CF698B.Fix a Tree

A tree is an undirected connected graph without cycles.

Let's consider a rooted undirected tree with n vertices, numbered 1 through n. There are many ways to represent such a tree. One way is to create an array with n integers _p_1, _p_2, ..., p__n, where p__i denotes a parent of vertex i (here, for convenience a root is considered its own parent).

For this rooted tree the array p is [2, 3, 3, 2].

Given a sequence _p_1, _p_2, ..., p__n, one is able to restore a tree:

1. There must be exactly one index r that p__r = r. A vertex r is a root of the tree.
2. For all other n - 1 vertices i, there is an edge between vertex i and vertex p__i.

A sequence _p_1, _p_2, ..., p__n is called valid if the described procedure generates some (any) rooted tree. For example, for n = 3 sequences (1,2,2), (2,3,1) and (2,1,3) are not valid.

You are given a sequence _a_1, _a_2, ..., a__n, not necessarily valid. Your task is to change the minimum number of elements, in order to get a valid sequence. Print the minimum number of changes and an example of a valid sequence after that number of changes. If there are many valid sequences achievable in the minimum number of changes, print any of them.

树是一类无向连通且无环的图。

考虑一棵以某顶点为根的无向树，其包含 $n$ 个顶点，编号为 $1$ 到 $n$。表示这样一颗树的方法有很多。其中一种方法是构造一个长度为 $n$ 的整数数组 $p_1,\,p_2,\,\dots,\,p_n$，其中 $p_i$ 表示顶点 $i$ 的父节点（为方便起见，规定根节点的父节点为其自身）。

对于该有根树，对应的数组 $p$ 为 $[2,\,3,\,3,\,2]$。

给定一个序列 $p_1,\,p_2,\,\dots,\,p_n$，我们可以据此还原出一棵树：

1. 必须恰好存在一个下标 $r$，使得 $p_r = r$。顶点 $r$ 即为该树的根；
2. 对其余 $n-1$ 个顶点 $i$，均存在一条连接顶点 $i$ 与顶点 $p_i$ 的边。

若按上述过程可生成某棵（任意）有根树，则称序列 $p_1,\,p_2,\,\dots,\,p_n$ 是合法的。例如，当 $n=3$ 时，序列 $(1,2,2)$、$(2,3,1)$ 和 $(2,1,3)$ 均不合法。

现给定一个序列 $a_1,\,a_2,\,\dots,\,a_n$，它未必合法。你的任务是通过修改最少数量的元素，使其变为合法序列。请输出所需的最少修改次数，以及一次修改后得到的合法序列。若存在多种方案均可达到最少修改次数，请输出其中任意一种即可。

The first line of the input contains an integer n (2 ≤ n ≤ 200 000) — the number of vertices in the tree.

The second line contains n integers _a_1, _a_2, ..., a__n (1 ≤ a__i ≤ n).

输入的第一行包含一个整数 $n$（$2 \leq n \leq 200\,000$）——树中顶点的数量。

第二行包含 $n$ 个整数 $a_1,\,a_2,\,...,\,a_n$（$1 \leq a_i \leq n$）。

In the first line print the minimum number of elements to change, in order to get a valid sequence.

In the second line, print any valid sequence possible to get from (_a_1, _a_2, ..., a__n) in the minimum number of changes. If there are many such sequences, any of them will be accepted.

第一行输出得到有效序列所需的最少修改元素个数。

第二行输出一个由 $(a_1,\,a_2,\,...,\,a_n)$ 经过最少次数修改后得到的有效序列。若存在多个满足条件的序列，输出任意一个即可。

In the first sample, it's enough to change one element. In the provided output, a sequence represents a tree rooted in a vertex 4 (because _p_4 = 4), which you can see on the left drawing below. One of other correct solutions would be a sequence 2 3 3 2, representing a tree rooted in vertex 3 (right drawing below). On both drawings, roots are painted red.

In the second sample, the given sequence is already valid.

在第一个样例中，只需修改一个元素即可。在所提供的输出中，序列表示一棵以顶点 4 为根的树（因为 $p_4 = 4$），如下图左侧所示。另一个正确的解法是序列 2 3 3 2，它表示一棵以顶点 3 为根的树（如下图右侧所示）。在两张图中，根节点均以红色标出。

在第二个样例中，给定的序列本身已是合法的。