Given n numbers representing the heights of bars in a histogram, you are asked to calculate the largest area that can be obtained in the histogram without going out of the bars.

All the bars in the histogram have a width of 1, while the heights are arbitrary nonnegative integers.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ ).

The next line contains n space-separated integers (0 ≤ ≤ ).

Output

The program should print the largest area possible to obtain from the bars of the histogram.

Examples

Input

Output

8
6 2 5 4 5 1 6 1

12

Hint

For each element in the histogram, you can calculate 2 numbers - the closest element that’s smaller than the current element on the left and on the right. That would be sufficient to calculate the area of the rectangle having the height of the current bar.