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.
/**
 * DA-IICT
 * Author : PARTH PATEL
 */
import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.fill;
import static java.lang.Math.*;
import static java.util.Arrays.sort;
import static java.util.Collections.sort;


public class D864 {

	public static int mod = 1;
	static FasterScanner in = new FasterScanner();
	static PrintWriter out = new PrintWriter(System.out);
	static int maxn = (int) (1e5 + 2);
	static ArrayList<Integer>[] adjacencylist = new ArrayList[maxn];
	static boolean[] visited = new boolean[maxn];
	static int[] color = new int[maxn];
	static class Pair implements Comparable<Pair>
	{
		int index;
		int frequency;
		public Pair(int index,int frequency) {
			// TODO Auto-generated constructor stub
			this.index=index;
			this.frequency=frequency;
		}
		@Override
		public int compareTo(Pair o) {
			// TODO Auto-generated method stub
			if(this.frequency==o.frequency)
				return this.index-o.index;
			return this.frequency-o.frequency;
		}
	}
	public static void main(String[] args) {

		int n=in.nextInt();
		int[] arr=in.nextIntArray(n);
		int[] frequency=new int[n+1];
		for(int i=0;i<n;i++)
		{
			frequency[arr[i]]++;
		}
		Pair[] pairs=new Pair[n];
		for(int i=0;i<n;i++)
		{
			pairs[i]=new Pair(i+1,frequency[i+1]);
		}
		Arrays.sort(pairs);
		int l=0;
		int count=0;
		boolean[] istaken=new boolean[n+1];
		for(int i=0;i<n;i++)
		{
			if(frequency[arr[i]]==1)
				continue;
			if(istaken[arr[i]]==true)
			{
				frequency[arr[i]]--;
				arr[i]=pairs[l].index;
				count++;
				l++;
				continue;
			}
			if(pairs[l].index<arr[i])
			{
				frequency[arr[i]]--;
				arr[i]=pairs[l].index;
				count++;
				l++;
			}
			else
				if(pairs[l].index>arr[i])
				{
					istaken[arr[i]]=true;
				}
		}
		out.println(count);
		for(int i=0;i<n;i++)
			out.print(arr[i]+" ");
		out.close();

	}

	public static void dfs(int vertex) {
		visited[vertex] = true;
		for (int i : adjacencylist[vertex]) {
			if (!visited[i]) {
				dfs(i);
			}
		}
	}

	/////////////////SEGMENT TREE (BUILD-UPDATE-QUERY)/////////////////////////////
	/////////////////UPDATE FOLLOWING METHODS AS PER NEED//////////////////////////
	/*
	public static void buildsegmenttree(int node,int start,int end)
	{
		if(start==end)
		{
			// Leaf node will have a single element
			segmenttree[node]=arr[start];
		}
		else
		{
			int mid=start+(end-start)/2;
			// Recurse on the left child
			buildsegmenttree(2*node, start, mid);
			// Recurse on the right child
			buildsegmenttree(2*node+1, mid+1, end);
			// Internal node will have the sum of both of its children
			segmenttree[node]=segmenttree[2*node]+segmenttree[2*node+1];
		}
	}
	
	public static void updatesegmenttree(int node,int start,int end,int idx,int val)
	{
		if(start==end)
		{
			//Leaf Node
			arr[idx]+=val;
			segmenttree[node]+=val;
		}
		else
		{
			int mid=start+(end-start)/2;
			if(start<=idx && idx<=mid)
			{
				// If idx is in the left child, recurse on the left child
				updatesegmenttree(2*node, start, mid, idx, val);
			}
			else
			{
				// if idx is in the right child, recurse on the right child
				updatesegmenttree(2*node+1, mid+1, end, idx, val);
			}
			// Internal node will have the sum of both of its children
			segmenttree[node]=segmenttree[2*node]+segmenttree[2*node+1];
		}
	}
	
	public static long querysegmenttree(int node,int start,int end,int l,int r)
	{
		if(r<start || end<l)
		{
			// range represented by a node is completely outside the given range
			return 0;
		}
		if(l <= start && end <= r)
	    {
	        // range represented by a node is completely inside the given range
	        return segmenttree[node];
	    }
		// range represented by a node is partially inside and partially outside the given range
		int mid=start+(end-start)/2;
		long leftchild=querysegmenttree(2*node, start, mid, l, r);
		long rightchild=querysegmenttree(2*node+1, mid+1, end, l, r);
		return (leftchild+rightchild);
	}
	*/

	public static long pow(long x, long n, long mod) {
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) {
			if ((n & 1) != 0) {
				res = (res * p % mod);
			}
		}
		return res;
	}

	public static long gcd(long n1, long n2) {
		long r;
		while (n2 != 0) {
			r = n1 % n2;
			n1 = n2;
			n2 = r;
		}
		return n1;
	}

	public static long lcm(long n1, long n2) {
		long answer = (n1 * n2) / (gcd(n1, n2));
		return answer;
	}

	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			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 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 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 int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}

}
