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.
//package code;
import java.io.*;
import java.util.*;
import java.util.Map.Entry;
import java.text.*;
import java.math.*;
import java.util.regex.*;
import java.awt.Point;
/**
 *
 * @author prabhat // use stringbuilder,TreeSet, priorityQueue, x+y=(x&y + x|y);
 */
   public class  a
   {
   public static int n,max1=100005,k,m,q,a[],cnt[];
   public static Point[] p1,p2;
   public static long mod=(long)1e9+7,nCr[][],dp[][][],pre[][],suf[][],ans;
   public static boolean[] isPrime;
   public static  ArrayList<Integer> divisor[],prime,adj[];
   public static  TreeSet<Integer> ts;
   public  static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
   static PrintWriter pw;
   public static void main(String[] args) {
	new Thread(null,null,"Prabhat Kumar",99999999)
	{
	   public void run() 
	   {
		   try
		   {
			   solve();
		   }
		   catch(Exception e)
		   {   
			   e.printStackTrace();
			   System.exit(1);
		   }
	   }
	}.start();
}
static void solve() throws IOException
 {
	InputReader in = new InputReader(System.in);
	pw=new PrintWriter(System.out);
		n=in.ii();
		a=in.iia(n);for(int i=0;i<n;i++)a[i]--;
		int[] freq=new int[n];
		for(int i:a)freq[i]++;
		int ans=0;
		int z=0;
		boolean[] used=new boolean[n];
		for(int i=0;i<n;i++)
		{
			if(freq[a[i]]>1){
			while(z<n && freq[z]!=0)z++;
			
			if(z<a[i]||used[a[i]])
			{
				freq[a[i]]--;
				a[i]=z;
				freq[z]++;
				ans++;
			}
		}
			used[a[i]]=true;
		}
		pw.println(ans);
		for(int i=0;i<n;i++)a[i]++;
		for(int i:a)pw.print(i+" ");
			pw.close();
 }
 
   static class Pair{
	   int x;int y;
	   Pair(int a,int b)
	   {
		   x=a;
		   y=b;
	   }
   }
  
static long ncr(int i,int  j)
{
 if(j==0||i==j)return 1;
 if(nCr[i][j]!=-1)return nCr[i][j];
 long res=ncr(i-1,j-1)+ncr(i-1,j);
 return nCr[i][j]=res;
}
public  static class DSU
{
	int[] parent;
	int[] rank;
	int cnt;
	public DSU(int n){
		parent=new int[n];
		rank=new int[n];
		for(int i=0;i<n;i++){
			parent[i]=i;
			rank[i]=1;
		}
		cnt=n;
	}
	int find(int i){
		while(parent[i] !=i){
			parent[i]=parent[parent[i]];
			i=parent[i];
		}
		return i;
	}
	int Union(int x, int y){
		int xset = find(x);
		int yset = find(y);
		if(xset!=yset)
			cnt--;
		if(rank[xset]<rank[yset]){
			parent[xset] = yset;
			rank[yset]+=rank[xset];
			rank[xset]=0;
			return yset;
		}else{
			parent[yset]=xset;
			rank[xset]+=rank[yset];
			rank[yset]=0;
			return xset;
		}
	}
}

static int gcd(int a,int b)
{
	while(a!=0)
	{
		int temp=a;
		a=b%a;
		b=temp;
	}
	return b;
}
static void Seive()
{
	isPrime=new boolean[max1];
	Arrays.fill(isPrime,true);
	prime=new ArrayList<>();
	divisor=new ArrayList[max1];
	for(int i=1;i<max1;i++)divisor[i]=new ArrayList<Integer>();
    isPrime[0]=isPrime[1]=false;
	for(int i=2;i<(max1);i++)
	{
         if(isPrime[i]){
			 divisor[i].add(i);
			 prime.add(i);
			for(int j=2*i;j<max1;j+=i)
			{
				isPrime[j]=false;
				divisor[j].add(i);
			}
		}
	}
}
public static long pow(long n,long p)
{
	 long  result = 1;
	  if(p==0)
	    return 1;

	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    
	    p >>=1;
	    n*=n;
	}
	return result;
}


static  class InputReader
{
   private InputStream stream;
   private byte[] buf = new byte[1024];

   private SpaceCharFilter filter;
    byte inbuffer[] = new byte[1024];
   int lenbuffer = 0, ptrbuffer = 0;
    final int M = (int) 1e9 + 7;
   int md=(int)(1e7+1);
    int[] SMP=new int[md];
   final double eps = 1e-6;
   final double pi = Math.PI;

	PrintWriter out;
   String check = "";
 InputStream   obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
   public InputReader(InputStream stream)
   {
       this.stream = stream;
   }

    int readByte() {
	        if (lenbuffer == -1) throw new InputMismatchException();
	        if (ptrbuffer >= lenbuffer) {
	            ptrbuffer = 0;
	            try {
	                lenbuffer = obj.read(inbuffer);
	            } catch (IOException e) {
	                throw new InputMismatchException();
	            }
	        }
	        if (lenbuffer <= 0) return -1;
	        return inbuffer[ptrbuffer++];
   }

   public  int read()
   {
       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;
   }

   String is() {
	        int b = skip();
	        StringBuilder sb = new StringBuilder();
	        while (!(isSpaceChar(b))) // when nextLine, (isSpaceChar(b) && b!=' ')
	        {
	            sb.appendCodePoint(b);
	            b = readByte();
	        }
	        return sb.toString();
   }
   public   int ii() {
	        int num = 0, b;
	        boolean minus = false;
	        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	        if (b == '-') {
	            minus = true;
	            b = readByte();
	        }
	        while (true) {
	            if (b >= '0' && b <= '9') {
	                num = num * 10 + (b - '0');
	            } else {
	                return minus ? -num : num;
	            }
	            b = readByte();
	        }
   }
 public   long il() {
	        long num = 0;
	        int b;
	        boolean minus = false;
	        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	        if (b == '-') {
	            minus = true;
	            b = readByte();
	        }
	        while (true) {
	            if (b >= '0' && b <= '9') {
	                num = num * 10 + (b - '0');
	            } else {
	                return minus ? -num : num;
	            }
	            b = readByte();
	        }
   }

	    boolean isSpaceChar(int c) {
	        return (!(c >= 33 && c <= 126));
	       }

	      int skip()
	        {
	        int b;
	        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
	        return b;
	        }

	    float nf() {
	        return Float.parseFloat(is());
	    }

	    double id() {
	        return Double.parseDouble(is());
	    }

	    char ic() {
	        return (char) skip();
	    }

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

	    long[] ila(int n) {
	        long a[] = new long[n];
	        for (int i = 0; i <n; i++) a[i] = il();
	        return a;
	    }

	    String[] isa(int n) {
	        String a[] = new String[n];
	        for (int i = 0; i < n; i++) a[i] = is();
	        return a;
	    }


		 long mul(long a, long b) { return a * b % M; }

		/*	long div(long a, long b)
				 {
					return mul(a, pow(b, M - 2,M));

		           }
*/


	    double[][] idm(int n, int m) {
	        double a[][] = new double[n][m];
	        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = id();
	        return a;
	        }

	    int[][] iim(int n, int m) {
	        int a[][] = new int[n][m];
	        for (int i = 0; i < n; i++) for (int j = 0; j <m; j++) a[i][j] = ii();
	        return a;
          }


   public String readLine() {
       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 interface SpaceCharFilter
   {
       public boolean isSpaceChar(int ch);
   }
   public boolean isEndOfLine(int c) {
       return c == '\n' || c == '\r' || c == -1;
   }
}

}
