7980: Square Pasture

农夫约翰决定翻修他的农场以简化其几何形状。

以前，他的牛在两个栅栏围起来的长方形牧场上吃草。

现在，约翰想要用栅栏修建一个新的正方形牧场。

正方形牧场需要覆盖之前两个长方形牧场所包围的全部区域。

请你确定，新修建的正方形牧场的面积最小是多少。

正方形牧场的边应与 x 轴和 y 轴平行。

输入格式

第一行包含四个整数 x1,y1,x2,y2，表示第一个长方形牧场的左下角坐标 (x1,y1) 和右上角坐标 (x2,y2)。

第二行同样包含四个整数 x1,y1,x2,y2，表示第二个长方形牧场的左下角坐标 (x1,y1) 和右上角坐标 (x2,y2)。

两个牧场之间不会发生重叠或接触。

输出格式

输出能够覆盖之前两个长方形牧场所包围的全部区域的正方形牧场的最小面积。

数据范围

0≤x1<x2≤10,

0≤y1<y2≤10


Farmer John has decided to update his farm to simplify its geometry. Previously, his cows grazed in two rectangular fenced-in pastures. Farmer John would like to replace these with a single square fenced-in pasture of minimum size that still covers all the regions of his farm that were previously enclosed by the former two fences.

Please help Farmer John figure out the minimum area he needs to make his new square pasture so that if he places it appropriately, it can still cover all the area formerly covered by the two older rectangular pastures. The square pasture should have its sides parallel to the x and y axes.

SAMPLE INPUT:

6 6 8 8
1 8 4 9

SAMPLE OUTPUT:

49

In the example above, the first original rectangle has corners (6,6)(6,6) and (8,8)(8,8). The second has corners at (1,8)(1,8) and (4,9)(4,9). By drawing a square fence of side length 7 with corners (1,6)(1,6) and (8,13)(8,13), the original areas can still be enclosed; moreover, this is the best possible, since it is impossible to enclose the original areas with a square of side length only 6. Note that there are several different possible valid placements for the square of side length 7, as it could have been shifted vertically a bit.

Problem credits: Brian Dean