```go
package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
)

type FastScanner struct {
	r *bufio.Reader
}

func NewFastScanner() *FastScanner {
	return &FastScanner{r: bufio.NewReaderSize(os.Stdin, 1<<20)}
}

func (fs *FastScanner) NextInt() int {
	sign, val := 1, 0
	c, _ := fs.r.ReadByte()
	for (c < '0' || c > '9') && c != '-' {
		c, _ = fs.r.ReadByte()
	}
	if c == '-' {
		sign = -1
		c, _ = fs.r.ReadByte()
	}
	for c >= '0' && c <= '9' {
		val = val*10 + int(c-'0')
		c, _ = fs.r.ReadByte()
	}
	fs.r.UnreadByte()
	return sign * val
}

func main() {
	in := NewFastScanner()
	n := in.NextInt()
	p := make([]int, n+1)
	for i := 1; i <= n; i++ {
		p[i] = in.NextInt()
	}

	vis := make([]bool, n+1)
	var cycles []int64

	for i := 1; i <= n; i++ {
		if !vis[i] {
			cnt := int64(0)
			x := i
			for !vis[x] {
				vis[x] = true
				cnt++
				x = p[x]
			}
			cycles = append(cycles, cnt)
		}
	}

	var ans int64
	for _, v := range cycles {
		ans += v * v
	}

	if len(cycles) >= 2 {
		sort.Slice(cycles, func(i, j int) bool {
			return cycles[i] > cycles[j]
		})
		a, b := cycles[0], cycles[1]
		ans = ans - a*a - b*b + (a+b)*(a+b)
	}

	fmt.Print(ans)
}
```