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 {
public:
    int candy(vector<int>& ratings) {
        if (ratings.empty())
            return 0;
        int n = ratings.size();
        vector<int> res(n, 1);
        
        for (int i = 0; i < n-1; i ++) {
            if (ratings[i] < ratings[i+1])
                res[i+1] = res[i] + 1;
        }
        
        for (int i = n-1; i > 0; i --) {
            if (ratings[i-1] > ratings[i])
                res[i-1] = max(res[i]+1, res[i-1]);
        }
        
        return accumulate(res.begin(),res.end(),0); 
    }
};