You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the i-th line are (i, 0) and (i, heighti).

Find two lines that together with the x-axis form a container, such that the container contains the most water.

Input

The first line contains the size n (n ≤ 105) of array height. Second line contains n positive integers - the elements of array height, that are no more than 109.

Output

Print the maximum amount of water a container can store.