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.*;

public class Solution {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		Task task = new Task();
		int t = 1;
		for (int i = 1; i <= t; i++) task.solve(i, in, out);
		out.close();
	}

	static class Task {
 		
		public void solve(int testNumber, InputReader in, OutputWriter out) throws IOException {
			int n = in.nextInt();
			int[] arr = in.nextIntArray(n + 1, 1);
			boolean[] s = new boolean[n + 1];
			DSU dsu = new DSU(n + 1);
			int[] cpy = Arrays.copyOf(arr, n + 1);
			for (int i = 1; i <= n; i++) {
				if (i == arr[i]) continue;
				int c = dsu.cal;
				dsu.union(i, arr[i]);
				if (c == dsu.cal) {
					arr[i] = i;
					s[i] = true;
				}
			}
			int r = -1;
			for (int i = 1; i <= n; i++) 
				if (arr[i] == i) {
					r = i;
					if (!s[i]) break;
				}
			for (int i = 1; i <= n; i++)
				if (arr[i] == i) arr[i] = r;
			int cnt = 0;
			for (int i = 1; i <= n; i++)
				if (arr[i] != cpy[i]) cnt++;
			out.println(cnt, "\n");
			out.printIntArray(arr, 1, n + 1);
 		}
	}
	
	static class DSU {
		int[] par, size, rank;
		boolean[] valid;
		int n, cal;
		
		public DSU(int n) {
			this.n = n;
			init(n);
		}
		
		public void init(int n) {
			par = new int[n];
			size = new int[n];
			rank = new int[n];
			valid = new boolean[n];
			cal = n;
			for (int i = 0; i < n; i++) {
				par[i] = i;
				size[i] = 1;
			}
		}
		
		public boolean isValid(int x) {
			return valid[x];
		}
		
		public int find(int x) {
			if (par[x] != x) return par[x] = find(par[x]);
			return par[x];
		}
		
		public boolean isSame(int x, int y) {
			return find(x) == find(y);
		}
		
		public void union(int x, int y) {
			x = find(x);
			y = find(y);
			if (x == y) {
				valid[x] = true;
				return;
			}
			size[x] = size[y] = size[x] + size[y];
			valid[x] = valid[y] = valid[x] | valid[y];
			if (rank[x] < rank[y]) par[x] = y;
			else par[y] = x;
			if (rank[x] == rank[y]) rank[x]++;
			cal--;
		}
		
		public int getSize(int x) {
			return size[find(x)];
		}
	}

	static class InputReader {
		private BufferedReader reader;
		private StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}
		
		private void tokenize() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}

		public String next() {
			tokenize();
			return tokenizer.nextToken();
		}

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

		public long nextLong() {
			return Long.parseLong(next());
		}
		
		public char nextChar() {
			return next().charAt(0);
		}
		
		public float nextFloat() {
			return Float.parseFloat(next());
		}
		
		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int size, int a) {
			tokenize();
			int[] arr=new int[size];
			for(int i = a; i < size; i++) {
				tokenize();
				arr[i] = Integer.parseInt(tokenizer.nextToken());
			}
			return arr;
		}
		
		public long[] nextLongArray(int size, int a) {
			tokenize();
			long[] arr=new long[size];
			for(int i = a; i < size; i++) {
				tokenize();
				arr[i] = Long.parseLong(tokenizer.nextToken());
			}
			return arr;
		}
		
		public float[] nextFloatArray(int size, int a) {
			tokenize();
			float[] arr=new float[size];
			for(int i = a; i < size; i++) {
				tokenize();
				arr[i] = Float.parseFloat(tokenizer.nextToken());
			}
			return arr;
		}

		public double[] nextDoubleArray(int size, int a) {
			tokenize();
			double[] arr=new double[size];
			for(int i = a; i < size; i++) {
				tokenize();
				arr[i] = Double.parseDouble(tokenizer.nextToken());
			}
			return arr;
		}

		public String[] nextStringArray(int size, int a) throws IOException {
			String[] arr=new String[size];
			for(int i = a; i < size; i++) 
				arr[i] = reader.readLine();
			return arr;
		}

		public char[] nextCharArray(int size) throws IOException {
			return reader.readLine().toCharArray();
		}
	}

	static class OutputWriter {
		public PrintWriter pw;

		public OutputWriter(OutputStream stream) {
			pw = new PrintWriter(stream);
		}
		
		public void println(Object... obj) {
			if (obj.length == 0) pw.println();
			else {
				String delimiter = (String) obj[obj.length - 1];
				for (int i = 0 ; i < obj.length - 1; i++) pw.print(obj[i] + delimiter);
			}
		}

		public void close() {
			pw.close();
		}

		public void flush() {
			pw.flush();
		}

		public void printStringArray(String[] arr, int a, int b) {
			for(int i = a; i < b; i++)
				pw.println(arr[i]);
		}
		
		public void printBooleanArray(boolean[] arr, int a, int b) {
			for(int i = a; i < b; i++)
				pw.print(arr[i] + " ");
		}

		public void printIntArray(int[] arr, int a, int b) {
			for(int i = a; i < b; i++)
				pw.print(arr[i] + " ");
		}

		public void printLongArray(long[] arr, int a, int b) {
			for(int i = a; i < b; i++)
				pw.print(arr[i] + " ");
		}

		public void printCharArray(char[] arr, int a, int b) {
			for(int i = a; i < b; i++)
				pw.print(arr[i] + " ");
		}

		public void printFloatArray(float[] arr, int a, int b) {
			for(int i = a; i < b; i++)
				pw.print(arr[i] + " ");
		}

		public void printDoubleArray(double[] arr, int a, int b) {
			for(int i = a; i < b; i++)
				pw.print(arr[i] + " ");
		}
		
		public void printIntArrayList(ArrayList<Integer> arr, int a, int b) {
			for(int i = a; i < b; i++)
				pw.print(arr.get(i) + " ");
		}
		
		public void printLongArrayList(ArrayList<Long> arr, int a, int b) {
			for(int i = a; i < b; i++)
				pw.print(arr.get(i) + " ");
		}
	}
}