Problem Statement

AtCoder Grand Contest (AGC), a regularly held contest with a world authority, has been held 54 times.

Just like the 230-th ABC ― the one you are in now ― is called ABC230, the N-th AGC is initially named with a zero-padded 3-digit number N. (The 1-st AGC is AGC001, the 2-nd AGC is AGC002, ...)

However, the latest 54-th AGC is called AGC055, where the number is one greater than 54. Because AGC042 is canceled and missing due to the social situation, the 42-th and subsequent contests are assigned numbers that are one greater than the numbers of contests held. (See also the explanations at Sample Inputs and Outputs.)

Here is the problem: given an integer N, print the name of the N-th AGC in the format AGCXXX, where XXX is the zero-padded 3-digit number.

Constraints

• 1 \leq N \leq 54
• N is an integer.

Sample Input 1

42

Sample Output 1

AGC043

As explained in Problem Statement, the 42-th and subsequent AGCs are assigned numbers that are one greater than the numbers of contests.
Thus, the 42-th AGC is named AGC043.

Sample Input 2

19

Sample Output 2

AGC019

The 41-th and preceding AGCs are assigned numbers that are equal to the numbers of contests.
Thus, the answer is AGC019.

Sample Input 3

1

Sample Output 3

AGC001

As mentioned in Problem Statement, the 1-st AGC is named AGC001.
Be sure to pad the number with zeros into a 3-digit number.

Sample Input 4

50

Sample Output 4

AGC051

Problem Statement

There are N people numbered 1 through N. Each person has a integer score called programming ability; person i's programming ability is P_i points. How many more points does person 1 need, so that person 1 becomes the strongest? In other words, what is the minimum non-negative integer x such that P_1 + x > P_i for all i \neq 1?

Constraints

• 1\leq N \leq 100
• 1\leq P_i \leq 100
• All input values are integers.

Sample Input 1

4
5 15 2 10

Sample Output 1

11

Person 1 becomes the strongest when their programming skill is 16 points or more, so the answer is 16-5=11.

Sample Input 2

4
15 5 2 10

Sample Output 2

0

Person 1 is already the strongest, so no more programming skill is needed.

Sample Input 3

3
100 100 100

Sample Output 3

1

Problem Statement

An election is taking place.

N people voted. The i-th person (1 \leq i \leq N) cast a vote to the candidate named S_i.

Find the name of the candidate who received the most votes. The given input guarantees that there is a unique candidate with the most votes.

Constraints

• 1 \leq N \leq 100
• S_i is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.
• N is an integer.
• There is a unique candidate with the most votes.

Sample Input 1

5
snuke
snuke
takahashi
takahashi
takahashi

Sample Output 1

takahashi

takahashi got 3 votes, and snuke got 2, so we print takahashi.

Sample Input 2

5
takahashi
takahashi
aoki
takahashi
snuke

Sample Output 2

takahashi

Sample Input 3

1
a

Sample Output 3

a

Problem Statement

There is a grid with H horizontal rows and W vertical columns, in which two distinct squares have a piece.

The state of the squares is represented by H strings S_1, \dots, S_H of length W. S_{i, j} = o means that there is a piece in the square at the i-th row from the top and j-th column from the left; S_{i, j} = - means that the square does not have a piece. Here, S_{i, j} denotes the j-th character of the string S_i.

Consider repeatedly moving one of the pieces to one of the four adjacent squares. It is not allowed to move the piece outside the grid. How many moves are required at minimum for the piece to reach the square with the other piece?

Constraints

• 2 \leq H, W \leq 100
• H and W are integers.
• S_i \, (1 \leq i \leq H) is a string of length W consisting of o and -.
• There exist exactly two pairs of integers 1 \leq i \leq H, 1 \leq j \leq W such that S_{i, j} = o.

Sample Input 1

2 3
--o
o--

Sample Output 1

3

The piece at the 1-st row from the top and 3-rd column from the left can reach the square with the other piece in 3 moves: down, left, left. Since it is impossible to do so in two or less moves, 3 should be printed.

Sample Input 2

5 4
-o--
----
----
----
-o--

Sample Output 2

4

Problem Statement

Takahashi, who governs the Kingdom of AtCoder, has decided to change the alphabetical order of English lowercase letters.

