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:
//package com.codeforces.competitions.year2016.julytoseptember.round363div2;

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

public final class TaskD
{
    public static void main(String[] args)
    {
        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);

		Solver solver = new Solver(in, out);
		solver.solve(1);

        out.flush();

        in.close();
        out.close();
    }

    static class Solver
    {
        int n;
		List<Integer> isRoot, isInCycle;
		Node[] nodes;
        InputReader in;
        OutputWriter out;

        public Solver(InputReader in, OutputWriter out)
        {
        	this.in = in;
        	this.out = out;
        }

		void solve(int testNumber)
		{
			n = in.nextInt();
			isRoot = new ArrayList<>();
			isInCycle = new ArrayList<>();
			nodes = new Node[n + 1];

			for (int i = 1; i <= n; i++)
				nodes[i] = new Node(i, in.nextInt());

			for (int i = 1; i <= n; i++)
				if (!nodes[i].visited)
					dfs(i, new HashSet<>());

//			System.out.println("roots : " + isRoot.toString());
//			System.out.println("isInCycle : " + isInCycle.toString());

			int count = 0;
			int size = isInCycle.size();

			if (isRoot.size() == 0)
			{
				nodes[isInCycle.get(0)].parent = isInCycle.get(0);
				count++;

				for (int i = 1; i < size; i++)
				{
					nodes[isInCycle.get(i)].parent = nodes[isInCycle.get(0)].index;
					count++;
				}
			}
			else
			{
				int rootsSize = isRoot.size();

				for (int i = 1; i < rootsSize; i++)
				{
					nodes[isRoot.get(i)].parent = isRoot.get(0);
					count++;
				}

				for (int i = 0; i < size; i++)
				{
					nodes[isInCycle.get(i)].parent = isRoot.get(0);
					count++;
				}
			}

			out.println(count);

			for (int i = 1; i <= n; i++)
				out.print(nodes[i].parent + " ");
		}

		void dfs(int index, Set<Integer> currChain)
		{
			Node temp = nodes[index];

			temp.visited = true;
			currChain.add(index);

			if (temp.parent == index)
				isRoot.add(index);
			else if (!nodes[temp.parent].visited)
				dfs(temp.parent, currChain);
			else if (currChain.contains(temp.parent))
				isInCycle.add(temp.parent);
		}

		class Node
		{
			int index, parent;
			boolean visited;

			public Node(int index, int parent)
			{
				this.index = index;
				this.parent = parent;
			}

		}

	}

    static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars)
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                } catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }

            return buf[curChar++];
        }

        public int nextInt()
        {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-')
            {
                sgn = -1;
                c = read();
            }

            int res = 0;

            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                res *= 10;
                res += c & 15;

                c = read();
            } while (!isSpaceChar(c));

            return res * sgn;
        }

        public int[] nextIntArray(int arraySize)
        {
            int array[] = new int[arraySize];

            for (int i = 0; i < arraySize; i++)
                array[i] = nextInt();

            return array;
        }

        public long nextLong()
        {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sign = 1;

            if (c == '-')
            {
                sign = -1;

                c = read();
            }

            long result = 0;

            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                result *= 10;
                result += c & 15;

                c = read();
            } while (!isSpaceChar(c));

            return result * sign;
        }

        public long[] nextLongArray(int arraySize)
        {
            long array[] = new long[arraySize];

            for (int i = 0; i < arraySize; i++)
                array[i] = nextLong();

            return array;
        }

        public float nextFloat() // problematic
        {
            float result, div;
            byte c;

            result = 0;
            div = 1;
            c = (byte) read();

            while (c <= ' ')
                c = (byte) read();

            boolean isNegative = (c == '-');

            if (isNegative)
                c = (byte) read();

            do
            {
                result = result * 10 + c - '0';
            } while ((c = (byte) read()) >= '0' && c <= '9');

            if (c == '.')
                while ((c = (byte) read()) >= '0' && c <= '9')
                    result += (c - '0') / (div *= 10);

            if (isNegative)
                return -result;

            return result;
        }

        public double nextDouble() // not completely accurate
        {
            double ret = 0, div = 1;
            byte c = (byte) read();

            while (c <= ' ')
                c = (byte) read();

            boolean neg = (c == '-');

            if (neg)
                c = (byte) read();

            do
            {
                ret = ret * 10 + c - '0';
            } while ((c = (byte) read()) >= '0' && c <= '9');

            if (c == '.')
                while ((c = (byte) read()) >= '0' && c <= '9')
                    ret += (c - '0') / (div *= 10);

            if (neg)
                return -ret;

            return ret;
        }

        public String next()
        {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            StringBuilder res = new StringBuilder();

            do
            {
                res.appendCodePoint(c);

                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String nextLine()
        {
            int c = read();

            StringBuilder result = new StringBuilder();

            do
            {
                result.appendCodePoint(c);

                c = read();
            } while (!isNewLine(c));

            return result.toString();
        }

        public boolean isNewLine(int c)
        {
            return c == '\n';
        }

        public void close()
        {
            try
            {
                stream.close();
            } catch (IOException e)
            {
                e.printStackTrace();
            }
        }

    }

    static class OutputWriter
    {
        private PrintWriter writer;

        public OutputWriter(OutputStream stream)
        {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
                    stream)));
        }

        public OutputWriter(Writer writer)
        {
            this.writer = new PrintWriter(writer);
        }

        public void println(int x)
        {
            writer.println(x);
        }

        public void print(int x)
        {
            writer.print(x);
        }

		public void println(char x)
		{
			writer.println(x);
		}

		public void print(char x)
		{
			writer.print(x);
		}

        public void println(int array[], int size)
        {
            for (int i = 0; i < size; i++)
                println(array[i]);
        }

        public void print(int array[], int size)
        {
            for (int i = 0; i < size; i++)
                print(array[i] + " ");
        }

        public void println(long x)
        {
            writer.println(x);
        }

        public void print(long x)
        {
            writer.print(x);
        }

        public void println(long array[], int size)
        {
            for (int i = 0; i < size; i++)
                println(array[i]);
        }

        public void print(long array[], int size)
        {
            for (int i = 0; i < size; i++)
                print(array[i]);
        }

        public void println(float num)
        {
            writer.println(num);
        }

        public void print(float num)
        {
            writer.print(num);
        }

        public void println(double num)
        {
            writer.println(num);
        }

        public void print(double num)
        {
            writer.print(num);
        }

        public void println(String s)
        {
            writer.println(s);
        }

        public void print(String s)
        {
            writer.print(s);
        }

        public void println()
        {
            writer.println();
        }

        public void printSpace()
        {
            writer.print(" ");
        }

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

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

    }

	static class CMath
	{
		static long power(long number, long power)
		{
			if (number == 1 || number == 0 || power == 0)
				return 1;

			if (power == 1)
				return number;

			if (power % 2 == 0)
				return power(number * number, power / 2);
			else
				return power(number * number, power / 2) * number;
		}

		static long modPower(long number, long power, long mod)
		{
			if (number == 1 || number == 0 || power == 0)
				return 1;

			number = mod(number, mod);

			if (power == 1)
				return number;

			long square = mod(number * number, mod);

			if (power % 2 == 0)
				return modPower(square, power / 2, mod);
			else
				return mod(modPower(square, power / 2, mod) * number, mod);
		}

		static long moduloInverse(long number, long mod)
		{
			return modPower(number, mod - 2, mod);
		}

		static long mod(long number, long mod)
		{
			return number - (number / mod) * mod;
		}

		static int gcd(int a, int b)
		{
			if (b == 0)
				return a;
			else
				return gcd(b, a % b);
		}

	}

}