CF1382B Sequential Nim

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.

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 $ .

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

In the first test case, the first player will win the game. His winning strategy is: 1. 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] $ . 2. 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] $ . 3. 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] $ . 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] $ . 5. 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] $ . 6. The second player will lose the game because all piles will be empty.