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## Problem Description

There are *N* boxes, indexed by a number from 1 to *N*. Each box may (or may not) be placed into other boxes. These boxes together form a tree structure, or a forest structure consisting of multiple independent trees.

You have to answer a series of queries of the following form: given a list of indices of the boxes, find the total number of boxes that the list of boxes actually contain.

For example, consider the following five boxes:

- If the query is the list "1", then the correct answer is "5", because box 1 contains all boxes.
- If the query is the list "4 5", then the correct answer is "2", for boxes 4 and 5 contain themselves and nothing else.
- If the query is the list "3 4", then the correct answer is "2".
- If the query is the list "2 3 4", then the correct answer is "4", since box 2 also contains box 5.
- If the query is the list "2", then the correct answer is "3", because box 2 contains itself and two other boxes.

## Limits

Subtask 1 (13%): 1 ≤ N ≤ 2000, 0 ≤ Q ≤ 2000, M = 1 for all queries.

Subtask 2 (22%): 1 ≤ N ≤ 2000, 0 ≤ Q ≤ 2000, Sum of M ≤ 2000000 for all testcases.

Subtask 3 (29%): 1 ≤ N ≤ 200000, 0 ≤ Q ≤ 200000, 1 ≤ M ≤ 2 for all queries.

Subtask 4 (36%): 1 ≤ N ≤ 200000, 0 ≤ Q ≤ 200000, Sum of M ≤ 2000000 for all testcases.

Subtask 5 (0%): Sample Testcase.

## Input

The first line of input will contain one integer *N*, the number of boxes.

The second line contains *N* integers. The *i ^{th}* integer is either the index of the box which contains the

*i*box, or

^{th}*0*if the

*i*box is not contained in any other box.

^{th}The third line contains an integer *Q*, the number of queries.

The following *Q* lines will have the following format: on each line, the first integer *M* is the length of the list of boxes in this query. Then, *M* space separated integers will follow on the same line, representing the indices of the boxes.

## Output

For each query, output a line which contains an integer representing the total number of boxes.

## Sample Testcase 1

### Input

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

### Output

5 2 2 4 3

### Credits

Task statement from 2016 ACM ICPC Asia Hong Kong Regional, sourced from Kattis. Testcases and subtasks are self-created.

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 13 | 9 | 1s | 256MB | Minimum |

2 | 22 | 38 | 1s | 256MB | Minimum |

3 | 29 | 22 | 1s | 256MB | Minimum |

4 | 36 | 64 | 1s | 256MB | Minimum |

5 | 0 | 1 | 1s | 256MB | Minimum |

### Judge Compile Command

g++ ans.cpp -o boxes_hkicpc -Wall -static -O2 -lm -m64 -s -w -std=gnu++14 -fmax-errors=512