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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ernesto Carvajal
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        int n;
        int[] parent;
        Graph graph;
        RecursiveIndependentSetSystem iss;
        int solution;
        int root;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.readInt();
            parent = IOUtils.readIntArray(in, n);
            MiscUtils.decreaseByOne(parent);
            graph = new Graph(n);
            for (int i = 0; i < n; i++) {
                int u = i;
                int v = parent[i];
                graph.addSimpleEdge(u, v);
                if (u != v) {
                    graph.addSimpleEdge(v, u);
                }
            }

            iss = new RecursiveIndependentSetSystem(n);
            solution = 0;
            root = -1;
            for (int i = 0; i < n; i++) {
                if (parent[i] == i) {
                    root = i;
                    break;
                }
            }

            if (root == -1) {
                root = selectRoot(-1, 0);
            }

            for (int i = 0; i < n; i++) {
                fixLoop(-1, i);
            }

            out.printLine(solution);
            MiscUtils.increaseByOne(parent);
            out.printLine(parent);
        }

        private void fixLoop(int prnt, int node) {
            if (iss.get(node) == iss.get(root)) {
                return;
            }
            for (int id = graph.firstOutbound(node); id != -1; id = graph.nextOutbound(id)) {
                int child = graph.destination(id);
                if (child == prnt) continue;
                if (iss.get(child) == iss.get(node)) {
                    if (parent[child] == node) {
                        solution++;
                        parent[child] = root;
                        iss.join(child, root);
                        return;
                    }
                    if (parent[node] == child) {
                        solution++;
                        parent[node] = root;
                        iss.join(node, root);
                        return;
                    }
                } else {
                    iss.join(child, node);
                    fixLoop(node, child);
                }
            }
        }

        private int selectRoot(int prnt, int node) {
            for (int id = graph.firstOutbound(node); id != -1; id = graph.nextOutbound(id)) {
                int child = graph.destination(id);
                if (child == prnt) continue;
                if (iss.get(child) == iss.get(node)) {
                    if (parent[child] == node) {
                        solution++;
                        parent[child] = child;
                        return child;
                    }
                    if (parent[node] == child) {
                        solution++;
                        parent[node] = node;
                        return node;
                    }
                } else {
                    iss.join(child, node);
                    int candidateRoot = selectRoot(node, child);
                    if (candidateRoot != -1) {
                        return candidateRoot;
                    }
                }
            }
            return -1;
        }

    }

    static class Graph {
        public static final int REMOVED_BIT = 0;
        protected int vertexCount;
        protected int edgeCount;
        private int[] firstOutbound;
        private int[] firstInbound;
        private Edge[] edges;
        private int[] nextInbound;
        private int[] nextOutbound;
        private int[] from;
        private int[] to;
        private long[] weight;
        public long[] capacity;
        private int[] reverseEdge;
        private int[] flags;

        public Graph(int vertexCount) {
            this(vertexCount, vertexCount);
        }

        public Graph(int vertexCount, int edgeCapacity) {
            this.vertexCount = vertexCount;
            firstOutbound = new int[vertexCount];
            Arrays.fill(firstOutbound, -1);

            from = new int[edgeCapacity];
            to = new int[edgeCapacity];
            nextOutbound = new int[edgeCapacity];
            flags = new int[edgeCapacity];
        }

        public int addEdge(int fromID, int toID, long weight, long capacity, int reverseEdge) {
            ensureEdgeCapacity(edgeCount + 1);
            if (firstOutbound[fromID] != -1)
                nextOutbound[edgeCount] = firstOutbound[fromID];
            else
                nextOutbound[edgeCount] = -1;
            firstOutbound[fromID] = edgeCount;
            if (firstInbound != null) {
                if (firstInbound[toID] != -1)
                    nextInbound[edgeCount] = firstInbound[toID];
                else
                    nextInbound[edgeCount] = -1;
                firstInbound[toID] = edgeCount;
            }
            this.from[edgeCount] = fromID;
            this.to[edgeCount] = toID;
            if (capacity != 0) {
                if (this.capacity == null)
                    this.capacity = new long[from.length];
                this.capacity[edgeCount] = capacity;
            }
            if (weight != 0) {
                if (this.weight == null)
                    this.weight = new long[from.length];
                this.weight[edgeCount] = weight;
            }
            if (reverseEdge != -1) {
                if (this.reverseEdge == null) {
                    this.reverseEdge = new int[from.length];
                    Arrays.fill(this.reverseEdge, 0, edgeCount, -1);
                }
                this.reverseEdge[edgeCount] = reverseEdge;
            }
            if (edges != null)
                edges[edgeCount] = createEdge(edgeCount);
            return edgeCount++;
        }

