Problem: 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 p1, p2, ..., pn, where pi denotes a parent of vertex i (here, for convenience a root is considered its own parent).

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

Given a sequence p1, p2, ..., pn, one is able to restore a tree:

  1. There must be exactly one index r that pr = 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 pi. 



A sequence p1, p2, ..., pn 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 a1, a2, ..., an, 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.

Input

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 a1, a2, ..., an (1 ≤ ai ≤ n).

Output

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 (a1, a2, ..., an) in the minimum number of changes. If there are many such sequences, any of them will be accepted.

Examples

Input

4
2 3 3 4


Output

1
2 3 4 4 


Input

5
3 2 2 5 3


Output

0
3 2 2 5 3 


Input

8
2 3 5 4 1 6 6 7


Output

2
2 3 7 8 1 6 6 7

Note

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 p4 = 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.

<image>

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

Solution (in JAVA):

Solution:
/*
Keep solving problems.
*/

import java.util.*;
import java.io.*;

public class CFA {
    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    private static final long MOD = 1000 * 1000 * 1000 + 7;
    private static final int[] dx = {0, -1, 0, 1};
    private static final int[] dy = {1, 0, -1, 0};
    private static final String yes = "Yes";
    private static final String no = "No";

    int n;
    List<List<Integer>> graph = new ArrayList<>();
    List<List<Integer>> comp = new ArrayList<>();
    boolean[] vis;
    int[] arr;
    void solve() throws IOException {
        n = nextInt();
        for (int i = 0; i < n; i++) {
            graph.add(new ArrayList<>());
        }
        arr = nextIntArr(n);
        for (int i = 0; i < n; i++) {
            int u = i;
            int v = arr[i] - 1;
            if (u != v) {
                graph.get(u).add(v);
                graph.get(v).add(u);
            }
        }

        int same = 0;
        for (int i = 0; i < n; i++) {
            if (i == arr[i] - 1) {
                same++;
            }
        }

        vis = new boolean[n];
        for (int i = 0; i < n; i++) {
            if (!vis[i]) {
                List<Integer> ls = new ArrayList<>();
                findComp(i, ls, -1);
                comp.add(ls);
            }
        }

        Arrays.fill(vis, false);
        List<Integer> roots = new ArrayList<>();
        for (List<Integer> com : comp) {
            roots.add(findRoot(com));
        }

        if (comp.size() == 1) {
            if (same == 1) {
                outln(0);
                for (int i = 0; i < n; i++) {
                    out(arr[i] + " ");
                }
                return;
            }
        }

        int[] res = Arrays.copyOf(arr, n);
        int cnt = 0;
        int root = -1;
        for (int v : roots) {
            if (v == arr[v] - 1) {
                root = v;
            }
        }

        if (root == -1) {
            root = roots.get(0);
            if (root != arr[root] - 1) {
                cnt++;
                res[root] = root + 1;
            }
            for (int i = 0; i < roots.size(); i++) {
                int cur = roots.get(i);
                if (cur != root) {
                    cnt++;
                    res[cur] = root + 1;
                }
            }

            outln(cnt);
            for (int i = 0; i < n; i++) {
                out(res[i] + " ");
            }

            return;
        }

        for (int v : roots) {
            if (v != root) {
                cnt++;
                res[v] = root + 1;
            }
        }

        outln(cnt);
        for (int i = 0; i < n; i++) {
            out(res[i] + " ");
        }
    }

    int findRoot(List<Integer> com) {
        int start = com.get(0);
        while (true) {
            if (vis[start]) {
                break;
            }

            vis[start] = true;
            start = arr[start] - 1;
        }

        return start;
    }

    void findComp(int cur, List<Integer> ls, int parent) {
        if (vis[cur]) {
            return;
        }

        ls.add(cur);
        vis[cur] = true;
        for (int nxt : graph.get(cur)) {
            if (nxt == parent) {
                continue;
            }
            findComp(nxt, ls, cur);
        }
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }

    long gcd(long a, long b) {
        while(a != 0 && b != 0) {
            long c = b;
            b = a % b;
            a = c;
        }
        return a + b;
    }

    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    private void formatPrint(double val) {
        System.out.format("%.9f%n", val);
    }
    public CFA() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFA();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}