Description: There are $$$n$$$ villages lying equidistant on a circle in the middle of a thick, impassable forest. From ancient times, it was impossible to move from one village to another, but technical progress has changed a lot. Now, there is a technology to build passable trails in the forest. The building process consists of $$$m$$$ events. Each event is either building a trail or querying if two villages are connected. Trails are built as straight lines connecting two villages. After a trail is built, anybody can walk along the trail from one village to another. Moreover, if two trails cross, anybody can turn at the intersection, and if other trails leave a village you have just reached, they can also be used to walk along. So, for example, if villages are numbered $$$1$$$ to $$$6$$$ in the order around the circle, and there are trails $$$1$$$ to $$$3$$$, $$$2$$$ to $$$4$$$, and $$$4$$$ to $$$6$$$, then all villages, except the $$$5$$$-th, are reachable from the $$$1$$$-st village. Given a list of $$$m$$$ events, for each query, find if two given villages are reachable from each other at that moment. Input Format: The first line contains two integers $$$n$$$ ($$$2 \le n \le 2\cdot 10^5$$$) and $$$m$$$ ($$$1 \le m \le 3\cdot 10^5$$$) — the number of villages and the number of events respectively. Next $$$m$$$ lines contain events. Each event description consists of three integers $$$e$$$ ($$$e$$$ is $$$1$$$ or $$$2$$$), $$$v$$$ ($$$1 \le v \le n$$$), and $$$u$$$ ($$$1 \le u \le n$$$, $$$u \ne v$$$). If $$$e = 1$$$, then the event is building a trail between villages $$$v$$$ and $$$u$$$. If $$$e = 2$$$, then the event is a query if the villages $$$v$$$ and $$$u$$$ are connected. It is guaranteed that each trail is built at most once. Villages are numbered $$$1$$$ to $$$n$$$ in clockwise order around the circle. Output Format: For each query print one character '0' if villages are not reachable, and '1' if villages are reachable from each other. Print answers for all queries as a single string in one line. Note: None