Problem Statement

A regular pentagon P is shown in the figure below.

Determine whether the length of the line segment connecting points S_1 and S_2 of P equals the length of the line segment connecting points T_1 and T_2.

Constraints

• Each of S_1, S_2, T_1, and T_2 is one of the characters A, B, C, D, and E.
• S_1 \neq S_2
• T_1 \neq T_2

Sample Input 1

AC
EC

Sample Output 1

Yes

The length of the line segment connecting point A and point C of P equals the length of the line segment connecting point E and point C.

Sample Input 2

DA
EA

Sample Output 2

No

The length of the line segment connecting point D and point A of P does not equal the length of the line segment connecting point E and point A.

Sample Input 3

BD
BD

Sample Output 3

Yes

Problem Statement

Takahashi wants to manage the waiting line in front of the AtCoder Restaurant. Initially, the waiting line is empty. Each person who joins the line holds a meal ticket with the menu number of the dish they will order.

Process Q queries in order. There are two types of queries, given in the following formats:

• 1 X: One person joins the end of the waiting line holding a ticket with menu number X.
• 2: Takahashi guides the person at the front of the waiting line into the restaurant. Print the menu number on that person’s ticket.

Constraints

• 1 \leq Q \leq 100
• 1 \leq X \leq 100
• For each query of the second type, there is at least one person in the line before guiding.
• All input values are integers.

Sample Input 1

6
1 3
1 1
1 15
2
1 3
2

Sample Output 1

3
1

Initially, the waiting line is empty.

• For the first query, a person holding a ticket with menu number 3 joins the end of the line. The sequence of menu numbers held by people in line from front to back is 3.
• For the second query, a person holding a ticket with menu number 1 joins the end of the line. The sequence becomes 3,1.
• For the third query, a person holding a ticket with menu number 15 joins the end of the line. The sequence becomes 3,1,15.
• For the fourth query, guide the person at the front into the restaurant. That person holds menu number 3, so print 3. The sequence becomes 1,15.
• For the fifth query, a person holding a ticket with menu number 3 joins the end of the line. The sequence becomes 1,15,3.
• For the sixth query, guide the person at the front into the restaurant. That person holds menu number 1, so print 1. The sequence becomes 15,3.

Sample Input 2

7
1 3
1 1
1 4
1 1
1 5
1 9
1 2

Sample Output 2

Note that there may be no queries of the second type.

Problem Statement

Given an integer N, find the number of integers X that satisfy all of the following conditions, modulo 998244353.

• X is an N-digit positive integer.
• Let X_1,X_2,\dots,X_N be the digits of X from top to bottom. They satisfy all of the following:
  • 1 \le X_i \le 9 for all integers 1 \le i \le N;
  • |X_i-X_{i+1}| \le 1 for all integers 1 \le i \le N-1.

Constraints

• N is an integer.
• 2 \le N \le 10^6

Sample Input 1

4

Sample Output 1

203

Some of the 4-digit integers satisfying the conditions are 1111,1234,7878,6545.

Sample Input 2

2

Sample Output 2

25

Sample Input 3

1000000

Sample Output 3

248860093

Be sure to find the count modulo 998244353.

Problem Statement

There is a slot machine with N reels.
The placement of symbols on the i-th reel is represented by a string S_i of length 10 containing each of 0, 1, \ldots, 9 exactly once.

Each reel has a corresponding button. For each non-negative integer t, Takahashi can press one of the buttons of his choice (or do nothing) t seconds after the reels start spinning.
If the button for the i-th reel is pressed t seconds after the start of the spin, the i-th reel will stop to display the ((t\bmod{10})+1)-th character of S_i.
Here, t\bmod{10} denotes the remainder when t is divided by 10.

Takahashi wants to stop all reels to make them display the same character.
Find the minimum number of seconds needed to achieve his objective after the start of the spin.

Constraints

• 2\leq N\leq 100
• N is an integer.
• S_i is a string of length 10 containing each of 0, 1, \ldots, 9 exactly once.

Sample Input 1

3
1937458062
8124690357
2385760149

Sample Output 1

6

Takahashi can make all reels display 8 in 6 seconds after the start of the spin by stopping them as follows.

• 0 seconds after the start of the spin, press the button for the 2-nd reel, making it stop to display the ((0\bmod{10})+1=1)-st character of S_2, 8.
• 2 seconds after the start of the spin, press the button for the 3-rd reel, making it stop to display the ((2\bmod{10})+1=3)-rd character of S_3, 8.
• 6 seconds after the start of the spin, press the button for the 1-st reel, making it stop to display the ((6\bmod{10})+1=7)-th character of S_1, 8.

There is no way to make all reels display the same character in five seconds or less, so the answer is 6.

Sample Input 2

5
0123456789
0123456789
0123456789
0123456789
0123456789

Sample Output 2

40

Note that he must stop all reels to make them display the same character.

Problem Statement

You are given a string S of length N consisting of uppercase and lowercase English letters.

Let us perform Q operations on the string S. The i-th operation (1\leq i\leq Q) is represented by a tuple (t _ i,x _ i,c _ i) of two integers and one character, as follows.

• If t _ i=1, change the x _ i-th character of S to c _ i.
• If t _ i=2, convert all uppercase letters in S to lowercase (do not use x _ i,c _ i for this operation).
• If t _ i=3, convert all lowercase letters in S to uppercase (do not use x _ i,c _ i for this operation).

Print the S after the Q operations.

Constraints

• 1\leq N\leq5\times10^5
• S is a string of length N consisting of uppercase and lowercase English letters.
• 1\leq Q\leq5\times10^5
• 1\leq t _ i\leq3\ (1\leq i\leq Q)
• If t _ i=1, then 1\leq x _ i\leq N\ (1\leq i\leq Q).
• c _ i is an uppercase or lowercase English letter.
• If t _ i\neq 1, then x _ i=0 and c _ i= 'a'.
• N,Q,t _ i,x _ i are all integers.

Sample Input 1

7
AtCoder
5
1 4 i
3 0 a
1 5 b
2 0 a
1 4 Y

Sample Output 1

atcYber

Initially, the string S is AtCoder.

• The first operation changes the 4-th character to i, changing S to AtCider.
• The second operation converts all lowercase letters to uppercase, changing S to ATCIDER.
• The third operation changes the 5-th character to b, changing S to ATCIbER.
• The fourth operation converts all uppercase letters to lowercase, changing S to atciber.
• The fifth operation changes the 4-th character to Y, changing S to atcYber.

After the operations, the string S is atcYber, so print atcYber.

Sample Input 2

35
TheQuickBrownFoxJumpsOverTheLazyDog
10
2 0 a
1 19 G
1 13 m
1 2 E
1 21 F
2 0 a
1 27 b
3 0 a
3 0 a
1 15 i

Sample Output 2

TEEQUICKBROWMFiXJUGPFOVERTBELAZYDOG