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Candy

Hard

There are n children standing in a line. Each child is assigned a rating value given in the integer list ratings .

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.

Produce the minimum number of candies you need to have to distribute the candies to the children .

Example 1

Input: ratings = [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: ratings = [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.

Constraints

  • n == ratings.length
  • 1 <= n <= 2 * 10^4
  • 0 <= ratings[i] <= 2 * 10^4

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