Bus Shuttle

Pasha is travelling in Rome. He has just reached the central train station, Stazione Termini, and he wants to get to the airport of Rome, Aeroporto Fiumicino, as soon as possible.

Right outside the exit of Termini he finds a stop of the Bus Shuttle service, which takes passengers straight to the airport for 8 Euros per person, luggage included. Pasha decides to wait for the bus.

The sign at the stop carries a time table with nothing but departure times on it. It is around 7:00 in the morning, so he has to wait until 7:45 for the first bus.

Pasha wants to know the travel time between Termini and Aeroporto. He asks the other passengers at the stop, but nobody knows it, and their English is too weak to explain. One passenger tells him this:

"Yesterday at 13:15 I was on a shuttle to Termini, and a shuttle going the other way, towards Aeroporto, passed us. I do not remember when I boarded or when we arrived. All I remember is the crossing at 13:15."

That is not enough on its own, but it helps. A few minutes later other passengers give Pasha the same kind of information: the time at which their bus crossed a shuttle coming from the opposite direction.

Finally Pasha finds a brochure of the shuttle service. It prints the time table for Termini to Aeroporto and the time table for Aeroporto to Termini.

Given the two time tables and the crossing times reported by the passengers, find the travel time between Termini and Aeroporto.

Every bus moves at a constant speed and never stops on the way. The travel time is the same in both directions and shorter than 24 hours. Each bus is parked once it reaches its destination. If $n$ buses leave Termini and $m$ buses leave Aeroporto during the day, then those $n + m$ buses are the only shuttles in Rome, and there are $n \times m$ possible crossings. A crossing counts at a station too, that is, when one bus departs at the exact moment a bus from the opposite direction arrives there.

The input holds several test cases.

The first line of each test case has two integers, $n$, the number of buses going from Termini to Aeroporto on that day, and $m$, the number of buses going from Aeroporto to Termini ($0 < n, m \le 100$).

The second line has $n$ distinct departure times from Termini, separated by spaces. A time is between 00:00 and 23:59 and is written as HH:MM, with a leading zero when the hour or the minute has a single digit. The third line has $m$ distinct departure times from Aeroporto in the same format. All $n + m$ departure times are even in minutes, or all of them are odd.

The fourth line has an integer $k$, the number of passengers who reported a crossing time to Pasha ($1 \le k \le 100$). The fifth line has those $k$ times in the same format, separated by spaces.

All buses leave on the same day, but a crossing can happen on the next one. With a travel time of 8 hours, the bus leaving Aeroporto at 22:00 and the bus leaving Termini at 23:00 cross at 02:30 the next morning. A reported time carries no date, so a report of 06:30 can also belong to the same morning: with a travel time of 2 hours, the bus that left Termini at 05:00 and the bus that left Aeroporto at 06:00 cross at 06:30.

The last line of the input has two zeros.

Print one line for each test case.

If exactly one travel time between 00:01 and 23:59 explains every reported crossing, print it as HH:MM, with two digits for the hours and two for the minutes. The travel time is always a whole number of minutes.

If no travel time matches what the passengers said, print il bugiardo passeggeri!.

If $c$ travel times are possible and $c > 1$, print c scelte, with c replaced by that count. For three of them, print 3 scelte.