Go

In the game of Go, two players alternate placing black and white stones on the lattice points of an $n \times n$ grid, each trying to surround as much territory (that is, regions of empty lattice points) as possible. At the end of the game, each player's score is the total area of the territory surrounded by their stones. Given the final positions of the black and white stones, compute each player's score and determine the winner.

Formally, two lattice points $(r, c)$ and $(r', c')$ are adjacent if $|r - r'| + |c - c'| = 1$. A connected region of empty lattice points belongs to a player's territory if every adjacent occupied lattice point holds a stone of that player (see Figure 1). A player's score is the number of empty lattice points in their territory.

Figure 1: A $9 \times 9$ Go board. Empty lattice points in black's territory are marked B, and those in white's territory are marked W. Neutral empty lattice points are left unmarked. Here white wins by $21 - 3 = 18$.

Note: this scoring does not correspond exactly to real Go. We assume all disputes have been settled, so that every region of territory is surrounded by stones of a single color.

The input contains multiple test cases. Each test case consists of three lines.

• The first line contains three integers $n$ ($1 \le n \le 19$), $b$, and $w$ ($b \ge 0$, $w \ge 0$, and $1 \le b + w \le n^2$): the board size, the number of black stones, and the number of white stones.
• The second line contains $b$ pairs of integers $r_1\ c_1\ \dots\ r_b\ c_b$ (with $1 \le r_i, c_i \le n$), the positions of the black stones.
• The third line contains $w$ pairs of integers $r'_1\ c'_1\ \dots\ r'_w\ c'_w$ (with $1 \le r'_i, c'_i \le n$), the positions of the white stones.

No two stones occupy the same lattice point. When $b = 0$ (or $w = 0$), the corresponding line is empty. The input ends with a line containing a single $0$, which must not be processed.

For each test case, print one line. Let $X$ be the positive difference between the two scores. Print White wins by X if white has the higher score, Black wins by X if black has the higher score, or Draw if the scores are equal.