Make a Permutation!

题意翻译

题意: 给出含有n个数的序列,每个数的范围是1~n.请你改变其中的一些数使这个序列成为一个1~n的全排列,若有多种变化方案,取改变次数最少且字典序最小的方案. 输入: 第一行一个整数n(2<=n<=200000) 第二行n个整数表示这个序列 输出: 第一行一个整数表示最少的改变次数 第二行改变后的全排列 感谢@凌幽 提供的翻译

题目描述

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 $ x_{i}<y_{i} $ , 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.

输入输出格式

输入格式

The first line contains an single integer $ n $ ( $ 2<=n<=200000 $ ) — the number of elements in Ivan's array. The second line contains a sequence of integers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=n $ ) — the description of Ivan's array.

输出格式

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.

输入输出样例

输入样例 #1

4
3 2 2 3

输出样例 #1

2
1 2 4 3 

输入样例 #2

6
4 5 6 3 2 1

输出样例 #2

0
4 5 6 3 2 1 

输入样例 #3

10
6 8 4 6 7 1 6 3 4 5

输出样例 #3

3
2 8 4 6 7 1 9 3 10 5 

说明

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.