Problem Statement

N players numbered 1 to N will play a soccer game.
When a player commits an offense, that player will receive a yellow card or a red card.
A player who satisfies one of the following conditions will be removed from the game.

• Accumulates two yellow cards.
• Receives a red card.

Once a player is removed, that player will no longer receive any cards.

You will watch this game. Initially, the players have not received any cards.
There will be Q events. Correctly answer the questions asked in the events.
There are three kinds of events, which are given in the format c x from the input, where c is 1, 2, or 3. The events are as follows.

• 1 x: Player x receives a yellow card.
• 2 x: Player x receives a red card.
• 3 x: You are asked whether player x has been removed from the game. Answer Yes or No.

Constraints

• 1 \leq N \leq 100
• 1 \leq Q \leq 100
• 1 \leq x \leq N in all events.
• There is at least one event of the third kind.
• A player who has been removed will no longer receive any cards.
• All values in the input are integers.

Sample Input 1

3 9
3 1
3 2
1 2
2 1
3 1
3 2
1 2
3 2
3 3

Sample Output 1

No
No
Yes
No
Yes
No

Here are all the events in chronological order.

In the 1-st event, you are asked whether player 1 has been removed from the game. Player 1 has not been removed, so you should print No.
In the 2-nd event, you are asked whether player 2 has been removed from the game. Player 2 has not been removed, so you should print No.
In the 3-rd event, player 2 receives a yellow card.
In the 4-th event, player 1 receives a red card and is removed from the game.
In the 5-th event, you are asked whether player 1 has been removed from the game. Player 1 has been removed, so you should print Yes.
In the 6-th event, you are asked whether player 2 has been removed from the game. Player 2 has not been removed, so you should print No.
In the 7-th event, player 2 receives a yellow card and is removed from the game.
In the 8-th event, you are asked whether player 2 has been removed from the game. Player 2 has been removed, so you should print Yes.
In the 9-th event, you are asked whether player 3 has been removed from the game. Player 3 has not been removed, so you should print No.

Problem Statement

On a non-empty string, a left shift moves the first character to the end of the string, and a right shift moves the last character to the beginning of the string.

For example, a left shift on abcde results in bcdea, and two right shifts on abcde result in deabc.

You are given a non-empty S consisting of lowercase English letters. Among the strings that can be obtained by performing zero or more left shifts and zero or more right shifts on S, find the lexicographically smallest string and the lexicographically largest string.

Constraints

• S consists of lowercase English letters.
• The length of S is between 1 and 1000 (inclusive).

Sample Input 1

aaba

Sample Output 1

aaab
baaa

By performing shifts, we can obtain four strings: aaab, aaba, abaa, baaa. The lexicographically smallest and largest among them are aaab and baaa, respectively.

Sample Input 2

z

Sample Output 2

z
z

Any sequence of operations results in z.

Sample Input 3

abracadabra

Sample Output 3

aabracadabr
racadabraab

Problem Statement

You are given a string S of length N. You are also given Q queries, which you should process in order.

The i-th query is as follows:

• Given an integer X_i and a character C_i, replace the X_i-th character of S with C_i. Then, print the number of times the string ABC appears as a substring in S.

Here, a substring of S is a string obtained by deleting zero or more characters from the beginning and zero or more characters from the end of S.
For example, ab is a substring of abc, but ac is not a substring of abc.

Constraints

• 3 \le N \le 2 \times 10^5
• 1 \le Q \le 2 \times 10^5
• S is a string of length N consisting of uppercase English letters.
• 1 \le X_i \le N
• C_i is an uppercase English letter.

Sample Input 1

7 4
ABCDABC
4 B
3 A
5 C
4 G

Sample Output 1

2
1
1
0

After processing each query, S becomes as follows.

• After the first query: S= ABCBABC. In this string, ABC appears twice as a substring.
• After the second query: S= ABABABC. In this string, ABC appears once as a substring.
• After the third query: S= ABABCBC. In this string, ABC appears once as a substring.
• After the fourth query: S= ABAGCBC. In this string, ABC appears zero times as a substring.

Sample Input 2

3 3
ABC
1 A
2 B
3 C

Sample Output 2

1
1
1

There are cases where S does not change through processing a query.

Sample Input 3

15 10
BBCCBCACCBACACA
9 C
11 B
5 B
11 B
4 A
8 C
8 B
5 B
7 B
14 B

Sample Output 3

0
0
0
0
1
1
2
2
1
1

Problem Statement

N students are taking a 4-day exam.

There is a 300-point test on each day, for a total of 1200 points.

The first three days of the exam are already over, and the fourth day is now about to begin. The i-th student (1 \leq i \leq N) got P_{i, j} points on the j-th day (1 \leq j \leq 3).

For each student, determine whether it is possible that he/she is ranked in the top K after the fourth day.
Here, the rank of a student after the fourth day is defined as the number of students whose total scores over the four days are higher than that of the student, plus 1.

Constraints

• 1 \leq K \leq N \leq 10^5
• 0 \leq P_{i, j} \leq 300 \, (1 \leq i \leq N, 1 \leq j \leq 3)
• All values in input are integers.

Sample Input 1

3 1
178 205 132
112 220 96
36 64 20

Sample Output 1

Yes
Yes
No

If every student scores 100 on the fourth day, the 1-st student will rank 1-st.
If the 2-nd student scores 100 and the other students score 0 on the fourth day, the 2-nd student will rank 1-st.
The 3-rd student will never rank 1-st.

Sample Input 2

2 1
300 300 300
200 200 200

Sample Output 2

Yes
Yes

Sample Input 3

4 2
127 235 78
192 134 298
28 56 42
96 120 250

Sample Output 3

Yes
Yes
No
Yes

Problem Statement

There are H \times W cookies in H rows and W columns.
The color of the cookie at the i-row from the top and j-th column from the left is represented by a lowercase English letter c_{i,j}.

We will perform the following procedure.

1. For each row, perform the following operation: if there are two or more cookies remaining in the row and they all have the same color, mark them.

2. For each column, perform the following operation: if there are two or more cookies remaining in the column and they all have the same color, mark them.

3. If there are any marked cookies, remove them all and return to 1; otherwise, terminate the procedure.

Find the number of cookies remaining at the end of the procedure.

Constraints

• 2 \leq H, W \leq 2000
• c_{i,j} is a lowercase English letter.

Sample Input 1

4 3
aaa
aaa
abc
abd

Sample Output 1

2

The procedure is performed as follows.

• 1. Mark the cookies in the first and second rows.
• 2. Mark the cookies in the first column.
• 3. Remove the marked cookies.

At this point, the cookies look like the following, where . indicates a position where the cookie has been removed.

...
...
.bc
.bd

• 1. Do nothing.
• 2. Mark the cookies in the second column.
• 3. Remove the marked cookies.

At this point, the cookies look like the following, where . indicates a position where the cookie has been removed.

...
...
..c
..d

• 1. Do nothing.
• 2. Do nothing.
• 3. No cookies are marked, so terminate the procedure.

The final number of cookies remaining is 2.

Sample Input 2

2 5
aaaaa
abcde

Sample Output 2

4

Sample Input 3

3 3
ooo
ooo
ooo

Sample Output 3

0