Background

Mirko and Slavko like playing marbles. On an exciting Friday, Mirko invented a marble game and wanted to show it to Slavko.

In the game, Mirko builds a directed graph where each vertex has outdegree at most $1$. Then he places a marble on one vertex. As long as the marble is at some vertex $X$, it moves to the adjacent vertex connected by the outgoing edge (if there is no such edge, it stays). The marble keeps moving until it reaches a vertex with outdegree $0$. It is also possible that the marble travels around the graph forever because there is no vertex with outdegree $0$. To make sure Slavko understands the rules, Mirko asks a series of queries.

The query types are:

1. 1 X: Unless the marble gets stuck in a cycle, find the index of the final stopping vertex after placing the marble at $X$.

2. 2 X: Delete the outgoing edge of vertex $X$. (It is guaranteed to exist.)

Note that the queries are ordered.

Problem Description

You are given a directed graph where each vertex has outdegree $0$ or $1$.

There are the following queries:

1. 1 X: Given the marble start vertex $X$, find where the marble stops.

2. 2 X: Delete the outgoing edge of vertex $X$. (It is guaranteed to exist.)

Marble movement rules:

Starting from the initial vertex, follow outgoing edges until reaching a vertex whose outdegree is $0$.

Input Format

The first line contains a positive integer $n$, the number of vertices in the graph.

The second line contains $n$ positive integers. The $i$-th number is the index of the vertex that the outgoing edge of $i$ points to; if it is $0$, then the edge does not exist.

The next line contains a positive integer $Q$, the number of queries.

The next $Q$ lines each contain one query in one of the formats above.

Output Format

For each query of type $1$, output the index of the vertex where the marble stops, in order, one per line.

If the marble never stops, output CIKLUS.

3
2 3 1
7
1 1
1 2
2 1
1 2
1 1
2 2
1 2

CIKLUS
CIKLUS
1
1
2

5
0 3 5 3 4
6
1 1
1 2
2 4
1 2
2 3
1 2

1
CIKLUS
4
3

Hint

Constraints

For $100\%$ of the testdata, $1 \le n,Q \le 3 \times 10^5$.

Notes

This problem is worth $120$ points.

Translated from COCI2010-2011 CONTEST #7 T5 KUGLICE。

Translated by ChatGPT 5