Problem Statement

One day, tired from going to school, Takahashi wanted to know how many days there were until Saturday.
We know that the day was a weekday, and the name of the day of the week was S in English.
How many days were there until the first Saturday after that day (including Saturday but not the starting day)?

Constraints

• S is Monday, Tuesday, Wednesday, Thursday, or Friday.

Sample Input 1

Wednesday

Sample Output 1

3

It was Wednesday, so there were 3 days until the first Saturday after that day.

Sample Input 2

Monday

Sample Output 2

5

Problem Statement

You are given a string S consisting of <, =, and >.
Determine whether S is a bidirectional arrow string.
A string S is a bidirectional arrow string if and only if there is a positive integer k such that S is a concatenation of one <, k =s, and one >, in this order, with a length of (k+2).

Constraints

• S is a string of length between 3 and 100, inclusive, consisting of <, =, and >.

Sample Input 1

<====>

Sample Output 1

Yes

<====> is a concatenation of one <, four =s, and one >, in this order, so it is a bidirectional arrow string.
Hence, print Yes.

Sample Input 2

==>

Sample Output 2

No

==> does not meet the condition for a bidirectional arrow string.
Hence, print No.

Sample Input 3

<>>

Sample Output 3

No

Problem Statement

You are given a sequence A=(A_1,A_2,\dots,A_N) of length N and a sequence B=(B_1,B_2,\dots,B_M) of length M. Here, all elements of A and B are pairwise distinct. Determine whether the sequence C=(C_1,C_2,\dots,C_{N+M}) formed by sorting all elements of A and B in ascending order contains two consecutive elements appearing in A.

Constraints

• 1 \leq N, M \leq 100
• 1 \leq A_i, B_j \leq 200
• A_1, A_2, \dots, A_N, B_1, B_2, \dots, B_M are distinct.
• All input values are integers.

Sample Input 1

3 2
3 2 5
4 1

Sample Output 1

Yes

C=(1,2,3,4,5). Since 2 and 3 from A occur consecutively in C, print Yes.

Sample Input 2

3 2
3 1 5
4 2

Sample Output 2

No

C=(1,2,3,4,5). Since no two elements from A occur consecutively in C, print No.

Sample Input 3

1 1
1
2

Sample Output 3

No

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

You are given a positive integer N.

Find the maximum value of a palindromic cube number not greater than N.

Here, a positive integer K is defined to be a palindromic cube number if and only if it satisfies the following two conditions:

• There is a positive integer x such that x^3 = K.
• The decimal representation of K without leading zeros is a palindrome. More precisely, if K is represented as K = \sum_{i = 0}^{L-1} A_i10^i using integers A_0, A_1, \ldots, A_{L-2} between 0 and 9, inclusive, and an integer A_{L-1} between 1 and 9, inclusive, then A_i = A_{L-1-i} for all i = 0, 1, \ldots, L-1.

Constraints

• N is a positive integer not greater than 10^{18}.

Sample Input 1

345

Sample Output 1

343

343 is a palindromic cube number, while 344 and 345 are not. Thus, the answer is 343.

Sample Input 2

6

Sample Output 2

1

Sample Input 3

123456789012345

Sample Output 3

1334996994331

Problem Statement

We have N cups of ice cream.
The flavor and deliciousness of the i-th cup are F_i and S_i, respectively (S_i is an even number).

You will choose and eat two of the N cups.
Your satisfaction here is defined as follows.

• Let s and t (s \ge t) be the deliciousness of the eaten cups.
  • If the two cups have different flavors, your satisfaction is \displaystyle s+t.
  • Otherwise, your satisfaction is \displaystyle s + \frac{t}{2}.

Find the maximum achievable satisfaction.

Constraints

• All input values are integers.
• 2 \le N \le 3 \times 10^5
• 1 \le F_i \le N
• 2 \le S_i \le 10^9
• S_i is even.

Sample Input 1

4
1 4
2 10
2 8
3 6

Sample Output 1

16

Consider eating the second and fourth cups.

• The second cup has a flavor of 2 and deliciousness of 10.
• The fourth cup has a flavor of 3 and deliciousness of 6.
• Since they have different flavors, your satisfaction is 10+6=16.

Thus, you can achieve the satisfaction of 16.
You cannot achieve a satisfaction greater than 16.

Sample Input 2

4
4 10
3 2
2 4
4 12

Sample Output 2

17

Consider eating the first and fourth cups.

• The first cup has a flavor of 4 and deliciousness of 10.
• The fourth cup has a flavor of 4 and deliciousness of 12.
• Since they have the same flavor, your satisfaction is 12+\frac{10}{2}=17.

Thus, you can achieve the satisfaction of 17.
You cannot achieve a satisfaction greater than 17.

Problem Statement

There is a rectangular cake with some strawberries on the xy-plane. The cake occupies the rectangular area \lbrace (x, y) : 0 \leq x \leq W, 0 \leq y \leq H \rbrace.

There are N strawberries on the cake, and the coordinates of the i-th strawberry are (p_i, q_i) for i = 1, 2, \ldots, N. No two strawberries have the same coordinates.

Takahashi will cut the cake into several pieces with a knife, as follows.

• First, cut the cake along A different lines parallel to the y-axis: lines x = a_1, x = a_2, \ldots, x = a_A.
• Next, cut the cake along B different lines parallel to the x-axis: lines y = b_1, y = b_2, \ldots, y = b_B.

As a result, the cake will be divided into (A+1)(B+1) rectangular pieces. Takahashi will choose just one of these pieces to eat. Print the minimum and maximum possible numbers of strawberries on the chosen piece.

