14121412 SUSTech Online Judge
Problem 1412 --Christmas tree

1412: Christmas tree

Time Limit: 1 Sec  Memory Limit: 256 MB  Special Judge
Submit: 369  Solved: 71
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Description

To celebrate the 10th anniversary of SUSTech and Christmas, $$Alice$$ want to construct a rooted christmas tree $$T$$, which root is node $$1$$. The tree has $$n$$ nodes and the brightness of node $$i$$ is $$a_i$$. We define $$d_i$$ is the depth of node $$i$$. Particularly, $$d_1=0$$. The darkness of a christmas tree is the number of nodes which brightness value not equal to it's depth. Now $$Alice$$ has $$n$$ nodes and she want to construct the tree and minimize the darkness of the christmas tree.
Note that $$f(T)=\sum_{i=1}^n[a_i \neq d_i]$$
$$Alice$$ wants to minimize $$f(T)$$. Can you help her?
Your task is to find the answer and construct the tree $$T$$.

Input

The first line contains an integer $$N(2 \leq N \leq 2 \times 10^5)$$ indicating the total number of nodes.
The next line contains $$N$$ integers $$a_1, a_2, \ldots , a_N(0 \leq a_i < N)$$, indicating the brightness value of each node.

Output

You should print two lines.
In first line, print out one integer representing the minimum $$f(T)$$.
In second line, print out $$N-1$$ integers $$f_2 , \ldots, f_N$$. Among them, $$f_i$$ represents the parent node of $$i$$.

Sample Input

5
1 0 0 4 3

Sample Output

3
3 1 5 2

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