== include(page="template/taskheader" task_id="christmas-balls") ==
Poveste şi cerinţă...
Christmas is coming, and Alessandro has to decorate his living room with a Christmas tree.
He heard that in Pordenone a new tree shop has just opened, so he decided to go there. This shop has a huge tree decorated with $N$ balls, one at each branching point (the root is node $0$). Of course the balls are quite spectacular, and he noticed that the balls come in $C$ different colors in total.
The peculiarity of this shop is that you can buy the whole tree, or cut a branch and buy just a subtree! You can make the cut just below a ball, so that you take that ball and the subtree rooted there.
Alessandro doesn't want just a random tree, he wants the nicest. His taste is in fact quite peculiar, he'd like that the amount of balls of each color to be well distributed. Precisely, let's call $x$ the number of balls of (one of) the most frequent color in a subtree, he wants to maximize the number of colors with $x$ balls each.
Help Alessandro finding where to cut the tree by printing the maximum amount of most-frequent colors he can get.
h2. Date de intrare
Fişierul de intrare $christmas-balls.in$ ...
The first line of the input file $christmas-balls.in$ contains the only integer $N$, $1 ≤ N ≤ 10^5$, the number of nodes of the tree.
The second line contains $N$ integers $C_i$ $0 ≤ C_i < N$, the colors of each ball.
The third line contains $N-1$ integers: $P_i$ (with $1 ≤ i < N$) is the index of the parent of the $i$-th node.
h2. Date de ieşire
În fişierul de ieşire $christmas-balls.out$ ...
The output file $christmas-balls.out$ contains a single line with an integer: chosen the optimal subtree, the number of colors with the highest frequency.
h2. Restricţii
h2. Restrictii
* $... ≤ ... ≤ ...$
* For tests worth $13$ points, the tree is a line.
* For tests worth $15$ more points, $1 ≤ N ≤ 1000$, $1 ≤ MAXC ≤ 2$.
* For tests worth $21$ more points, $1 ≤ N ≤ 1000$.
* For tests worth $17$ more points, $1 ≤ MAXC ≤ 2$.
* The scores obtained now may be different compared to the ones from the original contest
h2. Exemplu
table(example). |_. christmas-balls.in |_. christmas-balls.out |
| This is some
text written on
multiple lines.
| This is another
text written on
multiple lines.
| 8
1 2 0 2 0 0 1 1
0 0 1 1 3 4 4
| 3
|
table(example). |_. christmas-balls.in |_. christmas-balls.out |
| 5
0 1 1 0 0
0 1 2 3
| 2
|
h3. Explicaţie
...
In the first sample case, there are $8$ nodes in $3$ different colors. The solution is to cut the tree and take the subtree rooted at node $1$. This way we are left with $6$ nodes: the most frequent color has $2$ balls, and there are $3$ colors with that many balls.
If, for example, we have kept the entire tree, the most frequent color appears with $3$ balls, but there are only $2$ colors with $3$ balls, so this is worse than the aforementioned solution.
In the second sample case the tree forms a line with $5$ nodes. The optimal solution is to cut the subtree rooted at node $1$. The most frequent color appears with $2$ balls, and there are $2$ colors with that many balls.
== include(page="template/taskfooter" task_id="christmas-balls") ==
