There are N children standing in a line. Each child is assigned a rating value.

You are giving candies to these children subjected to the following requirements:

• Each child must have at least one candy.
• Children with a higher rating get more candies than their neighbors.

What is the minimum candies you must give?

Example 1:

Input: [1,0,2]
Output: 5
Explanation: You can allocate to the first, second and third child with 2, 1, 2 candies respectively.

Example 2:

Input: [1,2,2]
Output: 4
Explanation: 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.

class Solution:
    def candy(self, ratings: List[int]) -> int:
        res = [1]*len(ratings)
        
        lbase = rbase = 1
        
        # left scan
        for i in range(1, len(ratings)):
            lbase = lbase + 1 if ratings[i] > ratings[i-1] else 1
            res[i] = lbase
            
        # right scan
        for i in range(len(ratings)-2, -1, -1):
            rbase = rbase + 1 if ratings[i] > ratings[i+1] else 1
            res[i] = max(rbase, res[i])
            
        return sum(res)