        protected final GraphEdge createEdge(int id) {
            return new GraphEdge(id);
        }

        public final int addFlowWeightedEdge(int from, int to, long weight, long capacity) {
            if (capacity == 0) {
                return addEdge(from, to, weight, 0, -1);
            } else {
                int lastEdgeCount = edgeCount;
                addEdge(to, from, -weight, 0, lastEdgeCount + entriesPerEdge());
                return addEdge(from, to, weight, capacity, lastEdgeCount);
            }
        }

        protected int entriesPerEdge() {
            return 1;
        }

        public final int addWeightedEdge(int from, int to, long weight) {
            return addFlowWeightedEdge(from, to, weight, 0);
        }

        public final int addSimpleEdge(int from, int to) {
            return addWeightedEdge(from, to, 0);
        }

        public final int firstOutbound(int vertex) {
            int id = firstOutbound[vertex];
            while (id != -1 && isRemoved(id))
                id = nextOutbound[id];
            return id;
        }

        public final int nextOutbound(int id) {
            id = nextOutbound[id];
            while (id != -1 && isRemoved(id))
                id = nextOutbound[id];
            return id;
        }

        public final int destination(int id) {
            return to[id];
        }

        public final boolean flag(int id, int bit) {
            return (flags[id] >> bit & 1) != 0;
        }

        public final boolean isRemoved(int id) {
            return flag(id, REMOVED_BIT);
        }

        protected void ensureEdgeCapacity(int size) {
            if (from.length < size) {
                int newSize = Math.max(size, 2 * from.length);
                if (edges != null)
                    edges = resize(edges, newSize);
                from = resize(from, newSize);
                to = resize(to, newSize);
                nextOutbound = resize(nextOutbound, newSize);
                if (nextInbound != null)
                    nextInbound = resize(nextInbound, newSize);
                if (weight != null)
                    weight = resize(weight, newSize);
                if (capacity != null)
                    capacity = resize(capacity, newSize);
                if (reverseEdge != null)
                    reverseEdge = resize(reverseEdge, newSize);
                flags = resize(flags, newSize);
            }
        }

        protected final int[] resize(int[] array, int size) {
            int[] newArray = new int[size];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        private long[] resize(long[] array, int size) {
            long[] newArray = new long[size];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        private Edge[] resize(Edge[] array, int size) {
            Edge[] newArray = new Edge[size];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        protected class GraphEdge implements Edge {
            protected int id;

            protected GraphEdge(int id) {
                this.id = id;
            }

        }

    }

    static class IOUtils {
        public static int[] readIntArray(InputReader in, int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
                array[i] = in.readInt();
            return array;
        }

    }

    static interface IndependentSetSystem {
        public static interface Listener {
            public void joined(int joinedRoot, int root);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

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

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

        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(array[i]);
            }
        }

        public void printLine(int[] array) {
            print(array);
            writer.println();
        }

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

        public void printLine(int i) {
            writer.println(i);
        }

    }

    static interface Edge {
    }

    static class MiscUtils {
        public static void decreaseByOne(int[]... arrays) {
            for (int[] array : arrays) {
                for (int i = 0; i < array.length; i++)
                    array[i]--;
            }
        }

        public static void increaseByOne(int[]... arrays) {
            for (int[] array : arrays) {
                for (int i = 0; i < array.length; i++)
                    array[i]++;
            }
        }

    }

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

        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 readInt() {
            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 - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return isWhitespace(c);
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class RecursiveIndependentSetSystem implements IndependentSetSystem {
        private final int[] color;
        private final int[] rank;
        private int setCount;
        private IndependentSetSystem.Listener listener;

        public RecursiveIndependentSetSystem(int size) {
            color = new int[size];
            rank = new int[size];
            for (int i = 0; i < size; i++)
                color[i] = i;
            setCount = size;
        }

        public RecursiveIndependentSetSystem(RecursiveIndependentSetSystem other) {
            color = other.color.clone();
            rank = other.rank.clone();
            setCount = other.setCount;
        }

        public boolean join(int first, int second) {
            first = get(first);
            second = get(second);
            if (first == second)
                return false;
            if (rank[first] < rank[second]) {
                int temp = first;
                first = second;
                second = temp;
            } else if (rank[first] == rank[second])
                rank[first]++;
            setCount--;
            color[second] = first;
            if (listener != null)
                listener.joined(second, first);
            return true;
        }

        public int get(int index) {
            if (color[index] == index)
                return index;
            return color[index] = get(color[index]);
        }

    }
}