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.util.*; import java.io.*; import java.math.*;
public class Main{
	static void solve(){//Here is the main function
      int N = nextInt();
      Node[] list = new Node[N];
      UnionFind uf = new UnionFind(N);
      for(int i = 0; i < N; i++){
        list[i] = new Node(i);
      }
      int count = 0;
      ArrayList<Integer> root = new ArrayList<>();
      for(int i = 0; i < N; i++){
        int p = nextInt() - 1;
        if(i != p && uf.isSame(p, i)){
          list[i].parent = i;
        }else{
          uf.doUnion(i, p);
          list[i].parent = p;
          if(i == p){
            root.add(i);
          }
        }
      }
      int r = -1;
      if(root.size() > 0){
        r = root.get(0);
      }
      for(int i = 0; i < N; i++){
        if(list[i].parent == i){
          if(r == -1){
            r = i;
            count++;
          }else{
            if(r != i){
              list[i].parent = r;
              count++;
            }
          }
        }
      }
      myout(count);
      String[] output = new String[N];
      for(int i = 0; i < N; i++){
        output[i] = String.valueOf(list[i].parent + 1);
      }
      myout(myconv(output, 8));
	}
	//Method addition frame start

static class Node{
  int no;
  int parent = -1;
  Node(int no){
    this.no = no;
  }
}

static class UnionFind{
        int[] list;
        int group;
        UnionFind(int size){
                list = new int[size];
                Arrays.fill(list, -1);
                group = size;
        }
        boolean isSame(int L, int R){
                return getRootIndex(L) == getRootIndex(R);
        }
        int getRootIndex(int index){
                if(list[index] < 0){
                        return index;
                }else{
                        list[index] = getRootIndex(list[index]);
                        return list[index];
                }
        }
        void doUnion(int L, int R){
                int Lroot = getRootIndex(L);
                int Rroot = getRootIndex(R);
                if(Lroot != Rroot){
                        group--;
                        if(getSize(Lroot) >= getSize(Rroot)){
                                int tmp = Lroot;
                                Lroot = Rroot;
                                Rroot = tmp;
                        }
                        list[Lroot] += list[Rroot];
                        list[Rroot] = Lroot;
                }
        }
        int getSize(int index){
                return -list[getRootIndex(index)];
        }
        int getGroupCount(){
                return group;
        }
        boolean isRoot(int index){
                return getRootIndex(index) == index;
        }
}
  
	//Method addition frame end

	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.addAll(Arrays.asList(read.split(" ")));
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<>();
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static double nextDouble(){return Double.parseDouble(next());}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<String> nextStrArray(int size){
		ArrayList<String> ret = new ArrayList<>(size);
		for(int i = 0; i < size; i++){
			ret.add(next());
		}
		return ret;
	}
	static ArrayList<Integer> nextIntArray(int size){
		ArrayList<Integer> ret = new ArrayList<>(size);
		for(int i = 0; i < size; i++){
			ret.add(Integer.parseInt(next()));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(int size){
		ArrayList<Long> ret = new ArrayList<>(size);
		for(int i = 0; i < size; i++){
			ret.add(Long.parseLong(next()));
		}
		return ret;
	}
	@SuppressWarnings("unchecked")
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		solve();flush();
	}
	//Don't have to see. end------------------------------------------
}