Problem Statement

In the hexadecimal system, where the digits ABCDEF corresponding to 10,11,12,13,14, and 15 are used in addition to 0123456789, every integer between 0 and 255 is represented as a 1- or 2-digit numeral.
For example, 0 and 12 are represented as 1-digit hexadecimal numerals 0 and C; 99 and 255 are represented as 2-digit hexadecimals 63 and FF.

Given an integer N between 0 and 255, convert it to an exactly two-digit hexadecimal numeral, prepending leading 0s if necessary.

Notes

The judge is case-sensitive. Specifically, you cannot use abcdef as hexadecimal digits instead of ABCDEF.

Constraints

• 0 \leq N \leq 255
• N is an integer.

Sample Input 1

99

Sample Output 1

63

99 is represented as 63 in hexadecimal.

Sample Input 2

12

Sample Output 2

0C

12 is represented as C in hexadecimal.
Since we ask you to convert it to a two-digit hexadecimal numeral, the answer is 0C, where 0 is prepended to C.

Sample Input 3

0

Sample Output 3

00

Sample Input 4

255

Sample Output 4

FF

Problem Statement

In the figure shown in the image below, are the points numbered a and b directly connected by a line segment?

Constraints

• 1 \leq a \lt b \leq 10
• a and b are integers.

Sample Input 1

4 5

Sample Output 1

Yes

In the figure shown in the Problem Statement, the points numbered 4 and 5 are directly connected by a line segment.
Thus, Yes should be printed.

Sample Input 2

3 5

Sample Output 2

No

In the figure shown in the Problem Statement, the points numbered 3 and 5 are not directly connected by a line segment.
Thus, No should be printed.

Sample Input 3

1 10

Sample Output 3

Yes

Problem Statement

There is a grid with H rows and W columns. Let (i,j) denote the cell at the i-th row from the top and the j-th column from the left.

If S_{i,j} is #, the cell (i,j) is impassable; if it is ., the cell is passable and contains no house; if it is @, the cell is passable and contains a house.

Initially, Santa Claus is in cell (X,Y). He will act according to the string T as follows.

• Let |T| be the length of the string T. For i=1,2,\ldots,|T|, he moves as follows.
  • Let (x,y) be the cell he is currently in.
    • If T_i is U and cell (x-1,y) is passable, move to cell (x-1,y).
    • If T_i is D and cell (x+1,y) is passable, move to cell (x+1,y).
    • If T_i is L and cell (x,y-1) is passable, move to cell (x,y-1).
    • If T_i is R and cell (x,y+1) is passable, move to cell (x,y+1).
    • Otherwise, stay in cell (x,y).

Find the cell where he is after completing all actions, and the number of distinct houses that he passed through or arrived at during his actions. If the same house is passed multiple times, it is only counted once.

Constraints

• 3 \leq H,W \leq 100
• 1 \leq X \leq H
• 1 \leq Y \leq W
• All given numbers are integers.
• Each S_{i,j} is one of #, ., @.
• S_{i,1} and S_{i,W} are # for every 1 \leq i \leq H.
• S_{1,j} and S_{H,j} are # for every 1 \leq j \leq W.
• S_{X,Y}= .
• T is a string of length at least 1 and at most 10^4, consisting of U, D, L, R.

Sample Input 1

5 5 3 4
#####
#...#
#.@.#
#..@#
#####
LLLDRUU

Sample Output 1

2 3 1

Santa Claus behaves as follows:

• T_1= L, so he moves from (3,4) to (3,3). A house is passed.
• T_2= L, so he moves from (3,3) to (3,2).
• T_3= L, but cell (3,1) is impassable, so he stays at (3,2).
• T_4= D, so he moves from (3,2) to (4,2).
• T_5= R, so he moves from (4,2) to (4,3).
• T_6= U, so he moves from (4,3) to (3,3). A house is passed, but it has already been passed.
• T_7= U, so he moves from (3,3) to (2,3).

