Strictly Increasing Sequence by Removal

You are given a sequence of n integers. Your task is to determine whether it is possible to obtain a strictly increasing sequence by removing at most one element from the sequence. Note that if the sequence is already strictly increasing, you should return True.

A sequence a₁, a₂, ..., a_n is considered strictly increasing if a₁ < a₂ < ... < a_n.

Formally, given a sequence \(a_1, a_2, \dots, a_n\), determine if there exists an index \(i\) (possibly no removal is needed) such that after removing \(a_i\) (if necessary) the remaining sequence is strictly increasing.

For example, consider the sequence [1, 3, 2, 1]. Removing any one element does not lead to a strictly increasing sequence, so the answer is False. In contrast, for the sequence [1, 3, 2] you can remove the element 3 to obtain [1, 2] which is strictly increasing, so the answer is True.

inputFormat

The input is read from stdin and consists of two lines. The first line contains an integer n representing the number of elements in the sequence. The second line contains n space-separated integers.

outputFormat

Output to stdout a single line containing either True or False indicating whether a strictly increasing sequence can be obtained by removing at most one element from the given sequence.## sample

4
1 3 2 1

False