GL is making a new game called “Evil Resident”. This game contains $N$ chapters and the $i$-th chapter has $A_i$ evil residents initially.

GL wants to change the number of evil residents in certain chapters but also ensure the game has an increasing difficulty progression, that is the number of evil residents should be increasing throughout each chapter. Therefore, GL will perform $Q$ operations of the following types:

• 1 L R X :
  If $X \ge 0$, $A_i$ is increased by $X$ for $L \le i \le R$.
  If $X \lt 0$, $A_i$ is decreased by $-X$ for $L \le i \le R$.


• 2 : If $A_1 \lt A_2 \lt ... \lt A_N$, then output Good Game, otherwise output Bad Game.

Help GL perform the operations and report the outputs in order.

Input

The first line of input contains two integers, $N$ and $Q$.
The second line of input contains $N$ integers, where the $i$-th integer is $A_i$.
The following $Q$ lines of input each contains one of the operations described above.

Output

For each query of type 2, output Good Game if the requirement is satisfied, otherwise output Bad Game.

Subtasks

For all test cases:
$1 \le N, Q \le 10^5$
$0 \le |X|, A_i \le 10^9$
$1 \le L \le R \le N$
It is guaranteed that $A_i$ is always non-negative.

Subtask 1 (30 pts): $1 \le N, Q \le 1000$
Subtask 2 (30 pts): There are at most $10$ type 2 operations.
Subtask 3 (30 pts): For each query of type 1, $R - L + 1 \le 10$
Subtask 4 (10 pts): No additional constraints