Codeforces Round 658 (Div. 2) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

dp

games

*1100

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Sequential Nim

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are $$$n$$$ piles of stones, where the $$$i$$$-th pile has $$$a_i$$$ stones. Two people play a game, where they take alternating turns removing stones.

In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.

Input

The first line contains a single integer $$$t$$$ ($$$1\le t\le 1000$$$) — the number of test cases. Next $$$2t$$$ lines contain descriptions of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1\le n\le 10^5$$$) — the number of piles.

The second line of each test case contains $$$n$$$ integers $$$a_1,\ldots,a_n$$$ ($$$1\le a_i\le 10^9$$$) — $$$a_i$$$ is equal to the number of stones in the $$$i$$$-th pile.

It is guaranteed that the sum of $$$n$$$ for all test cases does not exceed $$$10^5$$$.

Output

For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".

Example

Input

7 3 2 5 4 8 1 1 1 1 1 1 1 1 6 1 2 3 4 5 6 6 1 1 2 1 2 2 1 1000000000 5 1 2 2 1 1 3 1 1 1

Output

First Second Second First First Second First

Note

In the first test case, the first player will win the game. His winning strategy is:

- The first player should take the stones from the first pile. He will take $$$1$$$ stone. The numbers of stones in piles will be $$$[1, 5, 4]$$$.
- The second player should take the stones from the first pile. He will take $$$1$$$ stone because he can't take any other number of stones. The numbers of stones in piles will be $$$[0, 5, 4]$$$.
- The first player should take the stones from the second pile because the first pile is empty. He will take $$$4$$$ stones. The numbers of stones in piles will be $$$[0, 1, 4]$$$.
- The second player should take the stones from the second pile because the first pile is empty. He will take $$$1$$$ stone because he can't take any other number of stones. The numbers of stones in piles will be $$$[0, 0, 4]$$$.
- The first player should take the stones from the third pile because the first and second piles are empty. He will take $$$4$$$ stones. The numbers of stones in piles will be $$$[0, 0, 0]$$$.
- The second player will lose the game because all piles will be empty.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/01/2023 09:33:49 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|