Longest Non-Decreasing Subsequence

Given an integer n and a sequence of n integers, your task is to determine the length of the longest non-decreasing subsequence that can be formed from the sequence.

A non-decreasing subsequence is defined such that for any two consecutive elements \(a_i\) and \(a_j\) in the subsequence where \(i < j\), it holds that \(a_i \le a_j\). Note that the subsequence is not required to be contiguous in the original sequence.

For example, if the input sequence is [10, 22, 9, 33, 21, 50, 41], one of the longest non-decreasing subsequences is [10, 22, 33, 50] with a length of 4.

inputFormat

The input is read from standard input (stdin) and consists of two parts:

1. An integer n representing the length of the sequence.
2. n space-separated integers that form the sequence.

If n = 0, the sequence will be empty.

outputFormat

Output the length of the longest non-decreasing subsequence. The result should be printed to standard output (stdout).

## sample

7
10 22 9 33 21 50 41

4

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