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A fence consists of n vertical boards. The width of each board is 1 and their heights may vary. You want to attach a rectangular advertisement to the fence. What is the maximum area of such an advertisement?

Input

The first input line contains an integer n: the width of the fence. After this, there are n integers k_1,k_2,\ldots,k_n: the height of each board.

Output

Print one integer: the maximum area of an advertisement.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$1 \le k_i \le 10^9$

Example

Input

8
4 1 5 3 3 2 4 1

Output

10