Great Circle

Airplanes fly close to the Great Circle route between two cities. The Great Circle route is the shortest arc, concentric with the Earth, that joins the two cities — that is, the shortest distance between the two cities along the surface of the Earth.

Given the latitude and longitude of two cities, find the most northerly latitude reached along the Great Circle route between them. If there is no unique answer, print undefined.

The first line contains an integer $N$, the number of test cases. Each of the next $N$ lines describes one case as four whitespace-separated tokens — lat1 lon1 lat2 lon2 — giving the latitude and longitude of the two cities in degrees, minutes, and direction.

A latitude token has the form degrees,minutesD, where D is N or S; a longitude token has the form degrees,minutesD, where D is E or W. One minute equals $1/60$ of a degree.

By convention, points on the equator have latitude 0,0N (not 0,0S); points on the poles have longitude 0,0W; and points at 180 degrees of longitude are written 180,0W (not 180,0E).

For each test case, print a single line with the most northerly latitude reached, written in the same degrees,minutesD format and rounded to the nearest minute. Print undefined if there is no unique answer.