Stripes

Stripes is a game for two players. To play it you need one board and rectangular stripes in three colors: red, green, and blue. Every red stripe has size $c \times 1$, every green stripe $z \times 1$, and every blue stripe $n \times 1$, where $c$, $z$, and $n$ are positive integers. Each player has an unlimited supply of stripes of every color.

The board is a $p \times 1$ rectangle made up of $p$ cells of size $1 \times 1$.

The players move alternately. A single move consists of placing one stripe of any color on the board, subject to the following rules:

• a stripe may not stick out of the board,
• a stripe may not cover, even partially, any stripe that was placed earlier,
• the two ends of a stripe must line up exactly with the cell boundaries of the board.

The player who cannot make a legal move loses. The player who moves first is called the first player. We say the first player has a winning strategy if he can always win, no matter how the second player plays.

Write a program that reads the stripe sizes and the length of one or more boards, and for each board decides whether the first player has a winning strategy.

The first line contains three integers $c$, $z$, and $n$ ($1 \le c, z, n \le 1000$), separated by single spaces: the lengths of the red, green, and blue stripes respectively.

The second line contains one integer $m$ ($1 \le m \le 1000$): the number of boards to consider.

Each of the next $m$ lines contains one integer $p$ ($1 \le p < 1000$): the length of the corresponding board.

Print $m$ lines. In the $i$-th line print a single integer:

• $1$ if the first player has a winning strategy on the $i$-th board,
• $2$ otherwise.