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.math.*;
import java.nio.file.attribute.AclEntry.Builder;
import java.security.KeyStore.Entry;
import java.util.*;
 
 
 
	 
	public  class Khatri {
		private InputStream is;
		private PrintWriter out;
		int time = 0, DP[], start[], end[], dist[],  black[];
		static int MOD = (int)(1e9+7);
		int arr[];
		int weight[][];
		int x[];
		int y[];
		int parent[];
		int MAX = 800000, N, K, L;
		long red[];
		ArrayList<Integer>[] amp;
		HashSet<Integer> hs = new HashSet<>();
		long Dp[][][][] = new long[110][110][12][12];
		public static void main(String[] args) throws Exception 
		{
			new Thread(null, new Runnable() 
			{
			public void run() 
			{
				try {
	 
			//new CODEFORCES().soln();
			} catch (Exception e) 
				{
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
			new Khatri().soln();
		}
		char ch[][]; 
		int n1, n2, k1, k2, M;
		static ArrayList<Integer>[] g;
        static ArrayList<Integer> ar[];
		static long ok[];	 
		static int phi[]=new int[500005];
		void solve()
        {
         
            
			int n=ni();
			int a[]=na(n);
			HashMap<Integer,Integer> hm=new HashMap();
			for(int i=1;i<=n;i++)
			{
				hm.put(i,0);
			}
			int tot[]=new int[n+1];
			
			for(int i=0;i<n;i++)
			{
				tot[a[i]]++;
				if(!hm.containsKey(a[i]))
					hm.put(a[i],1);
				else
					hm.put(a[i],hm.get(a[i])+1);
			}
	
			int ans=0;
			int rem[]=new int[n+1];
			Queue<Integer> Q=new LinkedList();
			for(int i=1;i<=n;i++)
			{
				
				if(hm.get(i)==0)
				{
					Q.add(i);
					ans++;
				}
				else if(hm.get(i)>1)
				{
					rem[i]+=(hm.get(i)-1);
				}
			}
			
			out.println(ans);
			int frs[]=new int[n+1];
			int b[]=Arrays.copyOf(a,n);
			for(int i=0;i<n;i++)
			{
				frs[a[i]]++;
				if(rem[a[i]]>0&&a[i]>Q.peek())
				{
					b[i]=Q.poll();
					rem[a[i]]--;
				}
				else if(rem[a[i]]>0&&a[i]<Q.peek())
				{
					int x=tot[a[i]]-frs[a[i]];
					if(x>=rem[a[i]])
						continue;
					else
					{
						b[i]=Q.poll();
						rem[a[i]]--;
					}
				}
				
			}
			for(int i=0;i<n;i++)
				out.print(b[i]+" ");
			
        }
		 
		
		public static int find(int v,int start,int end,int l,int r)
    	{
    	    if(r < start || end < l)
    	    {
    	    	
    	    	return 0;
    	    }
    	    if(l <= start && end <= r)
    	    {
    	        return (tre[v]);
    	    }
    	    int mid = (start + end) / 2;
    	    int p1 = find(2*v, start, mid, l, r);
    	    int p2 = find(2*v+1, mid+1, end, l, r);
    	    return p1+p2;          
    	}
		static int tre[]=new int[4000005];
		public static void Update(int v,int tl,int tr,int index,int val)
    	{
    		if(tl==tr)
    		{
    			
    			tre[v]+=val;
    		}
    		else
    		{
    			int mid=(tl+tr)/2;
    			if(tl <= index &&index <= mid)
    	        {
    	            Update(2*v,tl, mid, index, val);
    	        }
    	        else
    	        {
    	        	Update(2*v+1,mid+1,tr, index, val);
    	        }
    			tre[v]=(tre[2*v]+tre[2*v+1]);
    		}
    	}
		
			
		
		
		
        
		
		
	    
		
              
       
 
       
       
            boolean isPrime(int x)
            {
            if(x==0||x==1)
            	return false;
			for(int i = 2;i*1L*i<=x;i++) if(x%i==0) return false;
			return true;
		}
	    int  p ;
		void buildGraph(int n)
		{
			for(int i = 0; i<n ;i++){
				int x1 = ni() -1, y1 = ni()-1;
				amp[x1].add(y1);
				amp[y1].add(x1);
				x[i] = x1; y[i] = y1;
			}
		}
		long get(int x){
			long val = 0;
			for(int i = 0; i< N; i++){
				val += Math.abs(x-arr[i]);
				x+=L;
			}
			return val;
		}
		
		long modInverse(long a, long mOD2){
	        return  power(a, mOD2-2, mOD2);
		}
		long power(long x, long y, long m)
		{
			if (y == 0)
	    return 1;
		long p = power(x, y/2, m) % m;
		p = (p * p) % m;
	 
		return (y%2 == 0)? p : (x * p) % m;
		}
		
		public static long gcd(long a, long b){
			if(b==0) return a;
			return gcd(b,a%b);
		}
		
		public static int[] shuffle(int[] a, Random gen){
			for(int i = 0, n = a.length;i < n;i++)
			{ 
				int ind = gen.nextInt(n-i)+i; 
				int d = a[i]; 
				a[i] = a[ind];
				a[ind] = d; 
			} 
		return a; 
		}
	 
		
		class Pair1 implements Comparable<Pair1>{
			int v;
			int u;
			int we;
			Pair1(int u,int w,int we){
			this.v=u;
			this.u=w;
			this.we=we;
			}
			public int hashCode() {
				return Objects.hash();
			}
			
			@Override
			public int compareTo(Pair1 arg0) {
				return (int)(we-arg0.we);
			}
			
		}
		long power(long x, long y, int mod){
			long ans = 1;
			while(y>0){
				if(y%2==0){
					x = (x*x)%mod;
					y/=2;
				}
				else{
					ans = (x*ans)%mod;
					y--;
				}
			}
			return ans;
		}
		void soln() {
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
            out.flush();
		}
 		private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	 
		private int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}
	 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
	 
		private int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}
	 
		private double nd() {
			return Double.parseDouble(ns());
		}
	 
		private char nc() {
			return (char) skip();
		}
		private String ns() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { 
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		private char[] ns(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}
		private int[][] nm(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++)
			{
				for(int j=0;j<m;j++)
					map[i][j]=ni();
			}
			return map;
		}
	 
		private int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	 
		private int ni() {
			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();
			}
		}
	 
		private long nl() {
			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();
			}
		}
	 
		private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	 
		private void tr(Object... o) {
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	} 