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.util.*;
import java.io.*;
	import java.lang.*;
	
	public class graph1
	{
		public static int n;
		public static ArrayList<Integer> adj[];
		public static ArrayList<Integer> child[];
		public static boolean[] vis;
		public static int[] par;
		public static int[] level;
		public static int[] set;
		public static int[] a;
		public static int[] ans;
		public static int count;
		
		
		
		public static void main(String[] args)
		{
			InputReader in = new InputReader(System.in);
			PrintWriter pw = new PrintWriter(System.out);
	
	//		n = in.nextInt();
			int n = in.nextInt();
			
			
			a = new int[n+1];
			HashMap<Integer, Integer> map = new HashMap<>();
			for(int i=1; i<=n; i++) {
				a[i] = in.nextInt();
				map.put(a[i], i);
	
			}
			
			//children = new ArrayList[n+1];
			vis = new boolean[n+1];
			par = new int[n+1];
			set = new int[n+1];
			for(int i=0; i<=n; i++)
			{
				vis [i] = false;
				par[i] = -1;
			}
			
			
			
	/*		for(int i=0;i<=n;i++)
			{
				adj[i] = new ArrayList<Integer>();
			}
	
			for(int i=0; i<m; i++)
			{
				int v = in.nextInt();
				int u = in.nextInt();
				adj[v].add(u);
				adj[u].add(v);
				
			}
		*/
			
			count = 0;
			for(int i=1; i<=n; i++)
			{
				if(!vis[i])
				{
					fun(i);
					count++;
				}
				
			}
			
			ArrayList<Integer>[] list = new ArrayList[count];
			for(int i=0; i<count; i++)
				list[i] = new ArrayList<>();
			
			
			for(int i=1; i<=n; i++)
			{
				list[set[i]].add(i);
			}
			
			Arrays.sort(list, new Comparator<ArrayList<Integer>>() {

				public int compare(ArrayList<Integer> o1, ArrayList<Integer> o2) {
					// TODO Auto-generated method stub
					return o1.size()<o2.size()?1:-1;
				}
			});
				
			//for(int i=0; i<count; i++)
				//pw.println(list[i]);
			
			
			/*a[map.get(list[0].get(0))] = (list[1].get(0));
			a[map.get(list[1].get(0))] = (list[0].get(0));
			
			for(int i=1; i<=n; i++)
				pw.print(a[i]+" ");
			*/
			long ans = 0;
			for(int i=2; i<count; i++)
			{
				ans += (list[i].size()) * (long)list[i].size();
			}
			if(count>=2)
			ans += (long)(list[0].size()+(long)list[1].size())*(long)((long)list[0].size()+list[1].size());
			else
				ans += (long)list[0].size() * (long)list[0].size();
			
			pw.println(ans);
			
			//code ends....
			pw.flush();
			pw.close();
		}
		
		
		
		
		
		/*public static void bfs(int x)
		{
			Queue<Integer> queue = new LinkedList<>();
			queue.add(x);
			//level[x] = 1;
			
			//parent[x] = 0;
			vis[x] = true;
			while(!queue.isEmpty())
			{
				int last = queue.poll();
				for(int p : adj[last])
				{
					if(!vis[p])
					{
							//	children[last].add(a);
						queue.add(p);
					//	System.out.println(p+" ");
						
						vis[p] = true;
					//	parent[a] = last;
						//level[a] = level[last]+1;
						
					}
				}
			}
		}
		*/
		
		public static void fun(int s)
		{
			
			if(vis[s])
				return;
			set[s] = count;
			vis[s] = true;
			fun(a[s]);
			
		}
		
		/*

		public static boolean dfs(int s)
		{
			Stack<Integer> stk = new Stack<>();
	 		stk.add(s);
			par[s] = 0;
			vis[s] = true;
			while(!stk.isEmpty())
			{
				int last = stk.pop();
			///	System.out.println(last);
				boolean f = false;
				for(int a : adj[last])
				{
					if(!vis[a])
					{
						//child[last].add(a);
						stk.add(a);
						par[a] = last;
						level[a] = level[last] +1;
						vis[a] = true;
					}
				}
			
