# Problem F

Longest Increasing Subsequence

We say that an integer sequence is *increasing* if
the numbers in the sequence increase (rather than decrease or
stay the same). For example, the following is an increasing
sequence of length $7$:

A *subsequence* of a sequence uses some of the same
members, in the same order, but may leave some out. For
example, if we have the following (non-increasing) sequence of
length $7$:

then $(11, 53, 61)$ is a subsequence of length $3$. And this subsequence also happens to be increasing. However, for this example there are longer increasing subsequences; what is the longest you can find?

Write a program that, given a sequence of integers, finds a subsequence that is increasing and is as long as possible.

## Input

The input consists of between $1$ and $64$ test cases. Each test case has two lines. The first line has a positive integer $n \le 100\, 000$, indicating the length of a sequence. Then follows a line containing a sequence of $n$ integers, each in the range $[-2^{31}, 2^{31})$. Input ends at end of file.

## Output

For each test case, output a line containing the length of a longest increasing subsequence, followed by a line containing the indices of the elements in one such sequence (the first element has index $0$, the second index $1$, and so on). The indices should be given in ascending order. If multiple increasing subsequences have maximal length, report any one of them.

Sample Input 1 | Sample Output 1 |
---|---|

10 1 2 3 4 5 6 7 8 9 10 10 1 1 1 1 1 1 1 1 1 1 10 5 19 5 81 50 28 29 1 83 23 |
10 0 1 2 3 4 5 6 7 8 9 1 7 5 0 1 5 6 8 |