#USACOC2223C. Cereal 2

Cereal 2

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Description

Farmer John's cows like nothing more than cereal for breakfast! In fact, thecows have such large appetites that they will each eat an entire box of cerealfor a single meal.

The farm has recently received a shipment with MM different types of cereal. Unfortunately, there is only one box of each cereal! Eachof the NN cows has a favorite cereal and a second favoritecereal. When given a selection of cereals to choose from, a cow performs thefollowing process:

  1. If the box of her favorite cereal is still available, take it andleave.
  2. Otherwise, if the box of her second-favorite cereal is still available, take it and leave.
  3. Otherwise, she will moo with disappointment and leave without taking anycereal.

Find the minimum number of cows that go hungry if you permute them optimally.Also, find any permutation of the NN cows that achieves this minimum.

  • 2M1052\le M\le 10^5
  • 1N1051\le N\le 10^5

Input Format

The first line contains two space-separated integers NN and M.M.

For each 1iN,1\le i\le N, the ii-th line contains two space-separated integersfif_i and sis_i (1fi,siM1\le f_i,s_i\le M and fisif_i\neq s_i) denoting the favoriteand second-favorite cereals of the ii-th cow.

Output Format

Print the minimum number of cows that go hungry, followed by any permutation of1N1\ldots N that achieves this minimum. If there are multiple permutations, anyone will be accepted.

8 10
2 1
3 4
2 3
6 5
7 8
6 7
7 5
5 8
8 10
2 1
3 4
2 3
6 5
7 8
6 7
7 5
5 8

Scoring

  • In 44 out of 1414 test cases, N,M100N,M\le 100.
  • In 1010 out of 1414 test cases, no additional constraints.

Problem Credit

Problem credits: Dhruv Rohatgi