Farmer John's cows like nothing more than cereal for breakfast! In fact, the cows have such large appetites that they will each eat an entire box of cereal for a single meal.The farm has recently received a shipment with MM different types of cereal (2≤M≤105)(2≤M≤105). Unfortunately, there is only one box of each cereal! Each of the NN cows (1≤N≤105)(1≤N≤105) has a favorite cereal and a second favorite cereal. When given a selection of cereals to choose from, a cow performs the following process:

1. If the box of her favorite cereal is still available, take it and leave.
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 any cereal.

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.

INPUT FORMAT (input arrives from the terminal / stdin):

The first line contains two space-separated integers NN and M.M.For each 1≤i≤N,1≤i≤N, the ii-th line contains two space-separated integers fifi and sisi (1≤fi**,si≤M1≤fi,si≤M and fi≠si**fi≠si) denoting the favorite and second-favorite cereals of the ii-th cow.

OUTPUT FORMAT (print output to the terminal / stdout):

Print the minimum number of cows that go hungry, followed by any permutation of 1…N1…N that achieves this minimum. If there are multiple permutations, any one will be accepted.

SAMPLE INPUT:

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

SAMPLE OUTPUT:

1
1
3
2
8
4
6
5
7

In this example, there are 88 cows and 1010 types of cereal.

Note that we can effectively solve for the first three cows independently of the last five, since they share no favorite cereals in common.

If the first three cows choose in the order [1,2,3][1,2,3], then cow 11 will choose cereal 22, cow 22 will choose cereal 33, and cow 33 will go hungry.

If the first three cows choose in the order [1,3,2][1,3,2], then cow 11 will choose cereal 22, cow 33 will choose cereal 33, and cow 22 will choose cereal 44; none of these cows will go hungry.

Of course, there are other permutations that result in none of the first three cows going hungry. For example, if the first three cows choose in the order [3,1,2][3,1,2] then cow 33 will choose cereal 22, cow 11 will choose cereal 11, and cow 22 will choose cereal 33; again, none of cows [1,2,3][1,2,3] will go hungry.

It can be shown that out of the last five cows, at least one must go hungry.

SCORING:

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