408091: GYM102984 G Solo Tree Game

Whiteking and Blackking are about to play a stone game with long wooden boards.

In this game, you use $$$N$$$ wooden boards. The $$$i$$$-th wooden board has the shape of a two-dimensional stripe: a rectangle of size $$$1 \times A_i$$$. The game starts with a white stone on the first space of all wooden boards and a black stone on the last space.

On each turn, the king must move one of his colored stones. When moving, the king must move the stone to another space of the same board, but cannot jump over the opponent's stone or move to the same space. Kings take turns, and the king who cannot move in his turn is defeated.

For example, if a 6-long wood board has a white stone in cell 3 and a black stone in cell 5, the white stone can be moved to one of cells 1, 2 and 4, and the black stone can be moved to one of cells 4 and 6.

Assuming that kings are playing optimally, determine the game result.

The first line of the input contains one integer $$$N$$$ ($$$1 \le N \le 10^5$$$): the number of long wooden boards.

The second line contains $$$N$$$ integers $$$A_1$$$, $$$A_2$$$, $$$A_3$$$, $$$\ldots$$$, $$$A_N$$$ ($$$2 \le A_i \le 10^9$$$): the lengths of the long wooden boards.

The third line contains the name of the king to move first: either "Whiteking" or "Blackking".

On the first line, print the name of the king who wins. Note that the first letter is always capitalized.

2
3 3
Whiteking

Blackking

2
3 5
Whiteking

Whiteking