The construction of subway in Bertown is almost finished! The President of Berland will visit this city soon to look at the new subway himself.

There are n stations in the subway. It was built according to the Bertown Transport Law:

  1. For each station i there exists exactly one train that goes from this station. Its destination station is pi, possibly pi = i; 
  2. For each station i there exists exactly one station j such that pj = i. 



The President will consider the convenience of subway after visiting it. The convenience is the number of ordered pairs (x, y) such that person can start at station x and, after taking some subway trains (possibly zero), arrive at station y (1 ≤ x, y ≤ n).

The mayor of Bertown thinks that if the subway is not convenient enough, then the President might consider installing a new mayor (and, of course, the current mayor doesn't want it to happen). Before President visits the city mayor has enough time to rebuild some paths of subway, thus changing the values of pi for not more than two subway stations. Of course, breaking the Bertown Transport Law is really bad, so the subway must be built according to the Law even after changes.

The mayor wants to do these changes in such a way that the convenience of the subway is maximized. Help him to calculate the maximum possible convenience he can get! 

Input

The first line contains one integer number n (1 ≤ n ≤ 100000) — the number of stations.

The second line contains n integer numbers p1, p2, ..., pn (1 ≤ pi ≤ n) — the current structure of the subway. All these numbers are distinct.

Output

Print one number — the maximum possible value of convenience.

Examples

Input

3
2 1 3


Output

9


Input

5
1 5 4 3 2


Output

17

Note

In the first example the mayor can change p2 to 3 and p3 to 1, so there will be 9 pairs: (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3).

In the second example the mayor can change p2 to 4 and p3 to 5.
	import java.io.BufferedWriter;
	import java.io.IOException;
	import java.io.InputStream;
	import java.io.OutputStream;
	import java.io.OutputStreamWriter;
	import java.io.PrintWriter;
	import java.io.Writer;
	import java.util.Arrays;
	import java.util.InputMismatchException;
	import java.util.*;
	import java.io.*;
	import java.math.*;
	public class Main5{

	static class Pair
		{ 
			long x; 
			int y;
			public Pair(long x, int y) 
			{	 
				this.x = x; 
				this.y = y; 
			}	 
		} 
		static class Compare
		{ 
			static void compare(Pair arr[], int n) 
			{ 
				// Comparator to sort the pair according to second element 
				Arrays.sort(arr, new Comparator<Pair>() { 
					@Override public int compare(Pair p1, Pair p2) 
					{ 
						if(p1.x>p2.x)
						{
							return 1;
						}
						else if(p2.x>p1.x)
						{
							return -1;
						}
						else
						{
							if(p1.y>p2.y)
							{
								return 1;
							}
							else if(p1.y<p2.y)
							{
								return -1;
							}
							else
								return 0;
						} 
					} 
				}); 
			} 
		}
		public static long pow(long a, long b)
		{
			long result=1;
			while(b>0)
			{
				if (b % 2 != 0)
				{
					result=(result*a);
					b--;
				} 
				a=(a*a);
				b /= 2;
			}   
			return result;
		}
		public static long fact(long num)
		{
					long value=1;
					int i=0;
					for(i=2;i<num;i++)
					{
						value=((value%mod)*i%mod)%mod;
					}
					return value;
				}
				public static long gcd(long a, long b)
				{
					if (a == 0)
						return b;
					return gcd(b%a, a);
				}
				
				public static long lcm(int a,int b)
				{
					return a * (b / gcd(a, b));
				}
				public static long sum(int h)
				{
					return (h*(h+1)/2);
				}
				public static void dfs(int parent,boolean[] visited)
				{
					ArrayList<Integer> arr=new ArrayList<Integer>();
					arr=graph.get(parent);
					visited[parent]=true;
					
					for(int i=0;i<arr.size();i++)
					{
						int num=arr.get(i);
						if(visited[num]==false)
						{
							dfs(num,visited);
						}
					}
					count++;
					