			}
			return flag;
		}
				
	
		
		public static void dfsrec(int s)
		{
			if(vis[s])
				return;
			
			vis[s] = true;
			int k = 0;
			for(int p: adj[s])
			{
				boolean f2 = false;
				if(!vis[p])
				{
					k++;
					dfsrec(p);
				}
				
			}
			par[s] = k;
			
		}
		
		*/
		public static int find(int i) {
			
			
			if(par[i]==-1)
				return i;
			else
				return find(par[i]);
				
		}
		
		 public static void union( int x, int y)
		    {
		        int xset = find( x);
		        int yset = find(y);
		        par[xset] = yset;
		    }

		
		
		 public static boolean cycle(HashSet<pair> set) {
			 
			 
			 for(pair p: set)
			 {
				 int x = find(p.x);
				 int y = find(p.y);
				 if(x==y)
					 return true;
		
				 union(x, y);
				 
			 }
			 
			 return false;
		 }
		
		
		
		
		
		
		static class pair implements Comparable<pair>
		 
		{
			Integer x, y;
			pair(int x,int y)
			{
		
				this.x=x;
				this.y=y;
			}
			
			public int compareTo(pair o) {
				int result = x.compareTo(o.x);
				if(result==0)
					result = y.compareTo(o.y);
				
				return result;
			}  
			
			public String toString()
			{
				return x+" "+y;
			}
			
			public boolean equals(Object o)
			{
				if (o instanceof pair)
			    {
					pair p = (pair)o;
					return p.x == x && p.y == y ;
				}
				return false;
			}
			
			public int hashCode()
			{
				return new Long(x).hashCode()*31 + new Long(y).hashCode();
			}
		}
	
	
		static class triplet implements Comparable<triplet>
		{
			Integer x,y,z;
			triplet(int x,int y,int z)
			{
				this.x = x;
				this.y = y;
				this.z = z;
			}
			
			public  int compareTo(triplet o)
			{
				int result = x.compareTo(o.x);
				if(result==0)
					result =  y.compareTo(o.y);
				if(result==0)
					result = z.compareTo(o.z);
	
				return result;
			}
			
			public boolean equlas(Object o)
			{
				if(o instanceof triplet)
				{
					triplet p = (triplet)o;
					return x==p.x && y==p.y && z==p.z;
				}
				return false;
			}
			
			public String toString()
			{
				return x+" "+y+" "+z;
			}
			public int hashCode()
			{
				return new Long(x).hashCode()*31 + new Long(y).hashCode() + new Long(z).hashCode(); 
			}
		}
		
	
		
		
		
		static class InputReader 
		{
			 
			private final InputStream stream;
			private final byte[] buf = new byte[8192];
			private int curChar, snumChars;
			private SpaceCharFilter filter;
	 
			public InputReader(InputStream stream) 
			{
				this.stream = stream;
			}
	 
			public int snext() 
			{
				if (snumChars == -1)
					throw new InputMismatchException();
				if (curChar >= snumChars) 
				{
					curChar = 0;
					try 
					{
						snumChars = stream.read(buf);
					} 
					catch (IOException e) 
					{
						throw new InputMismatchException();
					}
					if (snumChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}
	 
			public int nextInt() 
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				int sgn = 1;
				if (c == '-')
			    {
					sgn = -1;
					c = snext();
				}
				int res = 0;
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public long nextLong()
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				int sgn = 1;
				if (c == '-') 
				{
					sgn = -1;
					c = snext();
				}
				long res = 0;
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public int[] nextIntArray(int n) 
			{
				int a[] = new int[n];
				for (int i = 0; i < n; i++) 
				{
					a[i] = nextInt();
				}
				return a;
			}
	 