The new alphabetical order is represented by a string X, which is a permutation of a, b, \ldots, z. The i-th character of X (1 \leq i \leq 26) would be the i-th smallest English lowercase letter in the new order.

The kingdom has N citizens, whose names are S_1, S_2, \dots, S_N, where each S_i (1 \leq i \leq N) consists of lowercase English letters.
Sort these names lexicographically according to the alphabetical order decided by Takahashi.

Constraints

• X is a permutation of a, b, \ldots, z.
• 2 \leq N \leq 50000
• N is an integer.
• 1 \leq |S_i| \leq 10 \, (1 \leq i \leq N)
• S_i consists of lowercase English letters. (1 \leq i \leq N)
• S_i \neq S_j (1 \leq i \lt j \leq N)

Sample Input 1

bacdefghijklmnopqrstuvwxzy
4
abx
bzz
bzy
caa

Sample Output 1

bzz
bzy
abx
caa

In the new alphabetical order set by Takahashi, b is smaller than a and z is smaller than y. Thus, sorting the citizens' names lexicographically would result in bzz, bzy, abx, caa in ascending order.

Sample Input 2

zyxwvutsrqponmlkjihgfedcba
5
a
ab
abc
ac
b

Sample Output 2

b
a
ac
ab
abc

Problem Statement

Takahashi is planning an N-day train trip.
For each day, he can pay the regular fare or use a one-day pass.

Here, for 1\leq i\leq N, the regular fare for the i-th day of the trip is F_i yen.
On the other hand, a batch of D one-day passes is sold for P yen. You can buy as many passes as you want, but only in units of D.
Each purchased pass can be used on any day, and it is fine to have some leftovers at the end of the trip.

Find the minimum possible total cost for the N-day trip, that is, the cost of purchasing one-day passes plus the total regular fare for the days not covered by one-day passes.

Constraints

• 1\leq N\leq 2\times 10^5
• 1\leq D\leq 2\times 10^5
• 1\leq P\leq 10^9
• 1\leq F_i\leq 10^9
• All input values are integers.

Sample Input 1

5 2 10
7 1 6 3 6

Sample Output 1

20

If he buys just one batch of one-day passes and uses them for the first and third days, the total cost will be (10\times 1)+(0+1+0+3+6)=20, which is the minimum cost needed.
Thus, print 20.

Sample Input 2

3 1 10
1 2 3

Sample Output 2

6

The minimum cost is achieved by paying the regular fare for all three days.

Sample Input 3

8 3 1000000000
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

3000000000

The minimum cost is achieved by buying three batches of one-day passes and using them for all eight days.
Note that the answer may not fit into a 32-bit integer type.

Problem Statement

Takahashi and Aoki are competing in an election.
There are N electoral districts. The i-th district has X_i + Y_i voters, of which X_i are for Takahashi and Y_i are for Aoki. (X_i + Y_i is always an odd number.)
In each district, the majority party wins all Z_i seats in that district. Then, whoever wins the majority of seats in the N districts as a whole wins the election. (\displaystyle \sum_{i=1}^N Z_i is odd.)
At least how many voters must switch from Aoki to Takahashi for Takahashi to win the election?

Constraints

• 1 \leq N \leq 100
• 0 \leq X_i, Y_i \leq 10^9
• X_i + Y_i is odd.
• 1 \leq Z_i
• \displaystyle \sum_{i=1}^N Z_i \leq 10^5
• \displaystyle \sum_{i=1}^N Z_i is odd.

Sample Input 1

1
3 8 1

Sample Output 1

3

Since there is only one district, whoever wins the seat in that district wins the election.
If three voters for Aoki in the district switch to Takahashi, there will be six voters for Takahashi and five for Aoki, and Takahashi will win the seat.

Sample Input 2

2
3 6 2
1 8 5

Sample Output 2

4

Since there are more seats in the second district than in the first district, Takahashi must win a majority in the second district to win the election.
If four voters for Aoki in the second district switch sides, Takahashi will win five seats. In this case, Aoki will win two seats, so Takahashi will win the election.

