Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Sorting by Subsequences

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a sequence *a*_{1}, *a*_{2}, ..., *a*_{n} consisting of different integers. It is required to split this sequence into the maximum number of subsequences such that after sorting integers in each of them in increasing order, the total sequence also will be sorted in increasing order.

Sorting integers in a subsequence is a process such that the numbers included in a subsequence are ordered in increasing order, and the numbers which are not included in a subsequence don't change their places.

Every element of the sequence must appear in exactly one subsequence.

Input

The first line of input data contains integer *n* (1 ≤ *n* ≤ 10^{5}) — the length of the sequence.

The second line of input data contains *n* different integers *a*_{1}, *a*_{2}, ..., *a*_{n} ( - 10^{9} ≤ *a*_{i} ≤ 10^{9}) — the elements of the sequence. It is guaranteed that all elements of the sequence are distinct.

Output

In the first line print the maximum number of subsequences *k*, which the original sequence can be split into while fulfilling the requirements.

In the next *k* lines print the description of subsequences in the following format: the number of elements in subsequence *c*_{i} (0 < *c*_{i} ≤ *n*), then *c*_{i} integers *l*_{1}, *l*_{2}, ..., *l*_{ci} (1 ≤ *l*_{j} ≤ *n*) — indices of these elements in the original sequence.

Indices could be printed in any order. Every index from 1 to *n* must appear in output exactly once.

If there are several possible answers, print any of them.

Examples

Input

6

3 2 1 6 5 4

Output

4

2 1 3

1 2

2 4 6

1 5

Input

6

83 -75 -49 11 37 62

Output

1

6 1 2 3 4 5 6

Note

In the first sample output:

After sorting the first subsequence we will get sequence 1 2 3 6 5 4.

Sorting the second subsequence changes nothing.

After sorting the third subsequence we will get sequence 1 2 3 4 5 6.

Sorting the last subsequence changes nothing.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/21/2019 05:26:25 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|