Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only 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

C. Unordered Subsequence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe sequence is called ordered if it is non-decreasing or non-increasing. For example, sequnces [3, 1, 1, 0] and [1, 2, 3, 100] are ordered, but the sequence [1, 3, 3, 1] is not. You are given a sequence of numbers. You are to find it's shortest subsequence which is not ordered.

A subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.

Input

The first line of the input contains one integer *n* (1 ≤ *n* ≤ 10^{5}). The second line contains *n* space-separated integers — the given sequence. All numbers in this sequence do not exceed 10^{6} by absolute value.

Output

If the given sequence does not contain any unordered subsequences, output 0. Otherwise, output the length *k* of the shortest such subsequence. Then output *k* integers from the range [1..*n*] — indexes of the elements of this subsequence. If there are several solutions, output any of them.

Examples

Input

5

67 499 600 42 23

Output

3

1 3 5

Input

3

1 2 3

Output

0

Input

3

2 3 1

Output

3

1 2 3

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/20/2020 22:00:19 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|