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.*;

public class main
{
	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	private static long mod = 1000000000 + 7;
	private static long mod1 = 1000000000 + 9;
	private static int block;
	static LinkedList<Integer>[] l;
	static int[] c;
	static int[] ans;
	static int k;
	static HashMap<Long,Integer> arr;
	static int[] arr1;
	private static void soln()
	{
		int n=nextInt();
		int[] arr=nextIntArray(n);
		int[] freq=new int[n+1];
		TreeSet<Integer> set=new TreeSet<>();
		for(int i=1;i<=n;i++)
			set.add(i);
		for(int i=0;i<n;i++) {
			freq[arr[i]]++;
			if(set.contains(arr[i]))
				set.remove(arr[i]);
		}
		pw.println(set.size());
		boolean[] used=new boolean[n+1];
		for(int i=0;i<n;i++) {
			if(freq[arr[i]]>1) {
				int x=set.first();
				if(x<arr[i] || used[arr[i]]) {
					freq[arr[i]]--;
					set.remove(x);
					arr[i]=x;
				}
			}
			used[arr[i]]=true;
			pw.print(arr[i]+" ");
		}
	}
	private static void dfs(int cur,int prev) {
		Iterator<Integer> it=l[cur].listIterator();
		//System.out.println(cur);
		int co=c[cur];
		long tmp=((long)co << 20) + (long)(arr1[co]);
		if(arr1[co]-k < 0)
			ans[cur]=-2;
		else {
			ans[cur]=arr.get(tmp-k);
		}
		arr.put(tmp,arr1[co]);
		arr1[co]++;
		while(it.hasNext()) {
			int x=it.next();
			if(x!=prev) {
				dfs(x,cur);
			}
		}
		arr.remove(tmp);
		arr1[co]--;
	}
	private static class Node{
		int val;
		Node left;
		Node right;
		public Node(int v) {
			val=v;
		}
	}
	public static class Segment {
		private int[] tree;
		private int[] base;
		private int size;
		private int n;
		private class node{
			private int a;
			private int b;
			private int c;
			public node(int x,int y,int z){
				a=x;
				b=y;
				c=z;
			}
		}
		public Segment(int n,int[] arr){
			//this.base=arr;
			int x = (int) (Math.ceil(Math.log(n) / Math.log(2)));
	        size = 2 * (int) Math.pow(2, x) - 1;
			tree=new int[size];
			base=arr;
			this.n=n;
			build(0,0,n-1);
		}
		public void build(int id,int l,int r) {
			if(l==r) {
				tree[id]=base[l];
				return;
			}
			int mid=l+((r-l)>>1);
			build((id<<1)+1,l,mid);
			build((id<<1)+2,mid+1,r);
			tree[id]=Math.max(tree[(id<<1)+1],tree[(id<<1)+2]);
		}
		public int query(int l,int r){
			return queryUtil(l,r,0,0,n-1);
		}
		private int queryUtil(int x,int y,int id,int l,int r){
			if(l>y || x>r) 
				return 0;
			if(x <= l && r<=y)
				return tree[id];
			int mid=l+((r-l)>>1);
			return Math.max(queryUtil(x,y,(id<<1)+1,l,mid),queryUtil(x,y,(id<<1)+2,mid+1,r));
		}
		public void update(int x,int colour,int id,int l,int r){
			//System.out.println(l+" "+r+" "+x);
			if(x>r || x<l)
				return;
			if(l==r){
				tree[id]+=colour;
				return;
			}
			int mid=l+(r-l)/2;
			update(x,colour,2*id+1,l,mid);
			update(x,colour,2*id+2,mid+1,r);
			tree[id]=tree[2*id+1]+tree[2*id+2];
		}
	}

	static void multiply(long[][] a, long[][] b, long m)
	{
		int n = a.length;
		long[][] mul = new long[n][n];
		for (int i = 0; i < n; i++)
		{
			for (int j = 0; j < n; j++)
			{
				mul[i][j] = 0;
				for (int k = 0; k < n; k++)
					mul[i][j] = (mul[i][j] + (a[i][k] * b[k][j]) % m) % m;
			}
		}
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++)
				a[i][j] = mul[i][j];
	}
	private static class DSU{
		int[] parent;
		int[] rank;
		int[][] lr;
		public DSU(int n){
			parent=new int[n];
			rank=new int[n];
			lr=new int[n][2];
			//cnt=new int[n];
			for(int i=0;i<n;i++){
				parent[i]=i;
				rank[i]=1;
				lr[i][0]=lr[i][1]=i;
				//cnt[i]=1;
			}
		}
		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)
	        	return 0;
	        	parent[yset]=xset;
	        	rank[xset]+=rank[yset];
	        	rank[yset]=0;
	        	lr[xset][1]=lr[yset][1];
	        	lr[yset][0]=lr[xset][0];
	        	//cnt[xset]+=cnt[yset];
	        	//cnt[yset]=0;
	        	return xset;
	    }
	}

	private static long pow(long a, long b, long c)
	{
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}
	private static class Mo implements Comparable<Mo>
	{
		int l;
		int r;
		int i;

		public Mo(int a, int b, int ind)
		{
			l = a;
			r = b;
			i = ind;
		}

		@Override
		public int compareTo(Mo arg0)
		{
			int b1 = this.l / block;
			int b2 = arg0.l / block;
			return (b1 != b2) ? (b1 - b2) : (this.r - arg0.r);
		}
	}

	private static long gcd(long n, long l)
	{
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}
	public static void main(String[] args) throws Exception
	{
		new Thread(null, new Runnable()
		{
			@Override
			public void run()
			{
				/*try { 
					InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\B-large-practice.in")); 
				} catch (FileNotFoundException e) { // TODO Auto-generated catch block
					e.printStackTrace(); 
				} */
				InputReader(System.in);
				pw = new PrintWriter(System.out);
				/*try { 
					pw=new PrintWriter(new FileOutputStream("C:\\Users\\hardik\\Desktop\\out.txt")); 
				} catch (FileNotFoundException e) { // TODO Auto-generated catch block
					e.printStackTrace();
				}*/
				soln();
				pw.close();
			}
		}, "1", 1 << 26).start();
	}

	public static void InputReader(InputStream stream1)
	{
		stream = stream1;
	}

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

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

	private static 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++];
	}

	private static 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;
	}

	private static 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;
	}

	private static String nextToken()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do
		{
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private static 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();
	}

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

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

	private static void pArray(int[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static void pArray(long[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static boolean isSpaceChar(int c)
	{
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private static char nextChar()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		char c1 = (char) c;
		while (!isSpaceChar(c))
			c = read();
		return c1;
	}

	private interface SpaceCharFilter
	{
		public boolean isSpaceChar(int ch);
	}
}