<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>

class Solution:
    # Function to calculate sum of first n natural numbers
    def count(self, n):
        return (n * (n + 1)) // 2
    def candy(self, ratings):
        if len(ratings) <= 1:
            return len(ratings)
        candies = 0
        up = 0
        down = 0
        oldSlope = 0
        for i in range(1, len(ratings)):
            newSlope = (
                1
                if ratings[i] > ratings[i - 1]
                else (-1 if ratings[i] < ratings[i - 1] else 0)
            )
            # slope is changing from uphill to flat or downhill
            # or from downhill to flat or uphill
            if (oldSlope > 0 and newSlope == 0) or (
                oldSlope < 0 and newSlope >= 0
            ):
                candies += self.count(up) + self.count(down) + max(up, down)
                up = 0
                down = 0
            # slope is uphill
            if newSlope > 0:
                up += 1
            # slope is downhill
            elif newSlope < 0:
                down += 1
            # slope is flat
            else:
                candies += 1
            oldSlope = newSlope
        candies += self.count(up) + self.count(down) + max(up, down) + 1
        return candies
20200