Giải bài trực tuyến

You are given a sequence of non-negative integers a₁, a₂, …, a_n. You are allowed to perform some operators on the sequence. Each operator consists of 2 steps: choosing an arbitrary value, then increasing (or decreasing) all elements of the selected value in the current sequence by 1.

For example, the sequence 1 9 9 2 2 will become 1 9 9 3 3 if you decide to increase all elements of value 2.

What is the minimum number of operators does it take to make the given sequence a non-decreasing sequence?

Input

• The first line consits of an integer N, the number of elements in the sequence.
• The second line consists of N elements of the sequence.

Output

• The mininum number of operators needed to make the sequence non-decreasing.

Example

Input:

5

1 9 9 2 2


Output:

7

Constraints

• 1 ≤ N ≤ 10⁵.
• Each element of the sequence is a non-negative integer not exceeding 10⁹.
• In 50% of the test cases, N does not exceed 10³.