20180번 - Two Buildings 다국어

There are n buildings along a horizontal street. The buildings are next to each other along the street, and the i-th building from left to right has width 1 and height h_i. Among the n buildings, we are to find two buildings, say the i-th building and j-th building with i < j, such that (h_i + h_j) × (j − i) is maximized.

For example, the right figure shows 5 buildings, with heights 1, 3, 2, 5, 4, from left to right. If we choose the first 2 buildings, then we get (1 + 3) × (2 − 1) = 4. If we choose the first and fifth buildings, then we (1 + 4) × (5 − 1) = 20. The maximum value is achieved by the second and fifth buildings with heights 3 and 4, respectively: (3 + 4) × (5 − 2) = 21.

Write a program that, given a sequence of building heights, prints max_{1≤i<𝑗≤n}(h_i + h_j) × (j − i).

Your program is to read from standard input. The input starts with a line containing an integer n (2 ≤ n ≤ 1,000,000), where n is the number of buildings. The buildings are numbered 1 to n from left to right. The second line contains the heights of n buildings separated by a space such that the i-th number is the height h_i of the i-th building (1 ≤ h_i ≤ 1,000,000).

Your program is to write to standard output. Print exactly one line. The line should contain max_{1≤i<𝑗≤n}(h_i + h_j) × (j − i).