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Tournament

Statement

 Goal

You are given the pairings of an elimination tournament with n = 2 ** k players of the game Starcraft. Each player plays one race from either: Terran, Protoss or Zerg.

You are very worried about game balance and decide to figure out the maximum number of Zerg players that can qualify in the successive k rounds. Print the result in k lines.

NOTE: The pairings are made by successively choosing two consecutive remaining players. That is:


Zerg    --
          |-- Next player --
Terran  --                  |
                            |-- Next player
Terran  --                  |
          |-- Next player --
Protoss --
Input
Line 1: An integer n for the number of players in the tournament.
Next n lines: The race of the player. Either Terran, Protoss or Zerg.
Output
k lines: An integer with the maximum number of Zerg at the current round.
Constraints
There is an integer k such that n = 2 ** k (n is a power of two).
4 <= n <= 64
Example
Input
4
Protoss
Zerg
Terran
Terran
Output
1
1
Game modes
Fastest, Shortest
Test cases
1. Example Test
Input
4 Protoss Zerg Terran Terran
Output
1 1
1. Example val Validator
Input
4 Terran Zerg Protoss Terran
Output
1 1
2. Zerg wing Test
Input
8 Protoss Zerg Terran Terran Zerg Zerg Zerg Zerg
Output
3 2 1
2. Zerg wing val Validator
Input
8 Zerg Zerg Zerg Zerg Protoss Zerg Terran Terran
Output
3 2 1
3. Terran imba Test
Input
4 Terran Terran Terran Terran
Output
0 0
3. Terran imba val Validator
Input
8 Terran Terran Terran Terran Terran Terran Terran Terran
Output
0 0 0
4. Can be anything Test
Input
8 Terran Zerg Terran Zerg Protoss Zerg Zerg Protoss
Output
4 2 1
4. Can be anything val Validator
Input
8 Zerg Protoss Terran Zerg Terran Zerg Terran Zerg
Output
4 2 1
4. RO16 AL Season 16 Test
Input
16 Zerg Terran Zerg Zerg Terran Protoss Terran Zerg Zerg Zerg Terran Protoss Terran Zerg Protoss Terran
Output
5 4 2 1
4. RO16 AL Season 16 val Validator
Input
16 Terran Protoss Zerg Terran Protoss Terran Zerg Zerg Zerg Terran Protoss Terran Zerg Zerg Terran Zerg
Output
5 4 2 1
5. Random RO32 Test
Input
32 Zerg Protoss Protoss Terran Zerg Terran Zerg Zerg Zerg Zerg Protoss Protoss Protoss Zerg Terran Terran Protoss Protoss Protoss Protoss Zerg Terran Terran Terran Zerg Zerg Terran Protoss Zerg Zerg Terran Protoss
Output
8 7 4 2 1
5. Random RO32 val Validator
Input
32 Protoss Protoss Terran Terran Protoss Protoss Zerg Terran Protoss Terran Terran Protoss Zerg Zerg Terran Protoss Terran Terran Zerg Protoss Terran Protoss Protoss Protoss Protoss Protoss Protoss Protoss Terran Zerg Zerg Protoss
Output
5 4 4 2 1
6. Random RO64 Test
Input
64 Zerg Protoss Terran Protoss Zerg Zerg Protoss Terran Protoss Protoss Protoss Terran Zerg Zerg Protoss Protoss Zerg Protoss Zerg Zerg Protoss Zerg Protoss Terran Zerg Terran Protoss Protoss Zerg Terran Protoss Protoss Protoss Terran Protoss Terran Terran Terran Zerg Terran Protoss Protoss Zerg Protoss Protoss Zerg Protoss Terran Zerg Zerg Zerg Terran Zerg Zerg Zerg Protoss Protoss Zerg Zerg Terran Protoss Protoss Zerg Zerg
Output
18 14 8 4 2 1
6. Random RO64 val Validator
Input
64 Zerg Zerg Terran Zerg Protoss Protoss Zerg Zerg Protoss Protoss Terran Protoss Terran Zerg Terran Zerg Zerg Zerg Protoss Protoss Protoss Zerg Zerg Protoss Terran Protoss Zerg Terran Terran Protoss Protoss Protoss Protoss Zerg Zerg Protoss Protoss Zerg Terran Terran Terran Protoss Zerg Terran Terran Protoss Terran Terran Terran Protoss Zerg Terran Protoss Protoss Terran Zerg Terran Zerg Protoss Zerg Protoss Zerg Terran Zerg
Output
19 13 8 4 2 1
Solution language
Solution
Stub generator input
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