Min Partition Score

Given a sequence of n integers, you are required to partition the sequence into strictly increasing continuous subsequences. The total score of a partition is defined as the number of indices i (with 1 ≤ i < n) such that \(a_i \ge a_{i+1}\). In other words, every time the sequence fails to increase from one element to the next, it contributes 1 to the score. Your task is to compute the minimum possible total score.

The score can be formulated as:

[ \text{score} = #{ i \mid 1 \le i < n,\ a_i \ge a_{i+1} } ]

For example, consider the sequence [1, 2, 3, 2, 4]. The score is 1 because the only decrease occurs from 3 to 2.

inputFormat

The input is given via standard input (stdin) and consists of two lines:

1. The first line contains a single integer \(n\) (\(1 \le n \le 10^5\)), representing the length of the sequence.
2. The second line contains \(n\) space-separated integers representing the sequence.

outputFormat

Output a single integer to standard output (stdout) — the minimum possible total score, which is equivalent to the number of positions where the sequence is not strictly increasing.

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