The number of houses he passed or arrived during his actions is 1.

Sample Input 2

6 13 4 6
#############
#@@@@@@@@@@@#
#@@@@@@@@@@@#
#@@@@.@@@@@@#
#@@@@@@@@@@@#
#############
UURUURLRLUUDDURDURRR

Sample Output 2

3 11 11

Sample Input 3

12 35 7 10
###################################
#.................................#
#..........@......................#
#......@................@.........#
#.............##............@.....#
#...##........##....##............#
#...##........##....##.......##...#
#....##......##......##....##.....#
#....##......##......##..##.......#
#.....#######.........###.........#
#.................................#
###################################
LRURRRUUDDULUDUUDLRLRDRRLULRRUDLDRU

Sample Output 3

4 14 1

Problem Statement

AtCoder currently holds four series of regular contests: ABC, ARC, AGC, and AHC.

What is the series of regular contests currently held by AtCoder in addition to S_1, S_2, and S_3?

Constraints

• Each of S_1, S_2, and S_3 is ABC, ARC, AGC, or AHC.
• S_1, S_2, and S_3 are pairwise different.

Sample Input 1

ARC
AGC
AHC

Sample Output 1

ABC

Given in input are ARC, AGC, and AHC. The rest is ABC.

Sample Input 2

AGC
ABC
ARC

Sample Output 2

AHC

Problem Statement

You are given a grid with N rows and N columns, where N is an even number. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left.

Each cell is painted black or white. If A_{i, j} = #, cell (i, j) is black; if A_{i, j} = ., it is white.

Find the color of each cell after performing the following operation for i = 1, 2, \ldots, \frac{N}{2} in this order.

• For all pairs of integers x, y between i and N + 1 - i, inclusive, replace the color of cell (y, N + 1 - x) with the color of cell (x, y). Perform these replacements simultaneously for all such pairs x, y.

Constraints

• N is an even number between 2 and 3000, inclusive.
• Each A_{i, j} is # or ..

Sample Input 1

8
.......#
.......#
.####..#
.####..#
.##....#
.##....#
.#######
.#######

Sample Output 1

........
#######.
#.....#.
#.###.#.
#.#...#.
#.#####.
#.......
########

The operations change the colors of the grid cells as follows:

.......#   ........   ........   ........   ........
.......#   ######..   #######.   #######.   #######.
.####..#   ######..   #....##.   #.....#.   #.....#.
.####..# → ##..##.. → #....##. → #.##..#. → #.###.#.
.##....#   ##..##..   #..####.   #.##..#.   #.#...#.
.##....#   ##......   #..####.   #.#####.   #.#####.
.#######   ##......   #.......   #.......   #.......
.#######   ########   ########   ########   ########

Sample Input 2

6
.#.#.#
##.#..
...###
###...
..#.##
#.#.#.

Sample Output 2

#.#.#.
.#.#.#
#.#.#.
.#.#.#
#.#.#.
.#.#.#

Sample Input 3

12
.......#.###
#...#...#..#
###.#..#####
..#.#.#.#...
.#.....#.###
.......#.#..
#...#..#....
#####.......
...#...#.#.#
..###..#..##
#..#.#.#.#.#
.####.......

Sample Output 3

.#..##...##.
#.#.#.#.#...
###.##..#...
#.#.#.#.#...
#.#.##...##.
............
............
.###.###.###
...#...#.#..
.###...#.###
...#...#...#
.###...#.###

Problem Statement

We have a grid with H horizontal rows and W vertical columns. (i, j) denotes the square at the i-th row from the top and j-th column from the left.
(i,j) has a character G_{i,j} written on it. G_{i,j} is U, D, L, or R.

You are initially at (1,1). You repeat the following operation until you cannot make a move.

