Nika likes the tale of the goldfish. Nika decided that she could draw a goldfish herself. Nika drew each part of the goldfish in the form of polygons without self-intersections. The tail of a goldfish is connected to the body at a single vertex, and the head is connected to the body along one common segment.
Nika was able to number all the vertices, she has got $$$n$$$ of them, but calculating the size of each part of the goldfish turned out to be a difficult task for her. Help Nika calculate how many segments the goldfish's head, trunk and tail consist of.
The first line contains an integer $$$n$$$ $$$(6\leq n \leq 10^5)$$$ — the number of vertices in the fish.
Next, $$$n+2$$$ lines are given, in which pairs of integers $$$a_i$$$, $$$b_i$$$ $$$(1 \leq a_i,~b_i \leq n)$$$ are specified — the numbers of vertices connected by a segment.
It is guaranteed that the head, trunk and tail consist of at least three segments.
It is guaranteed that the head and tail do not have common vertices.
In a single line, print three integers separated by a space – the number of segments in the head, trunk and tail of the goldfish, respectively.
111 21 42 34 39 1011 1011 95 77 94 66 88 104 5
3 7 4
The example goldfish looks like this:
