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.
//package math_codet;

import java.io.*;
import java.util.*;
 /******************************************
*    AUTHOR:         AMAN KUMAR SINGH        *
*    INSTITUITION:   KALYANI GOVERNMENT ENGINEERING COLLEGE  *
******************************************/
public class lets_do {
    InputReader in;
    PrintWriter out;
    Helper_class h;
    final long mod=1000000007;
    final int N=200005;
    final int MAX_Ai=1000005;
    public static void main(String[] args) throws java.lang.Exception{
        new lets_do().run();
    }
    void run() throws Exception{
        in=new InputReader(System.in);
        out = new PrintWriter(System.out);
        h = new Helper_class();
        int t=1;
        while(t-->0)
            solve();
        out.flush();    
        out.close();
    }
    ArrayList<Integer>[] graph;
    boolean[] visited;
    int count=0;
    void dfs(int v){
        visited[v]=true;
        count++;
        for(int u: graph[v]){
            if(!visited[u])
                dfs(u);
        }
    }
    void solve(){
        int n=h.ni();
        graph=new ArrayList[n+1];
        int i=0;
        for(i=1;i<=n;i++)
        	graph[i]=new ArrayList();
        
        for(i=1;i<=n;i++){
            int x=h.ni();
            graph[x].add(i);
            graph[i].add(x);
        }
        visited=new boolean[n+1];
        long max[]=new long[n];
        int p=0;
        for(i=1;i<=n;i++){
            if(!visited[i]){
                count=0;
                dfs(i);
                max[p++]=count;
            }
        }
        if(p==1)
           h.pn(max[p-1]*max[p-1]);
        else{
            long max1[]=new long[p];
            for(i=0;i<p;i++)
                max1[i]=max[i];
            Arrays.sort(max1);
            long sum=0;
            for(i=0;i<p-2;i++)
                sum+=max1[i]*max1[i];
            sum+=(max1[p-1]+max1[p-2])*(max1[p-1]+max1[p-2]);
            h.pn(sum);
        }
    }
    class Helper_class{
        long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
        int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
        long gcd1(long a, long b){return (b==0)?a:gcd(b,a%b);}
        int bitcount(long n){return (n==0)?0:(1+bitcount(n&(n-1)));}
        void p(Object o){out.print(o);}
        void pn(Object o){out.println(o);}
        void pni(Object o){out.println(o);out.flush();}
        String n(){return in.next();}
        String nln(){return in.nextLine();}
        int ni(){return in.nextInt();}
        long nl(){return in.nextLong();}
        double nd(){return in.nextDouble();}

        long mul(long a,long b){
            if(a>=mod)a%=mod;
            if(b>=mod)b%=mod;
            a*=b;
            if(a>=mod)a%=mod;
            return a;
        }
        long modPow(long a, long p){
            long o = 1;
            while(p>0){
                if((p&1)==1)o = mul(o,a);
                a = mul(a,a);
                p>>=1;
            }
            return o;
        }
        long add(long a, long b){
            if(a>=mod)a%=mod;
            if(b>=mod)b%=mod;
            if(b<0)b+=mod;
            a+=b;
            if(a>=mod)a-=mod;
            return a;
        }
    }

    class InputReader{
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
 
        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int peek() {
            if (numChars == -1)
                return -1;
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar];
        }
 
        public void skip(int x) {
            while (x-- > 0)
                read();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public String nextString() {
            return next();
        }
 
        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
 
            return res.toString();
        }
 
        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r')
                    buf.appendCodePoint(c);
                c = read();
            }
            return buf.toString();
        }
 
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
 
        public boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1)
                read();
            return value != -1;
        }
 
        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}