Problem Statement

There is a device with a screen that shows a single-digit number, and a button.

When the screen is showing a number k, pressing the button once changes the number on the screen to a_k.

The device currently shows 0. After pressing the button 3 times, what will be shown on the screen?

Constraints

• 0\leq a_i \leq 9
• All values in input are integers.

Sample Input 1

9 0 1 2 3 4 5 6 7 8

Sample Output 1

7

The number on the screen transitions as 0 \rightarrow 9 \rightarrow 8 \rightarrow 7.

Sample Input 2

4 8 8 8 0 8 8 8 8 8

Sample Output 2

4

The number on the screen transitions as 0 \rightarrow 4 \rightarrow 0 \rightarrow 4.

Sample Input 3

0 0 0 0 0 0 0 0 0 0

Sample Output 3

0

Problem Statement

Two characters x and y are called similar characters if and only if one of the following conditions is satisfied:

• x and y are the same character.
• One of x and y is 1 and the other is l.
• One of x and y is 0 and the other is o.

Two strings S and T, each of length N, are called similar strings if and only if:

• for all i\ (1\leq i\leq N), the i-th character of S and the i-th character of T are similar characters.

Given two length-N strings S and T consisting of lowercase English letters and digits, determine if S and T are similar strings.

Constraints

• N is an integer between 1 and 100.
• Each of S and T is a string of length N consisting of lowercase English letters and digits.

Sample Input 1

3
l0w
1ow

Sample Output 1

Yes

The 1-st character of S is l, and the 1-st character of T is 1. These are similar characters.

The 2-nd character of S is 0, and the 2-nd character of T is o. These are similar characters.

The 3-rd character of S is w, and the 3-rd character of T is w. These are similar characters.

Thus, S and T are similar strings.

Sample Input 2

3
abc
arc

Sample Output 2

No

The 2-nd character of S is b, and the 2-nd character of T is r. These are not similar characters.

Thus, S and T are not similar strings.

Sample Input 3

4
nok0
n0ko

Sample Output 3

Yes

Problem Statement

Naohiro had N+1 consecutive integers, one of each, but he lost one of them.

The remaining N integers are given in arbitrary order as A_1,\ldots,A_N. Find the lost integer.

The given input guarantees that the lost integer is uniquely determined.

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq 1000
• All input values are integers.
• The lost integer is uniquely determined.

Sample Input 1

3
2 3 5

Sample Output 1

4

Naohiro originally had four integers, 2,3,4,5, then lost 4, and now has 2,3,5.

Print the lost integer, 4.

Sample Input 2

8
3 1 4 5 9 2 6 8

Sample Output 2

7

Sample Input 3

16
152 153 154 147 148 149 158 159 160 155 156 157 144 145 146 150

Sample Output 3

151

Problem Statement

There were N participants in a contest. The participant ranked i-th had the nickname S_i.
Print the nicknames of the top K participants in lexicographical order.

Constraints

• 1 \leq K \leq N \leq 100
• K and N are integers.
• S_i is a string of length 10 consisting of lowercase English letters.
• S_i \neq S_j if i \neq j.

Sample Input 1

5 3
abc
aaaaa
xyz
a
def

Sample Output 1

aaaaa
abc
xyz

This contest had five participants. The participants ranked first, second, third, fourth, and fifth had the nicknames abc, aaaaa, xyz, a, and def, respectively.

The nicknames of the top three participants were abc, aaaaa, xyz, so print these in lexicographical order: aaaaa, abc, xyz.

Sample Input 2

4 4
z
zyx
zzz
rbg

Sample Output 2

rbg
z
zyx
zzz

Sample Input 3

3 1
abc
arc
agc

Sample Output 3

abc

Problem Statement

There is a directed graph with N vertices and N edges.
The i-th edge goes from vertex i to vertex A_i. (The constraints guarantee that i \neq A_i.)
Find a directed cycle without the same vertex appearing multiple times.
It can be shown that a solution exists under the constraints of this problem.

Notes

The sequence of vertices B = (B_1, B_2, \dots, B_M) is called a directed cycle when all of the following conditions are satisfied:

• M \geq 2
• The edge from vertex B_i to vertex B_{i+1} exists. (1 \leq i \leq M-1)
• The edge from vertex B_M to vertex B_1 exists.
• If i \neq j, then B_i \neq B_j.

Constraints

• All input values are integers.
• 2 \le N \le 2 \times 10^5
• 1 \le A_i \le N
• A_i \neq i

Sample Input 1

7
6 7 2 1 3 4 5

Sample Output 1

4
7 5 3 2

7 \rightarrow 5 \rightarrow 3 \rightarrow 2 \rightarrow 7 is indeed a directed cycle.

Here is the graph corresponding to this input:

Here are other acceptable outputs:

4
2 7 5 3

3
4 1 6

Note that the graph may not be connected.

