Longest strictly increasing run

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Problem

Read a positive natural number `n` followed by `n` integers forming a sequence `v[1], v[2], ..., v[n]`. A strictly increasing run is a contiguous portion `v[i], v[i+1], ..., v[j]` such that `v[i] < v[i+1] < ... < v[j]`. Determine the length of the longest such run and the position where it starts in the sequence, then print the elements of that run. If there are several runs of maximum length, choose the first one.

Input format

Input input.txt

The first line contains `n`. The second line contains `n` integers separated by spaces. - `1 <= n <= 1000` - elements are integers in `[-10^9, 10^9]` - a single element forms a strictly increasing run of length `1`

Output format

Output output.txt

The first line contains two numbers separated by a space: the length of the longest strictly increasing run, followed by the position of its first element in the sequence (positions numbered from `1`). The second line contains the elements of the run, separated by spaces.

Example

input

8

3 1 2 5 4 7 8 9

output

4 5

4 7 8 9

Sample cases (from the problem)

Sample Case 1

Input

8

3 1 2 5 4 7 8 9

Expected output

4 5

4 7 8 9

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