Let (i,j) be the square you are currently at.
If G_{i,j} is U and i \neq 1, move to (i-1,j).
If G_{i,j} is D and i \neq H, move to (i+1,j).
If G_{i,j} is L and j \neq 1, move to (i,j-1).
If G_{i,j} is R and j \neq W, move to (i,j+1).
Otherwise, you cannot make a move.

Print the square you end up at when you cannot make a move.
If you indefinitely repeat moving, print -1 instead.

Constraints

• 1 \leq H, W \leq 500
• G_{i,j} is U, D, L, or R.
• H and W are integers.

Sample Input 1

2 3
RDU
LRU

Sample Output 1

1 3

You will move as (1, 1) \to (1, 2) \to (2, 2) \to (2, 3) \to (1, 3), ending up here, so the answer is (1, 3).

Sample Input 2

2 3
RRD
ULL

Sample Output 2

-1

You will indefinitely repeat moving as (1, 1) \to (1, 2) \to (1, 3) \to (2, 3) \to (2, 2) \to (2, 1) \to (1, 1) \to (1, 2) \to \dots, so -1 should be printed in this case.

Sample Input 3

9 44
RRDDDDRRRDDDRRRRRRDDDRDDDDRDDRDDDDDDRRDRRRRR
RRRDLRDRDLLLLRDRRLLLDDRDLLLRDDDLLLDRRLLLLLDD
DRDLRLDRDLRDRLDRLRDDLDDLRDRLDRLDDRLRRLRRRDRR
DDLRRDLDDLDDRLDDLDRDDRDDDDRLRRLRDDRRRLDRDRDD
RDLRRDLRDLLLLRRDLRDRRDRRRDLRDDLLLLDDDLLLLRDR
RDLLLLLRDLRDRLDDLDDRDRRDRLDRRRLDDDLDDDRDDLDR
RDLRRDLDDLRDRLRDLDDDLDDRLDRDRDLDRDLDDLRRDLRR
RDLDRRLDRLLLLDRDRLLLRDDLLLLLRDRLLLRRRRLLLDDR
RRRRDRDDRRRDDRDDDRRRDRDRDRDRRRRRRDDDRDDDDRRR

Sample Output 3

9 5

Problem Statement

You initially have an empty string S.
Additionally, there are bags 1, 2, \dots, N, each containing some strings.
Bag i contains A_i strings S_{i,1}, S_{i,2}, \dots, S_{i,A_i}.

You will repeat the following steps for i = 1, 2, \dots, N:

• Choose and perform one of the following two actions:
  • Pay 1 yen, select exactly one string from bag i, and concatenate it to the end of S.
  • Do nothing.

Given a string T, find the minimum amount of money required to make the final S equal T.
If there is no way to make the final S equal T, print -1.

Constraints

• T is a string consisting of lowercase English letters with length between 1 and 100, inclusive.
• N is an integer between 1 and 100, inclusive.
• A_i is an integer between 1 and 10, inclusive.
• S_{i,j} is a string consisting of lowercase English letters with length between 1 and 10, inclusive.

Sample Input 1

abcde
3
3 ab abc abcd
4 f c cd bcde
2 e de

Sample Output 1

2

For example, doing the following makes the final S equal T with two yen, which can be shown to be the minimum amount required.

• For i=1, select abc from bag 1 and concatenate it to the end of S, making S= abc.
• For i=2, do nothing.
• For i=3, select de from bag 3 and concatenate it to the end of S, making S= abcde.

Sample Input 2

abcde
3
2 ab abc
3 f c bcde
1 e

Sample Output 2

-1

There is no way to make the final S equal T, so print -1.

Sample Input 3

aaabbbbcccc
6
2 aa aaa
2 dd ddd
2 ab aabb
4 bbaa bbbc bbb bbcc
2 cc bcc
3 ccc cccc ccccc

Sample Output 3

4

Problem Statement

You are given a directed graph with N vertices and M edges. The i-th edge (1 \leq i \leq M) is a directed edge from vertex u _ i to vertex v _ i.

