Sequential Nim (Codeforces 1382B)
Tags: DP, games

There 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".

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. 

Sample Inputs:
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

Sample Outputs:
First
Second
Second
First
First
Second
First

Solution (Python):
for s in [*open(0)][2::2]:
    i = 0
    while '1 ' == s[i:i + 2]:
        i += 2
    print('FSiercsotn d'[i // 2 % 2::2])

Solution (Python):
for s in [*open(0)][2::2]:
    i = 0
    while '1 ' == s[i:i + 2]:
        i += 2
    print('FSiercsotn d'[i // 2 % 2::2])

Solution (Python):
for s in [*open(0)][2::2]:
    i = 0
    while '1 ' == s[i:i + 2]:
        i += 2
    print(['First', 'Second'][i // 2 % 2])