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:


/**
 *
 * @author Abhishek Shankhadhar
 */
import java.io.*;
import java.util.*;
public class CF {

    InputStream obj;
    PrintWriter out;
    String check = "";


    //Solution !!

    void solution() {
        int n=inti();
        int arr[]=arri(n);
        boolean swi[]=new boolean[n];
        for(int i=0;i<n;i++){
            arr[i]-=1;
        }
        int cpy[]=Arrays.copyOf(arr, n);
        DisjointSet ds=new DisjointSet(n);
        for(int i=0;i<n;i++){
            int a=arr[i];
            int b=i;
            if(a==b)
                continue;
            int comp=ds.component;
            ds.merge(a, b);
            int newComp=ds.component;
            if(comp==newComp){
                arr[i]=i;
                swi[i]=true;
            }
        }
        int root = -1;
        for (int i = 0; i < n; i++) {
            if (arr[i] == i) {
                root = i;
                if (!swi[i])
                    break;
            }
        }
//        System.out.println(root);
        for (int i = 0; i < n; i++) {
            if (arr[i] == i) {
                arr[i] = root;
            }
        }

        int count=0;
        for(int i=0;i<n;i++){
            if(arr[i]!=cpy[i])
                count++;
        }
        out.println(count);
        for(int i=0;i<n;i++){
            out.print((arr[i]+1)+" ");
        }
        out.println();
    }
    static public class DisjointSet {
        public int rank[],parent[],size[];
        public int n,component;
        
        public DisjointSet(int n){
            this.n = n;
            makeSet();
        }
        
        public void makeSet(){
            rank = new int[n];
            parent = new int[n];
            for(int i=0;i<n;i++)
                parent[i] = i;
            size = new int[n];
            Arrays.fill(size, 1);
            component = n;
        }
        
        public int find(int x){
            if(parent[x] != x)
                parent[x] = find(parent[x]);
            return parent[x];
        }
        
        public void merge(int x,int y){
            int xRoot = find(x);
            int yRoot = find(y);
            
            if(xRoot == yRoot)
                return;
            
            size[xRoot] = size[yRoot] = size[xRoot] + size[yRoot];
            
            if(rank[xRoot] < rank[yRoot])
                parent[xRoot] = yRoot;
            else{
                parent[yRoot] = xRoot;
                if(rank[xRoot] == rank[yRoot]){
                    parent[yRoot] = xRoot;
                    rank[xRoot]++;
                }
            }
            component--;
        }
    
    }

    //------->ends !!


    public static void main(String[] args) throws IOException {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    new CF().ace();
                } catch (IOException e) {
                    e.printStackTrace();
                } catch (StackOverflowError e) {
                    System.out.println("RTE");
                }
            }
        }, "1", 1 << 26).start();
    }

    
    void ace() throws IOException {
        out = new PrintWriter(System.out);
        obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
//        obj=check.isEmpty() ? new FileInputStream("location of file") : new ByteArrayInputStream(check.getBytes());
//        long t1=System.currentTimeMillis();
        solution();
//        long t2=System.currentTimeMillis();
//        out.println(t2-t1);
        out.flush();
        out.close();
    }
    byte inbuffer[] = new byte[1024];
    int lenbuffer = 0, ptrbuffer = 0;

    int readByte() {
        if (lenbuffer == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuffer >= lenbuffer) {
            ptrbuffer = 0;
            try {
                lenbuffer = obj.read(inbuffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        if (lenbuffer <= 0) {
            return -1;
        }
        return inbuffer[ptrbuffer++];
    }

    boolean isSpaceChar(int c) {
        return (!(c >= 33 && c <= 126));
    }

    String stri() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) // when nextLine, (isSpaceChar(b) && b!=' ')
        {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }

    int inti() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    long loni() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    float fl() {
        return Float.parseFloat(stri());
    }

    double dou() {
        return Double.parseDouble(stri());
    }

    char chi() {
        return (char) skip();
    }

    int[] arri(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = inti();
        }
        return a;
    }

    long[] arrl(int n) {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = loni();
        }
        return a;
    }

    String[] stra(int n) {
        String a[] = new String[n];
        for (int i = 0; i < n; i++) {
            a[i] = stri();
        }
        return a;
    }

    private static void pa(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
//    uwi mod pow function

    public static long pow(long a, long n, long mod) {
//		a %= mod;
        long ret = 1;
        int x = 63 - Long.numberOfLeadingZeros(n);
        for (; x >= 0; x--) {
            ret = ret * ret % mod;
            if (n << 63 - x < 0) {
                ret = ret * a % mod;
            }
        }
        return ret;
    }

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