Mykola, Vasyl and a maze

Limits: 2 sec., 256 MiB

The Office of «Extralogic» is a real maze. Builders Vasyl and Mykola do not only can’t find a room, they have to paint the door, and got lost!

In order to somehow help the poor builders, the kind employees of «Extralogic» handed an office plan to Mykola and Vasyl. According to the plan, the office consists of $n$ rooms, some of which are connected by a passage. There are $n$ such passages. Each passage is bidirectional. It is guaranteed that there is a path between any pair of rooms in the office, and that there is no more than one passage between any pair of rooms in the office.

Mykola and Vasyl remember that they had to draw a door to one of the rooms, which is located in a cycle. A cycle is a sequence of different office rooms $a_1, a_2, ..., a_k$, that includes a passage between rooms $a_1$ and $a_2$, $a_2$ and $a_3$, ..., $a_{k-1}$ and $a_k$, $a_k$ and $a_1$. Help builders find lists of all office rooms that belong in at least one cycle.

Input

First line contains one integer $n$ – number of rooms in the ofice.

Next $n$ lines contain two integers $a_i$ and $b_i$ – describes $i$-th passage between rooms $a_i$ and $b_i$.

Output

In first line print one integer $k$ – number of rooms which belongs to at least one cycle.

In second line print $k$ integers – indecies of rooms in ascening order.

Constraints

$30\%$ tests: $3 \le n \le 100$.

$70\%$ tests: $3 \le n \le 10^5$.

For all tests: $1 \le a_i, b_i \le n$.

Samples

Input (stdin) сopy	Output (stdout) сopy
4 1 2 2 3 3 4 4 2	3 2 3 4

Notes

Rooms 2, 3 and 4 belong to a cycle. Room 1 does not belong to any cycle.