Longest Diagonal Canvas Selection

A framing workshop is choosing which rectangular canvas to mount on a display easel. Each candidate canvas is described by its length and width in centimeters. The workshop always mounts the canvas whose corner-to-corner diagonal brace is the longest, since that canvas needs the sturdiest support. If two or more candidate canvases tie for the longest diagonal, the workshop picks the one among the tied candidates that has the largest surface area. Given the list of candidate canvases, report the surface area of the canvas that gets mounted.

Input format

Line 1: one integer n — the number of candidate canvases. The next n lines (or, equivalently, the next 2n integers) each contain two integers, length and width, describing one candidate canvas.

Output format

Print a single integer: the area of the chosen canvas (the one with the longest diagonal, breaking ties by the largest area).

Constraints

• 1 <= n <= 100
• 1 <= length, width <= 100 for every candidate canvas.

2
9 3
8 6

48

2
3 4
4 3

12