Largest Square Area in Cityscape

You are given an array of non-negative building heights. Find the largest area of a square that fits beneath a contiguous run of buildings; side s is feasible if and only if there are s consecutive buildings each with height at least s. This criterion corresponds to the explicit condition in the source's solution section.

输入格式

n (1≤n≤200000), n heights h (0≤h≤10^9); the ranges are site-added.

输出格式

Output the largest square area.

样例 1

输入：

5
1 2 3 2 1

输出：

4

样例 2

输入：

2
0 0

输出：

0

样例 3

输入：

3
3 3 3

输出：

9