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:
import java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class Main {
    FastScanner in;
    PrintWriter out;

    static final String FILE = "";

    int n;
    int ans[];
    int start[];
    boolean used[];
    TreeSet<Integer> neig[];
    ArrayList<Integer> roots = new ArrayList<>();
    boolean isHaveRoot;
    int deep;
    ArrayList<Integer> vertices = new ArrayList<>();

    void dfs(int v, int last) {
        if (used[v]) {
            deep = v;
            return;
        }

        used[v] = true;
        vertices.add(v);
        for (Integer it : neig[v]) {
            if (it == last) {
                if (ans[v] == it && ans[it] == v)
                    deep = v;
                continue;
            }
            dfs(it, v);
        }
    }

    public void solve() {
        n = in.nextInt();
        ans = new int[n];
        start = new int[n];
        used = new boolean[n];

        neig = new TreeSet[n];
        for (int i = 0; i < n; i++)
            neig[i] = new TreeSet<>();

        for (int i = 0; i < n; i++) {
            int tmp = in.nextInt() - 1;
            ans[i] = tmp;
            start[i] = tmp;
            if (tmp == i) {
                roots.add(tmp);
            }

            if (i != tmp) {
                neig[i].add(tmp);
                neig[tmp].add(i);
            }
        }

        int curr = -1, last = -1;

        ArrayList<Integer> noRoots = new ArrayList<>();

        for (int i = 0; i < n; i++) {
            if (used[i])
                continue;

            vertices.clear();
            deep = i;
            dfs(i, i);

            isHaveRoot = false;
            for (Integer it : vertices) {
                if (ans[it] == it) {
                    isHaveRoot = true;
                    curr = it;
                }
            }

            if (!isHaveRoot) {
                noRoots.add(deep);
            } else {
                if (last == -1)
                    last = curr;
                ans[curr] = last;
            }
        }

        if (noRoots.size() > 0) {
            if (last == -1)
                last = noRoots.get(0);

            for (Integer it : noRoots)
                ans[it] = last;
        }

        int cnt = 0;
        for (int i = 0; i < n; i++) {
            if (ans[i] != start[i]) {
                cnt++;
            }
        }

        out.println(cnt);
        for (int i = 0; i < n; i++)
            out.print((ans[i] + 1) + " ");
    }

    public void run() {
        if (FILE.equals("")) {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
        } else {
            try {
                in = new FastScanner(new FileInputStream(FILE +
                        ".in"));
                out = new PrintWriter(new FileOutputStream(FILE +
                        ".out"));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }
        solve();
        out.close();
    }

    public static void main(String[] args) {
        (new Main()).run();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
                return "";
            }
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public float nextFloat() {
            return Float.parseFloat(next());
        }
    }

    class Pair<A extends Comparable<A>, B extends Comparable<B>>
            implements Comparable<Pair<A, B>> {
        public A a;
        public B b;

        public Pair(A a, B b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Pair<A, B> o) {
            if (o == null || o.getClass() != getClass())
                return 1;
            int cmp = a.compareTo(o.a);
            if (cmp == 0)
                return b.compareTo(o.b);
            return cmp;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Pair<?, ?> pair = (Pair<?, ?>) o;

            if (a != null ? !a.equals(pair.a) : pair.a != null) return
                    false;
            return !(b != null ? !b.equals(pair.b) : pair.b != null);
        }
    }

    class PairInt extends Pair<Integer, Integer> {
        public PairInt(Integer u, Integer v) {
            super(u, v);
        }
    }

    class PairLong extends Pair<Long, Long> {
        public PairLong(Long u, Long v) {
            super(u, v);
        }
    }

}