h2. Date de intrare

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 first line of the input file $christmasballs.in$ contains the only integer $N$ ($1 \le N \le 10^5$), the number of nodes of the tree.

The second line contains $N$ integers $C_i$ $0 &le; C_i < N$, the colors of each ball.

The second line contains $N$ integers $C_i$ ($0 &le; C_i < N$), the colors of each ball.

The third line contains $N-1$ integers: $P_i$ (with $1 &le; i < N$) is the index of the parent of the $i$-th node.

h2. Date de ieşire

For tests worth $13$ points, the tree is a line.

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.

For tests worth $15$ more points, ($1 ≤ N ≤ 1000$), ($1 ≤ MAXC ≤ 2$).
 
For tests worth $21$ more points, ($1 ≤ N ≤ 1000$).

h2. Restrictii

For tests worth $17$ more points, ($1 ≤ MAXC ≤ 2$).

* 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. Date de ieşire
 
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. Exemplu

table(example). |_. christmas-balls.in |_. christmas-balls.out |

table(example). |_. christmasballs.in |_. christmasballs.out |

| 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 |

table(example). |_. christmasballs.in |_. christmasballs.out |

| 5
0 1 1 0 0
0 1 2 3