Minimum Rewards Distribution

You are given n students standing in a line and each student has a score represented as an integer. Your task is to distribute rewards to these students according to the following rules:

• Each student must receive at least one reward.
• If a student has a higher score than an adjacent student, then this student must receive more rewards than that neighbor.

Formally, let \(s_i\) be the score of the \(i^{th}\) student and \(r_i\) the number of rewards given. Then for every adjacent pair:

• If \(s_i > s_{i-1}\), then \(r_i > r_{i-1}\).
• If \(s_i > s_{i+1}\), then \(r_i > r_{i+1}\).

Your goal is to determine the minimum total number of rewards required to satisfy these conditions.

inputFormat

The input is read from standard input and consists of two lines:

1. The first line contains an integer \(n\), the number of students.
2. The second line contains \(n\) integers separated by spaces, representing the scores of the students.

outputFormat

Print a single integer representing the minimum total number of rewards needed.

## sample

5
1 2 3 2 1

9

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