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.*;
import java.util.stream.Collectors;

public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
}

class Task {

    //    static int MAX = 1000001;
//    List<List<Integer>> g = new ArrayList<>();
//    int n;
//    char[] s;

    public void solve(Scanner in, PrintWriter out) {
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        int[] cc = new int[200001];
        boolean[] bb = new boolean[200001];
        for (int i = 0; i < n; i++) {
            cc[a[i]]++;
        }
        int zero = 0;
        int res = 0;
        for (int i = 0; i < n; i++) {
            if (cc[a[i]] > 1) {
                res++;
                cc[a[i]]--;
                do {
                    zero++;
                } while (cc[zero] != 0);
                if (zero < a[i]) {
                    a[i] = zero;
                } else {
                    if (bb[a[i]]) {
                        a[i] = zero;
                    } else {
                        bb[a[i]] = true;
                        zero--;
                        cc[a[i]]++;
                        res--;
                    }
                }
            }
        }
        out.println(res);
        for (int i = 0; i < n; i++) {
            out.print(a[i] + " ");
        }
        out.println();
    }
}

class Utils {

    public static int binarySearch(int[] a, int key) {
        int s = 0;
        int f = a.length;
        while (f > s) {
            int mid = (s + f) / 2;
            if (a[mid] > key) {
                f = mid - 1;
            } else if (a[mid] <= key) {
                s = mid + 1;
            }
        }
        return -1;
    }

    public static long gcd(long a, long b) {
        return b != 0 ? gcd(b, a % b) : a;
    }

    public static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }

    static List<Integer> prime(int number) {
        List<Integer> a = new ArrayList<>();
        for (int i = 2; i * i <= number; i++) {
            if (number % i == 0) {
                a.add(i);
                number /= i;
                i = 1;
            }
        }
        a.add(number);
        return a;
    }
}

class Pair<T, U> {
    public T a;
    public U b;

    public Pair(T a, U b) {
        this.a = a;
        this.b = b;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Pair<?, ?> pair = (Pair<?, ?>) o;

        if (a != null ? !a.equals(pair.a) : pair.a != null) return false;
        return b != null ? b.equals(pair.b) : pair.b == null;
    }

    @Override
    public int hashCode() {
        int result = a != null ? a.hashCode() : 0;
        result = 31 * result + (b != null ? b.hashCode() : 0);
        return result;
    }
}


class Vect {
    public int a;
    public int b;

    public Vect(int a, int b) {
        this.a = a;
        this.b = b;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Vect vect = (Vect) o;

        if (a != vect.a) return false;
        return b == vect.b;
    }

    @Override
    public int hashCode() {
        int result = a;
        result = 31 * result + b;
        return result;
    }
}

class Tri {
    public int a;
    public int b;
    public int c;

    public Tri(int a, int b, int c) {
        this.a = a;
        this.b = b;
        this.c = c;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Tri tri = (Tri) o;

        if (a != tri.a) return false;
        if (b != tri.b) return false;
        return c == tri.c;
    }

    @Override
    public int hashCode() {
        int result = a;
        result = 31 * result + b;
        result = 31 * result + c;
        return result;
    }
}

class Triple<T, U, P> {
    public T a;
    public U b;
    public P c;

    public Triple(T a, U b, P c) {
        this.a = a;
        this.b = b;
        this.c = c;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Triple<?, ?, ?> triple = (Triple<?, ?, ?>) o;

        if (a != null ? !a.equals(triple.a) : triple.a != null) return false;
        return b != null ? b.equals(triple.b) : triple.b == null;
    }

    @Override
    public int hashCode() {
        int result = a != null ? a.hashCode() : 0;
        result = 31 * result + (b != null ? b.hashCode() : 0);
        return result;
    }
}


class Scanner {
    BufferedReader in;
    StringTokenizer tok;

    public Scanner(InputStream in) {
        this.in = new BufferedReader(new InputStreamReader(in));
        tok = new StringTokenizer("");
    }

    private String tryReadNextLine() {
        try {
            return in.readLine();
        } catch (Exception e) {
            throw new InputMismatchException();
        }
    }

    public String nextToken() {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(next());
        }
        return tok.nextToken();
    }

    public String next() {
        String newLine = tryReadNextLine();
        if (newLine == null)
            throw new InputMismatchException();
        return newLine;
    }

    public int nextInt() {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() {
        return Long.parseLong(nextToken());
    }
}