Codeforces Round #325 (Div. 1) 解题报告

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A. Gennady the Dentist
题意：有n个孩子排队看病，每次排在第一的孩子进去看病，然后他会哭，最后在他之后的孩子的p值会依次减少vi,vi-1,vi-2……，0,0,0,0,……0。当某个孩子的p<0，则这个孩子也会哭，然后在他之后的所有孩子的p值都会减少di。问，最后医生能够给几个孩子看病。
做法：for套for，暴力模拟

B. Phillip and Trains
题意：3*n的网格，s在最左端某处，每次他可以往右走一步，然后再或上或下走一步或不动。有k个火车从右往左开，每次可以走两步。s先走，火车再走,s又走，火车又走，以此类推。问,s是否能够走到最右端。
做法：dp[r][c][t]，在时间t走到r行c列，这个状态能否走到最右断。

C. Alice, Bob, Oranges and Apples
题意：袋子里有x个苹果，y个橘子。a有一个苹果，b有一个橘子。每次你选择一个人把他的水果都给另一个人，然后他再从袋子里拿走他原来的水果数量。问，是否有方法把袋子里的水果刚好拿完。
做法：画一棵树根的三个儿子从左往右结点代表的数对分别是(0,1),(1,1),(1,0)的解答树，只需要判断给出的(x,y)是不是在这棵树中即可。判断方法就是若a>b，则走到(a-b,b)，若a<b，则走到(a,b-a)，只需要看能否走到(1,1)就知道这个结点是否存在。

D. Lizard Era: Beginning
题意：有n把游戏，每把有三个人的分数，你可以选择任意两个保留。没把都要选择，问，最后能否使得三个人的分数之和一样，且a的分数之和最大。

做法：先暴力出n/2的情况存到map[(b跟a的分数差，c跟a的分数差),(a的分数，把选择情况状压)]里，再暴力出剩下的情况，在map中看能否找到合适的使得他们组合在一起满足要求，不断用a的分数更新最大值即可。

Gennady is one of the best child dentists in Berland. Today n children got an appointment with him, they lined up in front of his office.

All children love to cry loudly at the reception at the dentist. We enumerate the children with integers from 1 to n in the order they go in the line. Every child is associated with the value of his cofidence pi. The children take turns one after another to come into the office; each time the child that is the first in the line goes to the doctor.

While Gennady treats the teeth of the i-th child, the child is crying with the volume of vi. At that the confidence of the first child in the line is reduced by the amount of vi, the second one — by value vi - 1, and so on. The children in the queue after the vi-th child almost do not hear the crying, so their confidence remains unchanged.

If at any point in time the confidence of the j-th child is less than zero, he begins to cry with the volume of dj and leaves the line, running towards the exit, without going to the doctor's office. At this the confidence of all the children after the j-th one in the line is reduced by the amount of dj.

All these events occur immediately one after the other in some order. Some cries may lead to other cries, causing a chain reaction. Once in the hallway it is quiet, the child, who is first in the line, goes into the doctor's office.

Help Gennady the Dentist to determine the numbers of kids, whose teeth he will cure. Print their numbers in the chronological order.

Input

The first line of the input contains a positive integer n (1 ≤ n ≤ 4000) — the number of kids in the line.

Next n lines contain three integers each vi, di, pi (1 ≤ vi, di, pi ≤ 106) — the volume of the cry in the doctor's office, the volume of the cry in the hall and the confidence of the i-th child.

Output

In the first line print number k — the number of children whose teeth Gennady will cure.

In the second line print k integers — the numbers of the children who will make it to the end of the line in the increasing order.

Sample test(s)
input
54 2 24 1 25 2 43 3 55 1 2
output
21 3 
input
54 5 15 3 94 1 22 1 84 1 9
output
41 2 4 5 

Note

In the first example, Gennady first treats the teeth of the first child who will cry with volume 4. The confidences of the remaining children will get equal to - 2, 1, 3, 1, respectively. Thus, the second child also cries at the volume of 1 and run to the exit. The confidence of the remaining children will be equal to 0, 2, 0. Then the third child will go to the office, and cry with volume 5. The other children won't bear this, and with a loud cry they will run to the exit.

In the second sample, first the first child goes into the office, he will cry with volume 4. The confidence of the remaining children will be equal to 5, - 1, 6, 8. Thus, the third child will cry with the volume of 1 and run to the exit. The confidence of the remaining children will be equal to 5, 5, 7. After that, the second child goes to the office and cry with the volume of 5. The confidences of the remaining children will be equal to 0, 3. Then the fourth child will go into the office and cry with the volume of 2. Because of this the confidence of the fifth child will be 1, and he will go into the office last.

