Rar the Cat$^($™$^)$ is the founder of ACM (Association of Cats and Magical Lights).
This is the story of the founding of ACM.
It is the second half of the year again and Rar the
Cat$^($™$^)$ is looking forward to Christmas.
When people think of Christmas, Christmas trees will surely
come into the picture. This year, Rar the Cat$^($™$^)$ decides to decorate a Christmas
tree with $N$ LED lights
with up to 100 different colours. Each LED light can only have
a single colour as Rar the Cat$^($™$^)$ is too poor to afford more
sophisticated models of LED lights.
Being a programmer himself, Rar the Cat$^($™$^)$ LED lights are arranged in a tree
formation on the Christmas tree. That being said, each LED
light can be represented as a node and the wires between
$2$ LED lights can be
represented as an edge. The whole formation consists of
$N$ nodes fully connected
by $N1$ edges. The nodes
are labelled from $1$ to
$N$ and each node can hold
colour denoted as $1$ to
$100$. It is noted that
each LED is connected to every other LED directly or indirectly
by wires and the tree formed is rooted at node $1$.
Hubert the Cow finds that Rar the Cat$^($™$^)$ Christmas tree is too boring
because it lacks some magical colours. A magical colour in a
subtree is defined as a colour whereby there is an odd number
of LEDs with that particular colour within the subtree
only.
In the tree to the right, the subtree of node
$1$ has
$3$ white nodes and
$4$ black nodes. As such, white is a
magical colour for the subtree of node
$1$. However, the subtree of node
$3$ has
$1$ white node and
$1$ black node, thus the number of
magical colour of the subtree of node
$3$ is
$2$. In addition, all leaf nodes of
the tree have
$1$ magical
colour by definition.
In order to improve on his Christmas tree decorations, Rar
the Cat$^($™$^)$ intends to modify the colours of
the LED lights on the tree. However, he does not know how to
count how many magical colours there are.
Your task, is now to answer how many magical colours there
are in a subtree requested by Rar the Cat$^($™$^)$. This will be done in between Rar
the Cat$^($™$^)$ modifications. There will be
$Q$ queries and
modifications in total.
Soon after this, Rar the Cat$^($™$^)$ Christmas tree with these magical
lights become so popular and Rar the Cat$^($™$^)$ founded ACM to further spread the adoption of such
trees worldwide.
Input
The first line will consists of $2$ integers, $N$ and $Q$. $N$ will be positive and not more than
$300\, 000$ while
$Q$ will be positive and
not more than $1\, 000\,
000$.
$N$ integers will
follow on the next line. The $i^{th}$ integer will be $C_ i$. $C_ i$ denotes the colour of node
$i$ and can only range
from $1$ to $100$ inclusive.
The next line will have $N1$ integers. The $i^{th}$ integer will be $P_{i+1}$, $P_{i+1}$ denotes the parent node of
node $i+1$.
$Q$ lines will then
follow with $2$ integers
each, $K$ followed by
$X$. If $K$ is $0$, then this line represents a query
for how many magical colours are there in the subtree of node
$X$. If $K$ is an integer between $1$ and $100$, then it means that the colour
of node $X$ is changed to
colour $K$.
Output
For each query when $K =
0$, output in one line: the number of magical colours in
the subtree of $X$
(inclusive).
Sample Input 1 
Sample Output 1 
10 5
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9
0 1
0 4
1 4
0 1
0 4

10
7
8
7

Sample Input 2 
Sample Output 2 
7 7
1 2 2 1 1 2 1
1 1 1 2 2 3
0 1
0 2
0 3
0 4
0 5
0 6
0 7

1
1
2
1
1
1
1
