There exist n rectangles in a 2D plane. You are given two 0-indexed 2D integer arrays bottomLeft and topRight, both of size n x 2, where bottomLeft[i] and topRight[i] represent the bottom-left and top-right coordinates of the ith rectangle respectively.
You can select a region formed from the intersection of two of the given rectangles. You need to find the largest area of a square that can fit inside this region if you select the region optimally.
\n\nReturn the largest possible area of a square, or 0 if there do not exist any intersecting regions between the rectangles.
\n
Example 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2024/01/05/example12.png\")
\n\nInput: bottomLeft = [[1,1],[2,2],[3,1]], topRight = [[3,3],[4,4],[6,6]]\nOutput: 1\nExplanation: A square with side length 1 can fit inside either the intersecting region of rectangle 0 and rectangle 1, or the intersecting region of rectangle 1 and rectangle 2. Hence the largest area is side * side which is 1 * 1 == 1.\nIt can be shown that a square with a greater side length can not fit inside any intersecting region.\n\n\n
Example 2:
\n![\"\"](\"https://assets.leetcode.com/uploads/2024/01/04/rectanglesexample2.png\")
\n\nInput: bottomLeft = [[1,1],[2,2],[1,2]], topRight = [[3,3],[4,4],[3,4]]\nOutput: 1\nExplanation: A square with side length 1 can fit inside either the intersecting region of rectangle 0 and rectangle 1, the intersecting region of rectangle 1 and rectangle 2, or the intersection region of all 3 rectangles. Hence the largest area is side * side which is 1 * 1 == 1.\nIt can be shown that a square with a greater side length can not fit inside any intersecting region.\nNote that the region can be formed by the intersection of more than 2 rectangles.\n\n\n
Example 3:
\n![\"\"](\"https://assets.leetcode.com/uploads/2024/01/04/rectanglesexample3.png\")
\n\nInput: bottomLeft = [[1,1],[3,3],[3,1]], topRight = [[2,2],[4,4],[4,2]]\nOutput: 0\nExplanation: No pair of rectangles intersect, hence, we return 0.\n\n\n
\n
Constraints:
\n\nn == bottomLeft.length == topRight.length2 <= n <= 103bottomLeft[i].length == topRight[i].length == 21 <= bottomLeft[i][0], bottomLeft[i][1] <= 1071 <= topRight[i][0], topRight[i][1] <= 107bottomLeft[i][0] < topRight[i][0]bottomLeft[i][1] < topRight[i][1]在二维平面上存在 n 个矩形。给你两个下标从 0 开始的二维整数数组 bottomLeft 和 topRight，两个数组的大小都是 n x 2 ，其中 bottomLeft[i] 和 topRight[i] 分别代表第 i 个矩形的 左下角 和 右上角 坐标。
我们定义 向右 的方向为 x 轴正半轴（x 坐标增加），向左 的方向为 x 轴负半轴（x 坐标减少）。同样地，定义 向上 的方向为 y 轴正半轴（y 坐标增加），向下 的方向为 y 轴负半轴（y 坐标减少）。
\n\n你可以选择一个区域，该区域由两个矩形的 交集 形成。你需要找出能够放入该区域 内 的 最大 正方形面积，并选择最优解。
\n\n返回能够放入交集区域的正方形的 最大 可能面积，如果矩形之间不存在任何交集区域，则返回 0。
\n\n
示例 1：
\n\n\n输入：bottomLeft = [[1,1],[2,2],[3,1]], topRight = [[3,3],[4,4],[6,6]]\n输出：1\n解释：边长为 1 的正方形可以放入矩形 0 和矩形 1 的交集区域，或矩形 1 和矩形 2 的交集区域。因此最大面积是边长 * 边长，即 1 * 1 = 1。\n可以证明，边长更大的正方形无法放入任何交集区域。\n\n\n
示例 2：
\n\n\n输入：bottomLeft = [[1,1],[2,2],[1,2]], topRight = [[3,3],[4,4],[3,4]]\n输出：1\n解释：边长为 1 的正方形可以放入矩形 0 和矩形 1，矩形 1 和矩形 2，或所有三个矩形的交集区域。因此最大面积是边长 * 边长，即 1 * 1 = 1。\n可以证明，边长更大的正方形无法放入任何交集区域。\n请注意，区域可以由多于两个矩形的交集构成。\n\n\n
示例 3：
\n\n\n输入：bottomLeft = [[1,1],[3,3],[3,1]], topRight = [[2,2],[4,4],[4,2]]\n输出：0\n解释：不存在相交的矩形，因此，返回 0 。\n\n\n
\n\n
提示：
\n\nn == bottomLeft.length == topRight.length2 <= n <= 103bottomLeft[i].length == topRight[i].length == 21 <= bottomLeft[i][0], bottomLeft[i][1] <= 1071 <= topRight[i][0], topRight[i][1] <= 107bottomLeft[i][0] < topRight[i][0]bottomLeft[i][1] < topRight[i][1]\\u7248\\u672c\\uff1a \\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528 \\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\"],\"java\":[\"Java\",\" \\u7248\\u672c\\uff1a \\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u88ab\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u5305\\u542b Pair \\u7c7b: https:\\/\\/docs.oracle.com\\/javase\\/8\\/javafx\\/api\\/javafx\\/util\\/Pair.html <\\/p>\"],\"python\":[\"Python\",\" \\u7248\\u672c\\uff1a 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