			public String readString()
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = snext();
				} while (!isSpaceChar(c));
				return res.toString();
			}
	 
			public String nextLine() 
			{
				int c = snext();
				while (isSpaceChar(c))
					c = snext();
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = snext();
				} while (!isEndOfLine(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;
			}
	 
			private boolean isEndOfLine(int c) 
			{
				return c == '\n' || c == '\r' || c == -1;
			}
	 
			public interface SpaceCharFilter
		    {
				public boolean isSpaceChar(int ch);
			}
		}
		
		public static long mod = 1000000007;
		public static int d;
		public static int p;
		public static int q;
		
		public static int[] suffle(int[] a,Random gen)
		{
			int n = a.length;
			for(int i=0;i<n;i++)
			{
				int ind = gen.nextInt(n-i)+i;
				int temp = a[ind];
				a[ind] = a[i];
				a[i] = temp;
			}
			return a;
		}
		
		public static void swap(int a, int b){
			int temp = a;
			a = b;
			b = temp;
		}
		
		public static HashSet<Integer> primeFactorization(int n)
		{
			HashSet<Integer> a =new HashSet<Integer>();
			for(int i=2;i*i<=n;i++)
			{
				while(n%i==0)
				{
					a.add(i);
					n/=i;
				}
			}
			if(n!=1)
				a.add(n);
			return a;
		}
		
		public static void sieve(boolean[] isPrime,int n)
		{
			for(int i=1;i<n;i++)
				isPrime[i] = true;
			
			isPrime[0] = false;
			isPrime[1] = false;
			
			for(int i=2;i*i<n;i++)
			{
				if(isPrime[i] == true)
				{
					for(int j=(2*i);j<n;j+=i)
						isPrime[j] = false;
				}
			}
		}
		
		public static int GCD(int a,int b)
		{
			if(b==0)
				return a;
			else
				return GCD(b,a%b);
		}
		
		public static long GCD(long a,long b)
		{
			if(b==0)
				return a;
			else
				return GCD(b,a%b);
		}
		
		public static void extendedEuclid(int A,int B)
		{
			if(B==0)
			{
				d = A;
				p = 1 ;
				q = 0;
			}
			else
			{
				extendedEuclid(B, A%B);
				int temp = p;
				p = q;
				q = temp - (A/B)*q;
			}
		}
		
		public static long LCM(long a,long b)
		{
			return (a*b)/GCD(a,b);
		}
		
		public static int LCM(int a,int b)
		{
			return (a*b)/GCD(a,b);
		}
		
		public static int binaryExponentiation(int x,int n)
		{
		    int result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=result * x;
		        x=x*x;
		        n=n/2;
		    }
		    return result;
		}
		
		public static long binaryExponentiation(long x,long n)
		{
		    long result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=result * x;
		        x=x*x;
		        n=n/2;
		    }
		    return result;
		}
		
		public static int modularExponentiation(int x,int n,int M)
		{
		    int result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=(result * x)%M;
		        x=(x*x)%M;
		        n=n/2;
		    }
		    return result;
		}
		
		public static long modularExponentiation(long x,long n,long M)
		{
		    long result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=(result * x)%M;
		        x=(x*x)%M;
		        n=n/2;
		    }
		    return result;
		}
		
		public static int modInverse(int A,int M)
		{
		    return modularExponentiation(A,M-2,M);
		}
		
		public static long modInverse(long A,long M)
		{
		    return modularExponentiation(A,M-2,M);
		}
		
		
		
		
		
		public static boolean isPrime(int n)
		{
		    
		    if (n <= 1)  return false;
		    if (n <= 3)  return true;
		    
		    if (n%2 == 0 || n%3 == 0) 
		    	return false;
		 
		    for (int i=5; i*i<=n; i=i+6)
		    {
		        if (n%i == 0 || n%(i+2) == 0)
		           return false;
		    }
		    
		    return true;
		}
		
		
	}