An interstellar relay network is built one handshake at a time. Whenever two beacons agree to relay for each other, one beacon sends a handshake request and the other beacon accepts it, and from that moment the two beacons are linked to each other. No unordered pair of beacons ever repeats a handshake, and a beacon never sends a handshake to itself. Mission control wants to know which beacon (or beacons) ended up with the most links once every handshake in the log has been processed.

Input format

• Line 1 contains a single integer n, the number of handshake records in the log.
• Each of the next n lines contains two integers u and v, meaning beacon u sent a handshake that beacon v accepted, permanently linking the two beacons. Every unordered pair {u, v} appears at most once across the whole log, and u ≠ v for every record.

Output format

Print two lines:

• The first line contains a single integer: the maximum total number of links held by any one beacon (a beacon's links are counted regardless of whether it was the sender or the accepter of each handshake).
• The second line contains the ids of every beacon that reaches that maximum, in strictly ascending order, separated by single spaces.

Constraints

• 1 ≤ n ≤ 2 × 10^5
• 1 ≤ u, v ≤ 2 × 10^5
• u ≠ v for every record
• No unordered pair {u, v} appears more than once in the log

3
1 2
3 2
3 4

2
2 3

1
1 2

1
1 2