Calvinball Championship, Again 2

No attempts yetTime limit1sMemory limit256 MB

Problem

A Calvinball game has nn players. Some pairs dislike each other (symmetrically). Split everyone into teams so no disliking pair shares a team, using as few teams as possible. Output any optimal division.

Input

Line 1: nn and mm, the player count and dislike-pair count. Next mm lines: distinct players aia_i and bib_i who dislike each other (1ai,bin1 \leq a_i, b_i \leq n).

Output

Line 1: team count tt. Next tt lines list players on each team in any order. Teams and players within a team may appear in any order.

Note

Batch data may be judged separately; the sample above is a normal stdin/stdout case.