Initially, you are at vertex 1. You want to repeat the following operations until you reach vertex N:

• Perform one of the two operations below:
  • Move along a directed edge from your current vertex. This incurs a cost of 1. More precisely, if you are at vertex v, choose a vertex u such that there is a directed edge from v to u, and move to vertex u.
  • Reverse the direction of all edges. This incurs a cost of X. More precisely, if and only if there was a directed edge from v to u immediately before this operation, there is a directed edge from u to v immediately after this operation.

It is guaranteed that, for the given graph, you can reach vertex N from vertex 1 by repeating these operations.

Find the minimum total cost required to reach vertex N.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq M \leq 2 \times 10^5
• 1 \leq X \leq 10^9
• 1 \leq u _ i \leq N \ (1 \leq i \leq M)
• 1 \leq v _ i \leq N \ (1 \leq i \leq M)
• For the given graph, it is guaranteed that you can reach vertex N from vertex 1 by the operations described.
• All input values are integers.

Sample Input 1

5 6 5
1 2
2 4
3 1
3 5
4 3
5 2

Sample Output 1

4

The given graph looks like this:

You can reach vertex 5 with a total cost of 4 by doing the following:

• Move to vertex 2 at a cost of 1.
• Move to vertex 4 at a cost of 1.
• Move to vertex 3 at a cost of 1.
• Move to vertex 5 at a cost of 1.

It is impossible to reach vertex 5 with a total cost of 3 or less, so print 4.

Sample Input 2

5 6 1
1 2
2 4
3 1
3 5
4 3
5 2

Sample Output 2

3

The graph is the same as in Sample 1, but the cost to reverse edges is different.

You can reach vertex 5 with a total cost of 3 as follows:

• Move to vertex 2 at a cost of 1.
• Reverse all edges at a cost of 1.
• Move to vertex 5 at a cost of 1.

It is impossible to reach vertex 5 with a total cost of 2 or less, so print 3.

Sample Input 3

8 7 613566756
2 1
2 3
4 3
4 5
6 5
6 7
8 7

Sample Output 3

4294967299

Note that the answer may exceed the 32-bit integer range.

Sample Input 4

20 13 5
1 3
14 18
18 17
12 19
3 5
4 6
13 9
8 5
14 2
20 18
8 14
4 9
14 8

Sample Output 4

21

Problem Statement

There are N scaffolds numbered from 1 to N arranged in a line. The height of scaffold i(1 \leq i \leq N) is H_i.

Takahashi decides to play a game of moving on the scaffolds. Initially, he freely chooses an integer i(1 \leq i \leq N) and gets on scaffold i.

When he is on scaffold i at some point, he can choose an integer j(1 \leq j \leq N) satisfying the following condition and move to scaffold j:

• H_j \leq H_i - D and 1 \leq |i-j| \leq R.

Find the maximum number of moves he can make when he repeats moving until he can no longer move.

Constraints

• 1 \leq N \leq 5 \times 10^5
• 1 \leq D,R \leq N
• H is a permutation of (1,2,\ldots,N).
• All input values are integers.

Sample Input 1

5 2 1
5 3 1 4 2

Sample Output 1

2

Takahashi initially gets on scaffold 1 and can move between the scaffolds as follows:

• First move: Since H_2 \leq H_1 -D and |2-1| \leq R, he can move to scaffold 2. Move from scaffold 1 to scaffold 2.
• Second move: Since H_3 \leq H_2 -D and |3-2| \leq R, he can move to scaffold 3. Move from scaffold 2 to scaffold 3.
• Since the height of scaffold 3 is 1, he can no longer move.

As shown above, he can move 2 times. Also, no matter how he chooses the scaffolds to move to, he cannot move 3 or more times. Therefore, output 2.

Sample Input 2

13 3 2
13 7 10 1 9 5 4 11 12 2 8 6 3

Sample Output 2

3