The mobile application store has a new game called "Subway Roller".

The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.

All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.

Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.

$\text{[math]}$

Input

Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 ≤ t ≤ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) — the number of sets.

Then follows the description of t sets of the input data.

The first line of the description of each set contains two integers n, k (2 ≤ n ≤ 100, 1 ≤ k ≤ 26) — the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.

Output

For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.

Sample test(s)
input
216 4...AAAAA........s.BBB......CCCCC........DDDDD...16 4...AAAAA........s.BBB....CCCCC.........DDDDD....
output
YESNO
input
210 4s.ZZ...........AAABB.YYYYYY...10 4s.ZZ..........AAAABB.YYYYYY...
output
YESNO

Note

In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.

Note that in this problem the challenges are restricted to tests that contain only one testset.

Alice and Bob decided to eat some fruit. In the kitchen they found a large bag of oranges and apples. Alice immediately took an orange for herself, Bob took an apple. To make the process of sharing the remaining fruit more fun, the friends decided to play a game. They put multiple cards and on each one they wrote a letter, either 'A', or the letter 'B'. Then they began to remove the cards one by one from left to right, every time they removed a card with the letter 'A', Alice gave Bob all the fruits she had at that moment and took out of the bag as many apples and as many oranges as she had before. Thus the number of oranges and apples Alice had, did not change. If the card had written letter 'B', then Bob did the same, that is, he gave Alice all the fruit that he had, and took from the bag the same set of fruit. After the last card way removed, all the fruit in the bag were over.

You know how many oranges and apples was in the bag at first. Your task is to find any sequence of cards that Alice and Bob could have played with.

Input

The first line of the input contains two integers, x, y (1 ≤ x, y ≤ 1018, xy > 1) — the number of oranges and apples that were initially in the bag.

Output

Print any sequence of cards that would meet the problem conditions as a compressed string of characters 'A' and 'B. That means that you need to replace the segments of identical consecutive characters by the number of repetitions of the characters and the actual character. For example, string AAABAABBB should be replaced by string 3A1B2A3B, but cannot be replaced by 2A1A1B2A3B or by3AB2A3B. See the samples for clarifications of the output format. The string that you print should consist of at most 106 characters. It is guaranteed that if the answer exists, its compressed representation exists, consisting of at most 106 characters. If there are several possible answers, you are allowed to print any of them.

If the sequence of cards that meet the problem statement does not not exist, print a single word Impossible.

Sample test(s)
input
1 4
output
3B
input
2 2
output
Impossible
input
3 2
output
1A1B

Note

In the first sample, if the row contained three cards with letter 'B', then Bob should give one apple to Alice three times. So, in the end of the game Alice has one orange and three apples, and Bob has one apple, in total it is one orange and four apples.

In second sample, there is no answer since one card is not enough for game to finish, and two cards will produce at least three apples or three oranges.

In the third sample, cards contain letters 'AB', so after removing the first card Bob has one orange and one apple, and after removal of second card Alice has two oranges and one apple. So, in total it is three oranges and two apples.

In the game Lizard Era: Beginning the protagonist will travel with three companions: Lynn, Meliana and Worrigan. Overall the game has nmandatory quests. To perform each of them, you need to take exactly two companions.

The attitude of each of the companions to the hero is an integer. Initially, the attitude of each of them to the hero of neutral and equal to 0. As the hero completes quests, he makes actions that change the attitude of the companions, whom he took to perform this task, in positive or negative direction.

Tell us what companions the hero needs to choose to make their attitude equal after completing all the quests. If this can be done in several ways, choose the one in which the value of resulting attitude is greatest possible.

Input

The first line contains positive integer n (1 ≤ n ≤ 25) — the number of important tasks.

Next n lines contain the descriptions of the tasks — the i-th line contains three integers li, mi, wi — the values by which the attitude of Lynn, Meliana and Worrigan respectively will change towards the hero if the hero takes them on the i-th task. All the numbers in the input are integers and do not exceed 107 in absolute value.

Output

If there is no solution, print in the first line "Impossible".

Otherwise, print n lines, two characters is each line — in the i-th line print the first letters of the companions' names that hero should take to complete the i-th task ('L' for Lynn, 'M' for Meliana, 'W' for Worrigan). Print the letters in any order, if there are multiple solutions, print any of them.

Sample test(s)
input
31 0 00 1 00 0 1
output
LMMWMW
input
70 8 95 9 -26 -8 -79 4 5-4 -9 9-4 5 2-6 8 -7
output
LMMWLMLWMWLMLW
input
21 0 01 1 0
output
Impossible

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