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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 $M$ different types of cereal. Unfortunately, there is only one box of each cereal! Eachof the $N$ 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 $N$ cows that achieves this minimum.

• $2\le M\le 10^5$
• $1\le N\le 10^5$

Input Format

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

For each $1\le i\le N,$ the $i$-th line contains two space-separated integers$f_i$ and $s_i$ ($1\le f_i,s_i\le M$ and $f_i\neq s_i$) denoting the favoriteand second-favorite cereals of the $i$-th cow.

Output Format

Print the minimum number of cows that go hungry, followed by any permutation of$1\ldots N$ 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 $4$ out of $14$ test cases, $N,M\le 100$.
• In $10$ out of $14$ test cases, no additional constraints.

Problem Credit

Problem credits: Dhruv Rohatgi