H. Can You Win
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There is a directed graph consisting of $$$n$$$ levels. Each level $$$i$$$ contains $$$a_i$$$ nodes arranged in a linear sequence.

  • Within each level, node $$$j$$$ in level $$$i$$$ has a directed edge to node $$$j+1$$$ for $$$1 \le j \lt a_i$$$.
  • Every node in level $$$i$$$ has a directed edge to the first node of level $$$i+1$$$, for $$$1 \le i \lt n$$$.
For example, if n = 3 and a=[3,3,2], then the graph becomes:
  • Level 1: nodes 1 to 3.
  • Level 2: nodes 4 to 6.
  • Level 3: nodes 7 and 8.

Alhelue and Ahdali are playing a game on a graph like this. Initially, a stone is placed at the first node in level $$$1$$$. Each player, on their turn, selects a node neighbor to the current stone position and moves the stone directly to that node.

The goal is to move the stone to the last node in level $$$n$$$. The player who performs this final move wins.

You are given:

  • An integer $$$n$$$ — the number of levels in the graph.
  • An array $$$a = [a_1, a_2, \ldots, a_n]$$$ — where $$$a_i$$$ represents the number of nodes in level $$$i$$$.

Determine which player has a winning strategy assuming both play optimally. The first player always starts.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$), representing the number of test cases.

The first line of each test cases contains an integer $$$n$$$ $$$(1 \le n \le 10^5)$$$.

The second line of each test cases contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ $$$(1 \le a_i \le 10^{18})$$$.

It's guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$10^5$$$.

Output

Print First if the first player has a winning strategy, or Second if the second player will win assuming optimal play.

Example
Input
2
3
4 3 2
1
3
Output
First
Second