Problem Statement
Game of Life is a cellular automaton invented by the recently deceased mathematician John H. Conway. We included this problem into today's set to honor his memory.
In our version of the Game of Life the world is a rectangular array of cells. Each cell is either alive ('X') or dead ('.'). Each cell has up to eight neighbors: horizontal, vertical, and diagonal. Cells at the boundary have fewer than eight neighbors.
The world evolves in steps. In each step some living cells may die and some dead cells may become alive. In particular, a cell that is currently dead will become a living cell in the next step if and only if it currently has exactly three neighbors that are alive.
You are given the
Definition
- Class:
- ThreeNeighbors
- Method:
- construct
- Parameters:
- int
- Returns:
- String[]
- Method signature:
- String[] construct(int N)
- (be sure your method is public)
Notes
- For the given constraints a solution always exists, and any valid solution will be accepted.
- We only care about the number of cells that change from dead to living. All other parameters of your world (dimensions, the number of cells that die, the total number of cells, etc.) may be arbitrary.
Constraints
- N will be between 1 and 500, inclusive.
Examples
2
Returns: {".....", ".XX..", ".X.X.", ".X...", "....." }
The return value corresponds to a configuration of cells known as a "glider": ..... .XX.. .X.X. .X... ..... Below, the two cells that will become alive in the next step are marked with asterisks. Each of these dead cells has exactly three neighbors that are alive. ..... .XX.. *X.X. .X*.. .....
6
Returns: {"........", ".XXX..X.", "..X..X..", "..X..X..", "..X...X.", "........" }
..*..... .XXX..X. ..X.*X*. .*X*.X*. ..X...X. ........
1
Returns: {"XXXX", "XXXX", ".XXX" }
XXXX XXXX *XXX
3
Returns: {"..................................................", "XXX...............................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
4
Returns: {"..................................................", "XXXX..............................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
5
Returns: {"..................................................", "XXXX..............................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
7
Returns: {"..................................................", "XXXXX.............................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
8
Returns: {"..................................................", "XXXXXX............................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
9
Returns: {"..................................................", "XXXXXX............................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
10
Returns: {"..................................................", "XXXXXXX...........................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
17
Returns: {"..................................................", "XXXXXXXXXX........................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
47
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXX.........................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
92
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
93
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
154
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
180
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX......", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
223
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXX.................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
224
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXX................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
375
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.....", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
368
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX........", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
447
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
474
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
496
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXX........................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
497
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXX........................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
498
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXX.......................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }
499
Returns: {"..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", "..................................................", "..................................................", "..................................................", "XXXXXXXXXXX.......................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................................................XX", "................................................X." }
500
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480
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435
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101
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100
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323
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237
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345
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98
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49
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242
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60
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390
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473
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51
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449
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120
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32
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173
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431
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489
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299
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358
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137
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