Given $n$ non-negative integers $a_1, a_2, \cdots, a_n$.

Magic and Spark play a game. They take turns, and in each turn, a player can remove a number from either the leftmost or the rightmost end of the array. The player with the larger XOR sum of the numbers they have collected wins.

Determine who will win assuming both players play optimally. Output First if the first player wins, Second if the second player wins, and Draw if it is a draw.

Input

The first line contains a positive integer $T$, representing the number of test cases.

For each test case: The first line contains an integer $n$, the length of $a$. The next line contains $n$ integers $a_1, a_2, \cdots, a_n$, representing the sequence $a$.

Output

For each test case, output a single string representing the result.

Examples

Input 1

3
2
3 3
2
3 5
3
4 4 4

Output 1

Draw
First
Second

Subtasks

For $100\%$ of the data, $1 \leq T \leq 40$, $1 \le n \le 5 \times 10^4$, $0 \le a_i < 2^{31}$.

• Subtask #1 (15 points): $n \le 15$.
• Subtask #2 (20 points): $n \le 10^3$.
• Subtask #3 (25 points): Each $a_i$ is guaranteed to be uniformly random in the range $[0, 2^{31}-1]$.
• Subtask #4 (40 points): No special restrictions.