Problem 1. Searching for soulmates 

Farmer John's cows each want to find their soulmate -- another cow with similar characteristics with whom they are maximally compatible. Each cow's personality is described by an integer pipi (1≤pi≤1018). Two cows with the same personality are soulmates. A cow can change her personality via a "change operation" by multiplying by 2, dividing by 2 (if pi is even), or adding 1.

Farmer John initially pairs his cows up in an arbitrary way. He is curious how many change operations would be needed to make each pair of cows into soulmates. For each pairing, decide the minimum number of change operations the first cow in the pair must make to become soulmates with the second cow.

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

The first line contains N (1≤N≤10), the number of pairs of cows. Each of the remaining N lines describes a pair of cows in terms of two integers giving their personalities. The first number indicates the personality of the cow that must be changed to match the second.

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

Please write N lines of output. For each pair, print the minimum number of operations required for the first cow to make her personality match that of the second.

SAMPLE INPUT:

6
31 13
12 8
25 6
10 24
1 1
997 120

SAMPLE OUTPUT:

8
3
8
3
0
20

For the first test case, an optimal sequence of changes is 31⟹32⟹16⟹8⟹9⟹10⟹11⟹12⟹1331⟹32⟹16⟹8⟹9⟹10⟹11⟹12⟹13.

For the second test case, an optimal sequence of changes is 12⟹6⟹7⟹812⟹6⟹7⟹8.

SCORING:

• Test cases 1-4 satisfy pi≤10.
• Test cases 5-12 satisfy no additional constraints.

Problem 2. Cow Frisbee

Farmer John's NN cows (N≤3×105)N≤3×105) have heights 1,2,…,N1,2,…,N. One day, the cows are standing in a line in some order playing frisbee; let h1…hNh1…hN denote the heights of the cows in this order (so the hh's are a permutation of 1…N1…N).

Two cows at positions ii and jj in the line can successfully throw the frisbee back and forth if and only if every cow between them has height lower than min(hi,hj)min(hi,hj).

Please compute the sum of distances between all pairs of locations i

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

The first line of input contains a single integer NN. The next line of input contains h1…hNh1…hN, separated by spaces.

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

Output the sum of distances of all pairs of locations at which there are cows that can throw the frisbee back and forth. Note that the large size of integers involved in this problem may require the use of 64-bit integer data types (e.g., a "long long" in C/C++).

SAMPLE INPUT:

7
4 3 1 2 5 6 7

SAMPLE OUTPUT:

24

The pairs of successful locations in this example are as follows:

(1, 2), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (4, 5), (5, 6), (6, 7)

SCORING

• Test cases 1-3 satisfy N≤5000N≤5000.
• Test cases 4-11 satisfy no additional constraints.

Problem 3. Cereal 2

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≠sifi≠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.