Alice is a kindergarten teacher. She wants to give some candies to the children in her class. All the children sit in a line and each of them has a rating score according to his or her performance in the class. Alice wants to give at least 1 candy to each child. If two children sit next to each other, then the one with the higher rating must get more candies. Alice wants to minimize the total number of candies she must buy.
For example, assume her students' ratings are [4, 6, 4, 5, 6, 2]. She gives the students candy in the following minimal amounts: [1, 2, 1, 2, 3, 1]. She must buy a minimum of 10 candies.
The first line of the input is an integer , the number of children in Alice's class represented in .
Each of the next lines contains an integer indicating the rating of the student at position i.
Output a single line containing the minimum number of candies Alice must buy.
Sample Input 0
Sample Output 0
Here 1, 2, 2 is the rating. Note that when two children have equal rating, they are allowed to have different number of candies. Hence optimal distribution will be 1, 2, 1.