H. Nim with Special Numberstime limit per test8 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputLet's recall the rules of the game "Nim". The game is played by two players who take turns. They have a certain number of piles of stones (the piles can be of the same size or different sizes; the size is defined as the number of stones in a pile). On their turn, a player must choose any non-empty pile of stones and remove any number of stones from it (at least one). The player who cannot make a move loses.In this problem, a modified version of the game will be used. There is a special set of numbers $$$S$$$ that prohibits certain moves. For each number $$$s_i$$$ in this set, if the current size of the pile of stones is strictly greater than $$$s_i$$$, it cannot be made strictly less than $$$s_i$$$ in one move. In other words, if the current size of the pile is $$$x$$$, and the player tries to make a move that results in a size of $$$y$$$, and $$$x > s_i > y$$$ for some number $$$s_i \in S$$$, such a move is not allowed.Your task is as follows. Initially, the set $$$S$$$ is empty. You need to process queries of three types: add a certain number $$$s_i$$$ to the set; remove a certain number $$$s_i$$$ from the set; determine who will win if this modified version of Nim is played with piles of stones of sizes $$$a_1, a_2, \dots, a_k$$$. Assume that both players play optimally. InputThe first line contains a single integer $$$q$$$ ($$$1 \le q \le 3 \cdot 10^5$$$) — the number of queries.Each query is given in one line in one of the following formats: $$$1$$$ $$$s_i$$$ ($$$1 \le s_i \le 3 \cdot 10^5$$$) — if the number $$$s_i$$$ is in the set $$$S$$$, remove it; otherwise, add it to $$$S$$$; $$$2$$$ $$$k_i$$$ $$$a_{i,1}$$$ $$$a_{i,2}$$$ ... $$$a_{i,k_i}$$$ ($$$1 \le k_i \le 3$$$; $$$1 \le a_{i,j} \le 3 \cdot 10^5$$$) — determine who will win the game if it uses $$$k_i$$$ piles of stones with sizes $$$a_{i,1}, a_{i,2}, \dots, a_{i,k_i}$$$. OutputFor each query of type $$$2$$$, output First if the player making the first move will win, or Second if they will lose.ExampleInput112 2 1 41 22 2 1 42 3 3 1 41 32 3 3 1 42 2 1 41 42 2 1 51 22 2 1 5OutputFirst
Second
Second
Second
Second
First
Second