f[a[i]]++;
                        }
                        else if(v[a[i]]==0){
                            v[a[i]]=1;
                        }

                    }

                }

            }
            w.println(ans);
            for(int i=0;i<n;i++)w.print(a[i]+" ");





            w.close();
        }
        static class pair2 implements  Comparable<pair2> {

            int a;
            int b;
            pair2(int a,int b){
                this.a=a;
                this.b=b;

            }
            public int compareTo(pair2 o){

                if(o.a!=this.a)return this.a-o.a;
                else
                    return this.b-o.b;



            }

        }
        static void diji(int s,long dist[],ArrayList <pair> adj[]){
            dist[s]=0;
            PriorityQueue <pair> q=new PriorityQueue<>(new cmp());
            q.add(new pair(s,0));
            while (!q.isEmpty())
            {
                pair p1=q.poll();
                for(pair ne:adj[p1.a]){

                    if((long)p1.b+(long)ne.b<dist[ne.a]){
                        dist[ne.a]=(long)p1.b+(long)ne.b;
                        pair p2=new pair(ne.a,dist[ne.a]);
                        q.add(p2);

                    }

                }
            }

        }
        static class cmp implements Comparator<pair>{

            public  int compare(pair o1,pair o2)
            {
                return o1.b<o2.b?-1:o1.b>o2.b?1:0;
            }

        }

        static class pair {
            int a;
            long b;
            pair(int a,long b){
                this.a=a;
                this.b=b;
            }
            public boolean equals(Object obj) {      //  override equals method for object to remove tem from arraylist and sets etc.......
                if (this == obj)
                    return true;
                if (obj == null)
                    return false;
                if (getClass() != obj.getClass())
                    return false;
                pair other = (pair) obj;
                if (b!= other.b||a!=other.a)
                    return false;
                return true;
            }
        }

        static long modinv(long a,long b)
        {
            long p=power(b,mod-2);

            p=a%mod*p%mod;
            p%=mod;

            return p;

        }

        static long power(long x,long y){
            if(y==0)return 1%mod;
            if(y==1)return x%mod;


            long res=1;
            x=x%mod;
            while(y>0){


                if((y%2)!=0){
                    res=(res*x)%mod;
                }


                y=y/2;
                x=(x*x)%mod;
            }


            return res;

        }
        static  long gcd(long a,long b){

            if(b==0)return a;
            return gcd(b,a%b);
        }

        static  void sev(int a[],int n){

            for(int i=2;i<=n;i++)a[i]=i;
            for(int i=2;i<=n;i++){

                if(a[i]!=0){
                    for(int j=2*i;j<=n;){

                        a[j]=0;
                        j=j+i;
                    }
                }

            }

        }



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







    }
