Problem Statement

Players Alice and Bob play a game using sequences $L$ and $R$ of length $N$, as follows.

• The game consists of $N$ turns.
• If $i$ is odd, turn $i$ is played by Alice; if $i$ is even, turn $i$ is played by Bob.
• Initially, there is a pile with some number of stones.
• For $i=1,2,\dots,N$ in this order, they perform the following operation (called turn $i$):
• The player who plays turn $i$ takes an integer number of stones between $L_i$ and $R_i$, inclusive, from the pile.
  • If the player cannot take stones satisfying the above, they lose, and the other player wins.
• If neither player has lost by the end of turn $N$, the game ends in a draw.

Before the game starts, both players are informed of the sequences $L$ and $R$ and the number of stones in the pile at the start of the game.

It can be proved that the game has exactly one of the following three consequences:

• Alice ... Alice has a winning strategy.
• Bob ... Bob has a winning strategy.
• Draw ... Neither player has a winning strategy.

Answer $Q$ queries about this game. The $i$-th query is as follows:

• Assume that the pile contains $C_i$ stones at the start of the game. Report the consequence of the game: Alice, Bob, or Draw.

Constraints

• $N$, $L_i$, $R_i$, $Q$, and $C_i$ are integers.
• $1 \le N \le 3 \times 10^5$
• $1 \le L_i \le R_i \le 10^9$
• $1 \le Q \le 3 \times 10^5$
• $1 \le C_i \le \sum_{i=1}^{N} R_i$

Input

The input is given from Standard Input in the following format:

N
L_1 R_1
L_2 R_2
\vdots
L_N R_N
Q
C_1
C_2
\vdots
C_Q

Output

Print $Q$ lines. The $i$-th line should contain the answer to the $i$-th query.