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Farmer John has purchased an Acme Time Machine. He can now travel forward in time normally (without using the machine) or else jump back to an arbitrary point in the past, at which point time will start to go forward again, but potentially with events unfolding in a new, different way. FJ can never travel forward in time in his time machine.
FJ wants to raise the best possible cow herd, so he is going to try several different ideas, keeping track of various statistics of his cow herd through different possible time and event paths.
One statistic FJ cares about is the ID number of the cow he has had for the shortest period of time. Please help him out by writing a program to keep track of his herd and, after each command, reporting the ID of the most recently acquired cow of the cows he owns (or -1 if he has no cows).
FJ has a set of N (1 <= N <= 80,000) queries Q_i, conveniently numbered 1..N, which represent consecutive updates from the point of view of FJ's personal timeline.
Each query is a single line of input. The line begins with a single character c (one of 'a', 's', or 't'). If c = 'a' or c = 't', then c is followed by a space and an integer K (1 <= K <= 1,000,000).
If c = 'a', then FJ acquires a cow with ID K; add the cow to the herd.
If c = 's', then FJ sold his most recently acquired cow (it is guaranteed that FJ will have at least one cow whenever this type of query appears); remove the cow from the herd.
If c = 't', then FJ traveled back in time to just before the Kth query. Note that this means that FJ can potentially travel between parallel time paths (see sample input for clarification). Revert to the herd that was present just before query K.
By way of example, consider a series of 12 queries, shown below along with the cow name list and the resulting output for each query.
Q# Query Owned Cows Output Comments 1 a 5 ->  => 5 Add a new cow with ID 5 2 a 3 -> [5,3] => 3 Add a new cow with ID 3 3 a 7 -> [5,3,7] => 7 Add a new cow with ID 7 4 s -> [5,3] => 3 Sell recent cow 7 5 t 2 ->  => 5 Revert time to before query 2 6 a 2 -> [5,2] => 2 Add a new cow with ID 2 7 t 4 -> [5,3,7] => 7 Revert time to before query 4 8 a 4 -> [5,3,7,4] => 4 Add a new cow with ID 4 9 s -> [5,3,7] => 7 Sell recent cow 4 10 t 7 -> [5,2] => 2 Revert time to before query 7 11 s ->  => 5 Sell recent cow 2 12 s ->  => -1 Sell recent cow 5
12 a 5 a 3 a 7 s t 2 a 2 t 4 a 4 s t 7 s s
5 3 7 3 5 2 7 4 7 2 5 -1