Sample Input 3

3
3 4 2
1 2 3
7 2 6

Sample Output 3

0

If Takahashi will win the election even if zero voters switch sides, the answer is 0.

Sample Input 4

10
1878 2089 16
1982 1769 13
2148 1601 14
2189 2362 15
2268 2279 16
2394 2841 18
2926 2971 20
3091 2146 20
3878 4685 38
4504 4617 29

Sample Output 4

86

Problem Statement

Integer Sequence Exhibition is taking place, where integer sequences are gathered in one place and evaluated. Here, every integer sequence of length N consisting of integers between 1 and K (inclusive) is evaluated and given an integer score between 1 and M (inclusive).

Print the number, modulo 998244353, of ways to give each of the evaluated sequences a score between 1 and M.

Here, two ways are said to be different when there is an evaluated sequence A = (A_1, A_2, \ldots, A_N) that is given different scores by the two ways.

Constraints

• 1 \leq N, K, M \leq 10^{18}
• N, K, and M are integers.

Sample Input 1

2 2 2

Sample Output 1

16

Four sequences are evaluated: (1, 1), (1, 2), (2, 1), and (2, 2). There are 16 ways to give each of these sequences a score between 1 and 2, as follows.

• Give 1 to (1, 1), 1 to (1, 2), 1 to (2, 1), and 1 to (2, 2)
• Give 1 to (1, 1), 1 to (1, 2), 1 to (2, 1), and 2 to (2, 2)
• Give 1 to (1, 1), 1 to (1, 2), 2 to (2, 1), and 1 to (2, 2)
• Give 1 to (1, 1), 1 to (1, 2), 2 to (2, 1), and 2 to (2, 2)
• \cdots
• Give 2 to (1, 1), 2 to (1, 2), 2 to (2, 1), and 2 to (2, 2)

Thus, we print 16.

Sample Input 2

3 14 15926535

Sample Output 2

109718301

Be sure to print the count modulo 998244353.

Problem Statement

In the Kingdom of Takahashi, N citizens numbered 1 to N took an examination of competitive programming.
There were two tests, and Citizen i ranked P_i-th in the first test and Q_i-th in the second test.
There were no ties in either test. That is, each of the sequences P and Q is a permutation of (1, 2, ..., N).

Iroha, the president of the kingdom, is going to select K citizens for the national team at the coming world championship of competitive programming.
The members of the national team must be selected so that the following is satisfied.

• There should not be a pair of citizens (x, y) where Citizen x is selected and Citizen y is not selected such that P_x > P_y and Q_x > Q_y.
  • In other words, if Citizen y got a rank smaller than that of Citizen x in both tests, it is not allowed to select Citizen x while not selecting Citizen y.

To begin with, Iroha wants to know the number of ways to select citizens for the national team that satisfy the condition above. Find it to help her.
Since this number can be enormous, print it modulo 998244353.

Constraints

• All values in input are integers.
• 1 \le N \le 300
• 1 \le K \le N
• Each of P and Q is a permutation of (1,2,...,N).

Sample Input 1

4 2
2 4 3 1
2 1 4 3

Sample Output 1

3

• It is fine to select Citizen 1 and Citizen 2 for the team.
• If Citizen 1 and Citizen 3 are selected, Citizen 4 ranked higher than Citizen 3 did in both tests, so the pair (x,y)=(3,4) would violate the condition in the Problem Statement.
• It is fine to select Citizen 1 and Citizen 4.
• If Citizen 2 and Citizen 3 are selected, the pair (x,y)=(3,1) would violate the condition.
• It is fine to select Citizen 2 and Citizen 4.
• If Citizen 3 and Citizen 4 are selected, the pair (x,y)=(3,1) would violate the condition.

The final answer is 3.

Sample Input 2

33 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Sample Output 2

168558757

All \binom{33}{16} = 1166803110 ways of selecting 16 from the 33 citizens satisfy the requirement.
Therefore, we should print 1166803110 modulo 998244353, that is, 168558757.

Sample Input 3

15 7
4 9 7 5 6 13 2 11 3 1 12 14 15 10 8
4 14 9 12 7 15 1 2 8 11 3 5 13 6 10

Sample Output 3

23