Step

N persons are standing in a row. The height of the i-th person from the front is A_i.

We want to have each person stand on a stool of some heights - at least zero - so that the following condition is satisfied for every person:

Condition: Nobody in front of the person is taller than the person. Here, the height of a person includes the stool.

Find the minimum total height of the stools needed to meet this goal.

Constraints

• 1 \leq N \leq 2\times 10^5
• 1 \leq A_i \leq 10^9
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 \ldots A_N

Output

Print the minimum total height of the stools needed to meet the goal.

Examples

Input

5 2 1 5 4 3

Output

4

Input

5 3 3 3 3 3

Output

0

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 \ldots A_N

outputFormat

Output

Print the minimum total height of the stools needed to meet the goal.

Examples

Input

5 2 1 5 4 3

Output

4

Input

5 3 3 3 3 3

Output

0

样例

5
3 3 3 3 3

0