package main

import (
	"io"
	"os"
	"strconv"
)

var parent []int
var val []int
var mx1 []int
var mx2 []int
var cnt1 []int

func calc(v int) int {
	a := mx1[v]
	if a < 0 {
		return 0
	}
	b := mx2[v]
	if cnt1[v] >= 2 {
		b = a
	}
	if b+1 > a {
		return b + 1
	}
	return a
}

func insertChild(p, childVal int) {
	if childVal > mx1[p] {
		mx2[p] = mx1[p]
		mx1[p] = childVal
		cnt1[p] = 1
	} else if childVal == mx1[p] {
		cnt1[p]++
	} else if childVal > mx2[p] {
		mx2[p] = childVal
	}
}

func increaseChild(p, oldVal, newVal int) {
	if newVal == oldVal {
		return
	}
	oldMax := mx1[p]
	if oldVal == oldMax {
		if cnt1[p] > 1 {
			mx2[p] = oldMax
		}
		mx1[p] = newVal
		cnt1[p] = 1
	} else {
		if newVal > oldMax {
			mx2[p] = oldMax
			mx1[p] = newVal
			cnt1[p] = 1
		} else if newVal == oldMax {
			cnt1[p]++
		} else if newVal > mx2[p] {
			mx2[p] = newVal
		}
	}
}

func main() {
	data, _ := io.ReadAll(os.Stdin)
	idx := 0
	nextInt := func() int {
		for idx < len(data) && (data[idx] < '0' || data[idx] > '9') {
			idx++
		}
		x := 0
		for idx < len(data) && data[idx] >= '0' && data[idx] <= '9' {
			x = x*10 + int(data[idx]-'0')
			idx++
		}
		return x
	}

	n := nextInt()
	size := n + 2

	parent = make([]int, size)
	val = make([]int, size)
	mx1 = make([]int, size)
	mx2 = make([]int, size)
	cnt1 = make([]int, size)

	for i := 0; i < size; i++ {
		mx1[i] = -1
		mx2[i] = -1
	}

	out := make([]byte, 0, n*4)
	nextID := 2

	for step := 0; step < n; step++ {
		p := nextInt()
		x := nextID
		nextID++
		parent[x] = p

		insertChild(p, 0)

		if p != 1 {
			oldv := val[p]
			newv := calc(p)
			if newv > oldv {
				val[p] = newv
				child := p
				oldChild := oldv
				newChild := newv
				for {
					par := parent[child]
					if par == 0 {
						break
					}
					increaseChild(par, oldChild, newChild)
					if par == 1 {
						break
					}
					oldp := val[par]
					newp := calc(par)
					if newp == oldp {
						break
					}
					val[par] = newp
					child = par
					oldChild = oldp
					newChild = newp
				}
			}
		}

		ans := 0
		if mx1[1] >= 0 {
			ans = mx1[1] + 1
		}
		out = strconv.AppendInt(out, int64(ans), 10)
		if step+1 < n {
			out = append(out, ' ')
		}
	}

	out = append(out, '\n')
	os.Stdout.Write(out)
}