package q3047

import "slices"

func intersectingSquareArea(bl1, tr1, bl2, tr2 []int) int64 {
	l1, r1, l2, r2 := bl1[0], tr1[0], bl2[0], tr2[0]
	iW := max(0, min(r1, r2)-max(l1, l2))

	l1, r1, l2, r2 = bl1[1], tr1[1], bl2[1], tr2[1]
	iH := max(0, min(r1, r2)-max(l1, l2))

	edge := min(iW, iH)
	return int64(edge * edge)
}

func largestSquareArea(bottomLeft [][]int, topRight [][]int) int64 {
	squares := make([]int, len(bottomLeft))
	for i := range squares {
		squares[i] = i
	}
	slices.SortFunc(squares, // bottom-up order
		func(a, b int) int { return bottomLeft[a][1] - bottomLeft[b][1] })

	var largest int64

	for i := range squares {
		for j := i + 1; j < len(squares); j++ {
			yI, yJ := topRight[squares[i]][1], bottomLeft[squares[j]][1]
			if yJ >= yI {
				break
			}

			largest = max(largest, intersectingSquareArea(
				bottomLeft[squares[i]], topRight[squares[i]],
				bottomLeft[squares[j]], topRight[squares[j]],
			))
		}
	}
	return largest
}

var _ = largestSquareArea