Sample Input 2

2
2 1

Sample Output 2

2
1 2

This case contains both of the edges 1 \rightarrow 2 and 2 \rightarrow 1.
In this case, 1 \rightarrow 2 \rightarrow 1 is indeed a directed cycle.

Here is the graph corresponding to this input, where 1 \leftrightarrow 2 represents the existence of both 1 \rightarrow 2 and 2 \rightarrow 1:

Sample Input 3

8
3 7 4 7 3 3 8 2

Sample Output 3

3
2 7 8

Here is the graph corresponding to this input:

Problem Statement

There are N stations on a certain line operated by AtCoder Railway. The i-th station (1 \leq i \leq N) from the starting station is named S_i.

Local trains stop at all stations, while express trains may not. Specifically, express trains stop at only M \, (M \leq N) stations, and the j-th stop (1 \leq j \leq M) is the station named T_j.
Here, it is guaranteed that T_1 = S_1 and T_M = S_N, that is, express trains stop at both starting and terminal stations.

For each of the N stations, determine whether express trains stop at that station.

Constrains

• 2 \leq M \leq N \leq 10^5
• N and M are integers.
• S_i (1 \leq i \leq N) is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.
• S_i \neq S_j \, (i \neq j)
• T_1 = S_1 and T_M = S_N.
• (T_1, \dots, T_M) is obtained by removing zero or more strings from (S_1, \dots, S_N) and lining up the remaining strings without changing the order.

Sample Input 1

5 3
tokyo kanda akiba okachi ueno
tokyo akiba ueno

Sample Output 1

Yes
No
Yes
No
Yes

Sample Input 2

7 7
a t c o d e r
a t c o d e r

Sample Output 2

Yes
Yes
Yes
Yes
Yes
Yes
Yes

Express trains may stop at all stations.

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. The state of each cell is represented by the character A_{i,j}, which means the following:

• .: An empty cell.
• #: An obstacle.
• S: An empty cell and the start point.
• T: An empty cell and the goal point.

Takahashi can move from his current cell to a vertically or horizontally adjacent empty cell by consuming 1 energy. He cannot move if his energy is 0, nor can he exit the grid.

There are N medicines in the grid. The i-th medicine is at the empty cell (R_i, C_i) and can be used to set the energy to E_i. Note that the energy does not necessarily increase. He can use the medicine in his current cell. The used medicine will disappear.

Takahashi starts at the start point with 0 energy and wants to reach the goal point. Determine if this is possible.

Constraints

• 1 \leq H, W \leq 200
• A_{i, j} is one of ., #, S, and T.
• Each of S and T exists exactly once in A_{i, j}.
• 1 \leq N \leq 300
• 1 \leq R_i \leq H
• 1 \leq C_i \leq W
• (R_i, C_i) \neq (R_j, C_j) if i \neq j.
• A_{R_i, C_i} is not #.
• 1 \leq E_i \leq HW

Sample Input 1

4 4
S...
#..#
#...
..#T
4
1 1 3
1 3 5
3 2 1
2 3 1

Sample Output 1

Yes

For example, he can reach the goal point as follows:

• Use medicine 1. Energy becomes 3.
• Move to (1, 2). Energy becomes 2.
• Move to (1, 3). Energy becomes 1.
• Use medicine 2. Energy becomes 5.
• Move to (2, 3). Energy becomes 4.
• Move to (3, 3). Energy becomes 3.
• Move to (3, 4). Energy becomes 2.
• Move to (4, 4). Energy becomes 1.

There is also medicine at (2, 3) along the way, but using it will prevent him from reaching the goal.

Sample Input 2

2 2
S.
T.
1
1 2 4

Sample Output 2

No

Takahashi cannot move from the start point.

Sample Input 3

4 5
..#..
.S##.
.##T.
.....
3
3 1 5
1 2 3
2 2 1

Sample Output 3

Yes

Problem Statement

In the country of AtCoder, there are N stations: station 1, station 2, \ldots, station N.

You are given M pieces of information about trains in the country. The i-th piece of information (1\leq i\leq M) is represented by a tuple of six positive integers (l _ i,d _ i,k _ i,c _ i,A _ i,B _ i), which corresponds to the following information:

• For each t=l _ i,l _ i+d _ i,l _ i+2d _ i,\ldots,l _ i+(k _ i-1)d _ i, there is a train as follows:
  • The train departs from station A _ i at time t and arrives at station B _ i at time t+c _ i.

No trains exist other than those described by this information, and it is impossible to move from one station to another by any means other than by train.
Also, assume that the time required for transfers is negligible.

Let f(S) be the latest time at which one can arrive at station N from station S.
More precisely, f(S) is defined as the maximum value of t for which there is a sequence of tuples of four integers \big((t _ i,c _ i,A _ i,B _ i)\big) _ {i=1,2,\ldots,k} that satisfies all of the following conditions:

• t\leq t _ 1
• A _ 1=S,B _ k=N
• B _ i=A _ {i+1} for all 1\leq i\lt k,
• For all 1\leq i\leq k, there is a train that departs from station A _ i at time t _ i and arrives at station B _ i at time t _ i+c _ i.
• t _ i+c _ i\leq t _ {i+1} for all 1\leq i\lt k.

