The "Dormi's Fone Service" is now the only telephone service provider in CCOland. There are $N$ houses in CCOland, numbered from $1$ to $N$. Each telephone line connects two distinct houses such that all the telephone lines that ever exist form a forest.

There is an issue where the phone lines are faulty, and each phone line only exists for a single interval of time. Two houses can call each other at a certain time if there is a path of phone lines that starts at one of the houses and ends in the other house at that time.

We would like to process $Q$ queries of the following forms:

• 1 x y: Add a phone line between houses $x$ and $y$. It is guaranteed that a phone line between houses $x$ and $y$ was never added before.
• 2 x y: Remove the phone line between houses $x$ and $y$. It is guaranteed that a phone line currently exists between houses $x$ and $y$.
• 3 t: Compute the number of pairs of different houses that can call each other at some time between the current query and $t$ queries ago. To be more clear, let $G_q$ be the state of CCOland after the $q$-th query, where $G_0$ is the state of CCOland before any queries. If this is the $s$-th query, then count the number of pairs of houses that are connected in at least one of $G_{s-t},G_{s-t+1},\dots ,G_s$.

Also, some test cases may be encrypted. For the test cases that are encrypted, the arguments $x$, $y$, or $t$ are given as the bitwise xor of the true argument and the answer to the last query of type 3 (if there have been no queries of type 3, then the arguments are unchanged).

Input Specification

The first line of input will contain $E$ $(E\in \{0,1\})$. $E=0$ denotes that the input is not encrypted, while $E=1$ denotes that the input is encrypted.

The second line contains two space-separated integers $N$ and $Q$, representing the number of houses in CCOland and the number of queries, respectively.

The next $Q$ lines contain queries as specified above (queries are encrypted or not depending on $E$).

For the $q$-th query $(1\le q\le N)$, it is guaranteed that (after decrypting if $E=1$) $1\le x,y\le N$ for type 1 and 2 queries and $0\le t\le q$ for type 3 queries.

Output Specification

For each query of type 3, output the answer to the query on a new line.

Sample Input 1

0
4 12
3 0
1 1 2
3 0
1 1 3
3 0
3 5
2 2 1
3 0
3 8
1 1 4
3 0
3 11

Sample Output 1

0
1
3
3
1
3
3
5

Explanation of Output for Sample Input 1

This test case is not encrypted.

For the $1^{\text{st}}$ query, no pairs of different houses could have called each other.

For the $3^{\text{rd}}$ query, only houses $1$ and $2$ could have called each other.

For the $5^{\text{th}}$ query, $(1,2),(1,3),(2,3)$ is the set of pairs that could have called each other.

The $6^{\text{th}}$ query is the same.

For the $8^{\text{th}}$ query, only houses $1$ and $3$ could have called each other.

For the $9^{\text{th}}$ query, there is a point in time where $(1,2),(1,3),(2,3)$ could have called each other.

For the ${11}^{\text{th}}$ query, the set of pairs that could have called each other is $(1,3),(1,4),(3,4)$.

For the ${12}^{\text{th}}$ query, the set of pairs that could have called each other at any previous time is $(1,2),(1,3),(1,4),(2,3),(3,4)$.

Explanation of Output for Sample Input 2

Encrypted version of sample 1.

Sample Input 2

1
4 12
3 0
1 1 2
3 0
1 0 2
3 1
3 6
2 1 2
3 3
3 9
1 2 7
3 3
3 8

Sample Output 2

0
1
3
3
1
3
3
5

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