<p>There are <code>n</code> children standing in a line. Each child is assigned a rating value given in the integer array <code>ratings</code>.</p>

<p>You are giving candies to these children subjected to the following requirements:</p>

<ul>
	<li>Each child must have at least one candy.</li>
	<li>Children with a higher rating get more candies than their neighbors.</li>
</ul>

<p>Return <em>the minimum number of candies you need to have to distribute the candies to the children</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> ratings = [1,0,2]
<strong>Output:</strong> 5
<strong>Explanation:</strong> You can allocate to the first, second and third child with 2, 1, 2 candies respectively.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> ratings = [1,2,2]
<strong>Output:</strong> 4
<strong>Explanation:</strong> You can allocate to the first, second and third child with 1, 2, 1 candies respectively.
The third child gets 1 candy because it satisfies the above two conditions.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == ratings.length</code></li>
	<li><code>1 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= ratings[i] &lt;= 2 * 10<sup>4</sup></code></li>
</ul>

from typing import List

class Solution:
    def candy(self, ratings: List[int]) -> int:
        n = len(ratings)
        if n <= 1:
            return n

        total_candies = 1  # Start with one candy for the first child
        up = 1            # Length of the last ascending sequence
        down = 0          # Length of the last descending sequence
        peak = 1          # Candies at the peak of the last ascending sequence

        for i in range(1, n):
            if ratings[i] > ratings[i - 1]:
                up += 1
                peak = up
                down = 0
                total_candies += up
            elif ratings[i] == ratings[i - 1]:
                up = 1
                down = 0
                peak = up
                total_candies += up
            else:
                down += 1
                up = 1
                total_candies += down
                if down >= peak:
                    # Add one extra candy to the peak child
                    total_candies += 1

        return total_candies
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