				}
				static int edges=0,count=0;
				static TreeSet<Integer> ts;
				static int f=0;
				static long mod=1000000007L;
				static ArrayList<ArrayList<Integer>> graph;
				static int[] color;
				public static void bfs(int num,boolean[] visited)
				{
					Queue<Integer> q=new LinkedList<>();
					q.add(num);
					visited[num]=true;
					while(!q.isEmpty())
					{
						int x=q.poll();
						ArrayList<Integer> al=graph.get(x);
						for(int i=0;i<al.size();i++)
						{
							int y=al.get(i);
							if(visited[y]==false)
							{
								q.add(y);
								visited[y]=true;
							}
						}
					}
				}
							  
				
				
				public static void main(String args[])throws IOException
				{
				//	InputReader in=new InputReader(System.in);
				//	OutputWriter out=new OutputWriter(System.out);
				//	long a=pow(26,1000000005);
				    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
					ArrayList<Integer> ar=new ArrayList<>();
					ArrayList<Integer> ar1=new ArrayList<>();
					ArrayList<Integer> ar2=new ArrayList<>();
					ArrayList<Integer> ar3=new ArrayList<>();
					ArrayList<Integer> ar4=new ArrayList<>();
					TreeSet<Integer> ts1=new TreeSet<>();
					TreeSet<String> pre=new TreeSet<>();
					HashMap<Long,Long> hash=new HashMap<>();
					//HashMap<Long,Integer> hash1=new HashMap<Long,Integer>();
					HashMap<Long,Integer> hash2=new HashMap<Long,Integer>();
				/*	boolean[] prime=new boolean[10001];
					for(int i=2;i*i<=10000;i++)
					{
						if(prime[i]==false)
						{
							for(int j=2*i;j<=10000;j+=i)
							{
								prime[j]=true;
								
							}
						}
					}*/
					int n=i();
					int[] a=new int[n];
					int[] b=new int[n];
					graph=new ArrayList<>();
					for(int i=0;i<n;i++)
					{
						graph.add(new ArrayList<>());
					}
					for(int i=0;i<n;i++)
					{
						a[i]=i()-1;
						graph.get(i).add(a[i]);
						graph.get(a[i]).add(i);
					}
			//		pln(graph+"");
					boolean[] visited=new boolean[n];
					int flag=0;
					PriorityQueue<Integer> pq=new PriorityQueue<>(Collections.reverseOrder());
					for(int i=0;i<n;i++)
					{
						if(visited[i]==false)
						{	
							dfs(i,visited);
							pq.add(count);
							count=0;
						}
					}
					long ans=0;
				//	pln(pq+"");
					if(pq.size()>1)
					{
						int num=pq.poll();
						int num1=pq.poll();
						ans+=(long)(num+num1)*(long)(num+num1);
						while(pq.size()>0)
						{
							int num3=pq.poll();
							ans+=num3*(long)num3;
						}
					}
					else
					{
						ans=pq.poll();
						ans=ans*ans;
					}
					pln(ans+"");
				}
	
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				/**/
				static InputReader in=new InputReader(System.in);
					static OutputWriter out=new OutputWriter(System.out);
					public static long l()
					{
						String s=in.String();
						return Long.parseLong(s);
					}
					public static void pln(String value)
					{
						System.out.println(value);
					}
					public static int i()
					{
						return in.Int();
					}
					public static String s()
					{
						return in.String();
					}
		}
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			class InputReader {
				 
				private InputStream stream;
				private byte[] buf = new byte[1024];
				private int curChar;
				private int numChars;
				private 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 Int() {
					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 String String() {
					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) {
					if (filter != null)
						return filter.isSpaceChar(c);
					return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
				}
			 
				public String next() {
					return String();
				}
			 
				public interface SpaceCharFilter {
					public boolean isSpaceChar(int ch);
				}
			}
			 
			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(Object...objects) {
					for (int i = 0; i < objects.length; i++) {
						if (i != 0)
							writer.print(' ');
						writer.print(objects[i]);
					}
				}
			 
				public void printLine(Object...objects) {
					print(objects);
					writer.println();
				}
			 
				public void close() {
					writer.close();
				}
			 
				public void flush() {
					writer.flush();
				}
			 
				}
			 
				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.Int();
					return array;
				}
			 
				} 