Here, it is guaranteed that there are no strawberries along the edges of the final pieces. For a more formal description, refer to the constraints below.

Constraints

• 3 \leq W, H \leq 10^9
• 1 \leq N \leq 2 \times 10^5
• 0 \lt p_i \lt W
• 0 \lt q_i \lt H
• i \neq j \implies (p_i, q_i) \neq (p_j, q_j)
• 1 \leq A, B \leq 2 \times 10^5
• 0 \lt a_1 \lt a_2 \lt \cdots \lt a_A \lt W
• 0 \lt b_1 \lt b_2 \lt \cdots \lt b_B \lt H
• p_i \not \in \lbrace a_1, a_2, \ldots, a_A \rbrace
• q_i \not \in \lbrace b_1, b_2, \ldots, b_B \rbrace
• All input values are integers.

Sample Input 1

7 6
5
6 1
3 1
4 2
1 5
6 2
2
2 5
2
3 4

Sample Output 1

0 2

There are nine pieces in total: six with zero strawberries, one with one strawberry, and two with two strawberries. Therefore, when choosing just one of these pieces to eat, the minimum possible number of strawberries on the chosen piece is 0, and the maximum possible number is 2.

Sample Input 2

4 4
4
1 1
3 1
3 3
1 3
1
2
1
2

Sample Output 2

1 1

Each piece has one strawberry on it.

Problem Statement

There are N squares called Square 1 though Square N. You start on Square 1.

Each of the squares from Square 1 through Square N-1 has a die on it. The die on Square i is labeled with the integers from 0 through A_i, each occurring with equal probability. (Die rolls are independent of each other.)

Until you reach Square N, you will repeat rolling a die on the square you are on. Here, if the die on Square x rolls the integer y, you go to Square x+y.

Find the expected value, modulo 998244353, of the number of times you roll a die.

Notes

It can be proved that the sought expected value is always a rational number. Additionally, if that value is represented \frac{P}{Q} using two coprime integers P and Q, there is a unique integer R such that R \times Q \equiv P\pmod{998244353} and 0 \leq R \lt 998244353. Find this R.

Constraints

• 2 \le N \le 2 \times 10^5
• 1 \le A_i \le N-i(1 \le i \le N-1)
• All values in input are integers.

Sample Input 1

3
1 1

Sample Output 1

4

The sought expected value is 4, so 4 should be printed.

Here is one possible scenario until reaching Square N:

• Roll 1 on Square 1, and go to Square 2.
• Roll 0 on Square 2, and stay there.
• Roll 1 on Square 2, and go to Square 3.

This scenario occurs with probability \frac{1}{8}.

Sample Input 2

5
3 1 2 1

Sample Output 2

332748122

Problem Statement

There is an N\times N grid, and the cell at the i-th row from the top and the j-th column from the left (1\leq i,j\leq N) contains the integer A _ {i,j}.

You are given an integer M. When choosing three non-overlapping M\times M grids, find the maximum possible sum of the integers written in the chosen grids.

Constraints

• 2\leq N\leq 1000
• 1\leq M\leq N/2
• 0\leq A _ {i,j}\leq10 ^ 9
• All input values are integers.

Sample Input 1

7 3
3 1 4 1 5 9 2
6 5 3 5 8 9 7
9 3 2 3 8 4 6
2 6 4 3 3 8 3
2 7 9 5 0 2 8
8 4 1 9 7 1 6
9 3 9 9 3 7 5

Sample Output 1

154

From the given grid, if we choose three 3\times3 grids as shown in the figure below (this corresponds to setting (i _ 1,j _ 1,i _ 2,j _ 2,i _ 3,j _ 3)=(1,5,2,1,5,2)), the sum of the numbers written in the chosen grids will be 154.

There is no way to make the sum 155 or greater while satisfying the conditions in the problem statement, so print 154.

Sample Input 2

7 1
3 1 4 1 5 9 2
6 5 3 5 8 9 7
9 3 2 3 8 4 6
2 6 4 3 3 8 3
2 7 9 5 0 2 8
8 4 1 9 7 1 6
9 3 9 9 3 7 5

Sample Output 2

27

The following choice is optimal.

Sample Input 3

16 4
74 16 58 32 97 52 43 51 40 58 13 24 65 11 63 29
98 75 40 77 15 50 83 85 35 46 38 37 56 38 63 55
95 42 10 70 53 40 25 10 70 32 33 19 52 79 74 58
33 91 53 11 65 63 78 77 81 46 81 63 11 82 55 62
39 95 92 69 77 89 14 84 53 78 71 81 66 39 96 29
74 26 60 55 89 35 32 64 17 26 74 92 84 33 59 82
23 69 10 95 94 14 58 58 97 95 62 58 72 55 71 43
93 77 27 87 74 72 91 37 53 80 51 71 37 35 97 46
81 88 26 79 78 30 53 68 83 28 59 28 74 55 20 86
93 13 25 19 53 53 17 24 69 14 67 81 10 19 69 90
88 83 62 92 22 31 27 34 67 48 42 32 68 14 96 87
44 69 25 48 68 42 53 82 44 42 96 31 13 56 68 83
63 87 24 75 16 70 63 99 95 10 63 26 56 12 77 49
94 83 69 95 48 41 40 97 45 61 26 38 83 91 44 31
43 69 54 64 20 60 17 15 62 25 58 50 59 63 88 70
72 95 21 28 41 14 77 22 64 78 33 55 67 51 78 40

Sample Output 3

3295

The following choice is optimal.