There are n children standing in a line. Each child is assigned a rating value given in the integer array 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.
Return the minimum number of candies you need to have to distribute the candies to the children.
Examples
Example 1
Input: ratings = [4,3,5]
Output: 5
You can allocate to the first, second and third child with 2, 1, 2 candies respectively.
Example 2
Input: ratings = [2,3,3]
Output: 4
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
1 <= ratings.length <= 200000 <= ratings[i] <= 20000