If no such t exists, set f(S)=-\infty.

Find f(1),f(2),\ldots,f(N-1).

Constraints

• 2\leq N\leq2\times10 ^ 5
• 1\leq M\leq2\times10 ^ 5
• 1\leq l _ i,d _ i,k _ i,c _ i\leq10 ^ 9\ (1\leq i\leq M)
• 1\leq A _ i,B _ i\leq N\ (1\leq i\leq M)
• A _ i\neq B _ i\ (1\leq i\leq M)
• All input values are integers.

Sample Input 1

6 7
10 5 10 3 1 3
13 5 10 2 3 4
15 5 10 7 4 6
3 10 2 4 2 5
7 10 2 3 5 6
5 3 18 2 2 3
6 3 20 4 2 1

Sample Output 1

55
56
58
60
17

The following diagram shows the trains running in the country (information about arrival and departure times is omitted).

Consider the latest time at which one can arrive at station 6 from station 2. As shown in the following diagram, one can arrive at station 6 by departing from station 2 at time 56 and moving as station 2\rightarrow station 3\rightarrow station 4\rightarrow station 6.

It is impossible to depart from station 2 after time 56 and arrive at station 6, so f(2)=56.

Sample Input 2

5 5
1000000000 1000000000 1000000000 1000000000 1 5
5 9 2 6 2 3
10 4 1 6 2 3
1 1 1 1 3 5
3 1 4 1 5 1

Sample Output 2

1000000000000000000
Unreachable
1
Unreachable

There is a train that departs from station 1 at time 10 ^ {18} and arrives at station 5 at time 10 ^ {18}+10 ^ 9. There are no trains departing from station 1 after that time, so f(1)=10 ^ {18}. As seen here, the answer may not fit within a 32\operatorname{bit} integer.

Also, both the second and third pieces of information guarantee that there is a train that departs from station 2 at time 14 and arrives at station 3 at time 20. As seen here, some trains may appear in multiple pieces of information.

Sample Input 3

16 20
4018 9698 2850 3026 8 11
2310 7571 7732 1862 13 14
2440 2121 20 1849 11 16
2560 5115 190 3655 5 16
1936 6664 39 8822 4 16
7597 8325 20 7576 12 5
5396 1088 540 7765 15 1
3226 88 6988 2504 13 5
1838 7490 63 4098 8 3
1456 5042 4 2815 14 7
3762 6803 5054 6994 10 9
9526 6001 61 8025 7 8
5176 6747 107 3403 1 5
2014 5533 2031 8127 8 11
8102 5878 58 9548 9 10
3788 174 3088 5950 3 13
7778 5389 100 9003 10 15
556 9425 9458 109 3 11
5725 7937 10 3282 2 9
6951 7211 8590 1994 15 12

Sample Output 3

720358
77158
540926
255168
969295
Unreachable
369586
466218
343148
541289
42739
165772
618082
16582
591828

Problem Statement

There is a cleaning robot on the square (0, 0) in an infinite two-dimensional grid.

The robot will be given a program represented as a string consisting of four kind of characters L, R, U, D.
It will read the characters in the program from left to right and perform the following action for each character read.

1. Let (x, y) be the square where the robot is currently on.
2. Make the following move according to the character read:
   • if L is read: go to (x-1, y).
   • if R is read: go to (x+1, y).
   • if U is read: go to (x, y-1).
   • if D is read: go to (x, y+1).

You are given a string S consisting of L, R, U, D. The program that will be executed by the robot is the concatenation of K copies of S.

Squares visited by the robot at least once, including the initial position (0, 0), will be cleaned.
Print the number of squares that will be cleaned at the end of the execution of the program.

Constraints

• S is a string of length between 1 and 2 \times 10^5 (inclusive) consisting of L, R, U, D.
• 1 \leq K \leq 10^{12}

Sample Input 1

RDRUL
2

Sample Output 1

7

The robot will execute the program RDRULRDRUL. It will start on (0, 0) and travel as follows:
(0, 0) \rightarrow (1, 0) \rightarrow (1, 1) \rightarrow (2, 1) \rightarrow (2, 0) \rightarrow (1, 0) \rightarrow (2, 0) \rightarrow (2, 1) \rightarrow (3, 1) \rightarrow (3, 0) \rightarrow (2, 0).
In the end, seven squares will get cleaned: (0, 0), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1).

Sample Input 2

LR
1000000000000

Sample Output 2

2

Sample Input 3

UUURRDDDRRRUUUURDLLUURRRDDDDDDLLLLLLU
31415926535

Sample Output 3

219911485785