Finding the Stop Key

A factory robot has malfunctioned and is running out of control. To stop it, you must find which of the 8 keys is the stop key. The robot has also started shuffling the keys, and it moves them too fast for the human eye to follow. Fortunately, you know the algorithm the robot uses to shuffle the keys and the starting position of the stop key.

Each key is numbered from $0$ to $7$, and the keys sit on distinct points $P_0, P_1, \cdots, P_7$. The robot reads a sequence of length $N$ given in advance, one command at a time from the front, and shuffles the keys with each command. A command that encodes the integer $2^i + 2^j$ with $i < j$ swaps the positions of key $i$ and key $j$. That is, if key $i$ is at $P_k$ and key $j$ is at $P_l$, then key $i$ moves to $P_l$ and key $j$ moves to $P_k$.

The sequence may contain invalid commands. A command $x$ is invalid if no pair of integers $0 \leq i < j \leq 7$ satisfies $x = 2^i + 2^j$. When the robot recognizes an invalid command, it ignores it and moves on to the next command.

The first line contains $N$ ($1 \leq N \leq 200\,000$), the length of the command sequence.

The second line contains the commands $a_1, a_2, \cdots, a_N$ separated by spaces ($0 \leq a_i < 256 = 2^8$).

The third line contains $K$ ($0 \leq K \leq 7$), the number of the stop key.

Print $t$ ($0 \leq t \leq 7$), the index of the point $P_t$ where the stop key is located after all commands are applied.