## IOI '15 P5 - Sorting (Standard I/O)

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Points: 25 (partial)
Time limit: 4.0s
Memory limit: 256M

Problem type

Aizhan has a sequence of integers . The sequence consists of distinct numbers from to . She is trying to sort this sequence in ascending order by swapping some pairs of elements. Her friend Ermek is also going to swap some pairs of elements — not necessarily in a helpful way.

Ermek and Aizhan are going to modify the sequence in a series of rounds. In each round, first Ermek makes a swap and then Aizhan makes another swap. More precisely, the person making a swap chooses two valid indices and swaps the elements at those indices. Note that the two indices do not have to be distinct. If they are equal, the current person swaps an element with itself, which does not change the sequence.

Aizhan knows that Ermek does not actually care about sorting the sequence . She also knows the exact indices Ermek is going to choose. Ermek plans to take part in rounds of swapping. We number these rounds from to . For each between and inclusive, Ermek will choose the indices and in round .

Aizhan wants to sort the sequence . Before each round, if Aizhan sees that the sequence is already sorted in ascending order, she will terminate the entire process. Given the original sequence and the indices Ermek is going to choose, your task is to find a sequence of swaps, which Aizhan can use to sort the sequence . In addition, in some subtasks you are required to find a sequence of swaps that is as short as possible. You may assume that it is possible to sort the sequence in or fewer rounds.

Note that if Aizhan sees that the sequence is sorted after Ermek's swap, she can choose to swap two equal indices (e.g., and ). As a result the sequence is also sorted after the entire round, so Aizhan reaches her goal. Also note that if the initial sequence is already sorted, the minimal number of rounds needed to sort it is .

##### Example 1

Suppose that:

• The initial sequence is .
• Ermek is willing to make swaps.
• The sequences and that describe the indices Ermek is going to choose are and . In other words, the pairs of indices that Ermek plans to choose are , , , , , and .

In this setting Aizhan can sort the sequence into the order in three rounds. She can do so by choosing the indices , , and then .

The following table shows how Ermek and Aizhan modify the sequence.

RoundPlayerPair of swapped indicesSequence
beginning
Ermek
Aizhan
Ermek
Aizhan
Ermek
Aizhan
##### Example 2

Suppose that:

• The initial sequence is .
• Ermek is willing to make swaps.
• The pairs of indices that Ermek plans to choose are , , , , and .

In this setting Aizhan can sort the sequence in three rounds, for example by choosing the pairs of indices , , and then . The following table shows how Ermek and Aizhan modify the sequence.

RoundPlayerPair of swapped indicesSequence
beginning
Ermek
Aizhan
Ermek
Aizhan
Ermek
Aizhan

Given the sequence , the number , and the sequence of indices and , compute a sequence of swaps, which Aizhan can use to sort the sequence . In subtasks 5 and 6 the sequence of swaps you find has to be the shortest possible.

You may assume that there exists a solution that requires or fewer rounds.

#### Input Specification

Line of input will contain the single integer , representing the length of the sequence .
Line will contain an array of space-separated integers representing the initial sequence .
Line will contain the single integer representing the number of swaps Ermek plans to make.
Lines will each contain a pair of space-separated integers and , respectively representing the length arrays and . For , in round Ermek plans to swap numbers of indices and .

#### Output Specification

Use the input arrays to report one possible sequence of swaps Aizhan can make to sort the sequence .
Line of output should contain a single value representing the length of the sequence of swaps that your program has found.
Line , for should contain a pair of space-separated integers and , representing the indices Aizhan should choose in round .

#### Sample Input 1

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

#### Sample Output 1

3
0 4
1 3
3 4

#### Sample Input 2

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

#### Sample Output 2

3
1 4
4 2
2 2

subtask points extra constraints on , requirement on
1 8 for all
2 12 for all
3 16 for all
4 18 none
5 20 none minimum possible
6 26 none minimum possible

You may assume that there exists a solution that requires or fewer rounds.