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 cp;
import java.util.*;
import java.lang.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
    public void dfs(TreeSet<Integer> tt,TreeSet<Integer>[] tree,int[] arr,int[] visited,int source ,int beforesource) {
        visited[source]=1;
        for(int i: tree[source]) {
            //System.out.println(source+" "+i);
            if(visited[i]==0) {
                this.dfs(tt,tree, arr, visited, i,source);
            }
            else if(i!=beforesource){
                if(arr[i]==source) {
                    arr[i]=i;
                    tt.add(i);
                }
                else if(arr[source]==i) {
                    arr[source]=source;
                    tt.add(source);
                }
            }
        }
    }
    public void dfs1(TreeSet<Integer>[] tree,int[] parent,int[] visited,int source) {
        visited[source]=1;
        for(int i:tree[source]) {
            if(visited[i]==0) {
                parent[i]=parent[source];
                this.dfs1(tree, parent, visited,i);
            }
        }
    }
    public static void main(String[] args) throws Exception{
        // TODO Auto-generated method stub
        Reader.init(System.in);
        Main mm=new Main();
        int n=Reader.nextInt();
        int[] arr=new int[n];
        for(int i=0;i<n;i++) {
            arr[i]=Reader.nextInt()-1;
        }
        //ArrayList<Integer> l=new ArrayList<Integer>();
        TreeSet<Integer>Set =new TreeSet<Integer>();
        for(int i=0;i<n;i++) {
            if(arr[i]!=-1 && arr[arr[i]]==i && arr[i]!=i) {
                arr[i]=i;
                Set.add(i);
            }
        }
        
        TreeSet<Integer>[] tree=new TreeSet[n];
        for(int i=0;i<n;i++) {
            tree[i]=new TreeSet<Integer>();
        }
        for(int i=0;i<n;i++) {
            //System.out.print(arr[i]+" ");
        }
        //System.out.println();
        for(int i=0;i<n;i++) {
            if(arr[i]!=-1 && arr[i]!=i) {
                tree[i].add(arr[i]);
                tree[arr[i]].add(i);
            }
        }
        int[] visited=new int[n];
        for(int i=0;i<n;i++) {
            if(visited[i]==0) {
                mm.dfs(Set,tree, arr, visited, i,-1);
            }
        }
        for(int i=0;i<n;i++) {
            //System.out.print(arr[i]+" ");
        }
        //System.out.println();
        tree=new TreeSet[n];
        for(int i=0;i<n;i++) {
            tree[i]=new TreeSet<Integer>();
        }
        for(int i=0;i<n;i++) {
            if(arr[i]!=-1 && arr[i]!=i) {
                tree[i].add(arr[i]);
                tree[arr[i]].add(i);
            }
        }
        
        visited=new int[n];
        int[] parent=new int[n];
       TreeSet<Integer> temp=new TreeSet<Integer>();
        //HashMap<Integer,TreeSet<Integer>> map=new HashMap<Integer,TreeSet<Integer>>();
        for(int i=0;i<n;i++) {
            if(arr[i]==i) {
                parent[i]=i;
                temp.add(i);
                //map.put(i,new TreeSet<Integer>());
                mm.dfs1(tree, parent, visited, i);
            }
        }
        
        dsu ds=new dsu(n,parent);
        //System.out.println(temp.size());
        int  ans=0;
       // System.out.println(temp.size());
        for(int i: Set) {
            if(temp.size()>1) {
                int one=ds.find(i);
                int second=-1;
                if(temp.lower(one)!=null) {
                    second=temp.lower(one);
                    temp.remove(ds.union(one, second));
                    //System.out.println(i+" "+second);
                    arr[i]=second;
                    ans++;
                }
                else if(temp.higher(one)!=null){
                    second=temp.higher(one);
                    temp.remove(i);
                    //System.out.println(i+" "+second);
                    arr[i]=second;
                    ans++;
                }
                else {
                    //System.out.println("dd");
                    arr[i]=i;
                    ans++;
                }
            }
            else {
                ans++;
            }
        }
        for(int i=0;i<n;i++) {
            if(arr[i]==i && temp.size()>1 && !Set.contains(i)) {
                int one=ds.find(i);
                int second=-1;
                if(temp.lower(one)!=null) {
                    second=temp.lower(one);
                    temp.remove(i);
                    arr[i]=second;
                    ans++;
                }
                else if(temp.higher(one)!=null){
                    second=temp.higher(one);
                    temp.remove(i);
                    arr[i]=second;
                    ans++;
                }
            }
        }
        System.out.println(ans);
        for(int i=0;i<n;i++) {
            System.out.print((arr[i]+1)+" ");
        }
        
        
}
}
class dsu{
    int[] parent;
    int[] rank;
    dsu(int a,int[] parent){
        //parent=new int[a];
        rank=new int[a];
        for(int i=0;i<a;i++) {
            //parent[i]=i;
            rank[i]=0;
        }
        this.parent=parent;
    }
    public int find(int a) {
        int temp=a+0;
        while(parent[temp]!=temp) {
            temp=parent[temp];
        }
        parent[a]=temp;
        return temp;
    }
    public boolean istrue(int a,int b){
        if(find(a)!=find(b)) {
            return false;
        }
 
    else {
        return true;
    }
    }
    public int union(int a,int b) {
        int x=find(a);
        int y=find(b);
        if(x!=y) {
            if(rank[x]==rank[y]) {
                parent[x]=y;
                rank[y]+=1;
                return x;
            }
            else if(rank[x]>rank[y]) {
                parent[y]=x;
                return y;
            }
            else {
                parent[x]=y;
                return x;
            }
        }
        return x;
    }
}
class pair{
        int f;
        int s;
        pair(int f,int s){
            this.f=f;
            this.s=s;
        }
        
}
class a implements Comparator<pair>{
        public int compare(pair n1,pair n2) {
            return n1.s-n2.s;
        }
}

class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}