Let'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 $$$x \gt s_i \gt y$$$ 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.

Input

The 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 $$$a_{i,1}, a_{i,2}, \dots, a_{i,k_i}$$$.

Output

For each query of type $$$2$$$, output First if the player making the first move will win, or Second if they will lose.

Nim with Special Numbers

Examples