Problem Statement

You are given a sequence of N integers: A=(A _ 1,A _ 2,\ldots,A _ N).

Print all even numbers in A without changing the order.

Constraints

• 1\leq N\leq 100
• 1\leq A _ i\leq 100\ (1\leq i\leq N)
• A contains at least one even number.
• All values in the input are integers.

Sample Input 1

5
1 2 3 5 6

Sample Output 1

2 6

We have A=(1,2,3,5,6). Among them are two even numbers, A _ 2=2 and A _ 5=6, so print 2 and 6 in this order, with a space in between.

Sample Input 2

5
2 2 2 3 3

Sample Output 2

2 2 2

A may contain equal elements.

Sample Input 3

10
22 3 17 8 30 15 12 14 11 17

Sample Output 3

22 8 30 12 14

Problem Statement

Takahashi turns on the light of his room at S o'clock (on the 24-hour clock) every day and turns it off at T o'clock every day.
The date may change while the light is on.

Determine whether the light is on at 30 minutes past X o'clock.

Constraints

• 0 \leq S, T, X \leq 23
• S \neq T
• All values in input are integers.

Sample Input 1

7 20 12

Sample Output 1

Yes

The light is on between 7 o'clock and 20 o'clock. At 30 minutes past 12 o'clock, it is on, so we print Yes.

Sample Input 2

20 7 12

Sample Output 2

No

The light is on between 0 o'clock and 7 o'clock, and between 20 o'clock and 0 o'clock (on the next day). At 30 minutes past 12 o'clock, it is off, so we print No.

Sample Input 3

23 0 23

Sample Output 3

Yes

Problem Statement

You are given a sequence of length N consisting of integers: A=(A_1,\ldots,A_N).

Find the smallest non-negative integer not in (A_1,\ldots,A_N).

Constraints

• 1 \leq N \leq 2000
• 0 \leq A_i \leq 2000
• All values in input are integers.

Sample Input 1

8
0 3 2 6 2 1 0 0

Sample Output 1

4

The non-negative integers are 0,1,2,3,4,\ldots.
We have 0,1,2,3 in A, but not 4, so the answer is 4.

Sample Input 2

3
2000 2000 2000

Sample Output 2

0

Problem Statement

The AtCoder amusement park has an attraction that can accommodate K people. Now, there are N groups lined up in the queue for this attraction.

The i-th group from the front (1\leq i\leq N) consists of A_i people. For all i (1\leq i\leq N), it holds that A_i \leq K.

Takahashi, as a staff member of this attraction, will guide the groups in the queue according to the following procedure.

Initially, no one has been guided to the attraction, and there are K empty seats.

1. If there are no groups in the queue, start the attraction and end the guidance.
2. Compare the number of empty seats in the attraction with the number of people in the group at the front of the queue, and do one of the following:
   • If the number of empty seats is less than the number of people in the group at the front, start the attraction. Then, the number of empty seats becomes K again.
   • Otherwise, guide the entire group at the front of the queue to the attraction. The front group is removed from the queue, and the number of empty seats decreases by the number of people in the group.
3. Go back to step 1.

Here, no additional groups will line up after the guidance has started. Under these conditions, it can be shown that this procedure will end in a finite number of steps.

Determine how many times the attraction will be started throughout the guidance.

Constraints

• 1\leq N\leq 100
• 1\leq K\leq 100
• 1\leq A_i\leq K\ (1\leq i\leq N)
• All input values are integers.

Sample Input 1

7 6
2 5 1 4 1 2 3

Sample Output 1

4

Initially, the seven groups are lined up as follows:

Part of Takahashi's guidance is shown in the following figure:

• Initially, the group at the front has 2 people, and there are 6 empty seats. Thus, he guides the front group to the attraction, leaving 4 empty seats.
• Next, the group at the front has 5 people, which is more than the 4 empty seats, so the attraction is started.
• After the attraction is started, there are 6 empty seats again, so the front group is guided to the attraction, leaving 1 empty seat.
• Next, the group at the front has 1 person, so they are guided to the attraction, leaving 0 empty seats.

In total, he starts the attraction four times before the guidance is completed. Therefore, print 4.

Sample Input 2

7 10
1 10 1 10 1 10 1

Sample Output 2

7

Sample Input 3

15 100
73 8 55 26 97 48 37 47 35 55 5 17 62 2 60

Sample Output 3

8

Problem Statement

For two strings A and B, let A+B denote the concatenation of A and B in this order.

You are given N strings S_1,\ldots,S_N. Modify and print them as follows, in the order i=1, \ldots, N:

• if none of S_1,\ldots,S_{i-1} is equal to S_i, print S_i;
• if X (X>0) of S_1,\ldots,S_{i-1} are equal to S_i, print S_i+ ( +X+ ), treating X as a string.

Constraints

• 1 \leq N \leq 2\times 10^5
• S_i is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.

Sample Input 1

5
newfile
newfile
newfolder
newfile
newfolder

Sample Output 1

newfile
newfile(1)
newfolder
newfile(2)
newfolder(1)

Sample Input 2

11
a
a
a
a
a
a
a
a
a
a
a

Sample Output 2

a
a(1)
a(2)
a(3)
a(4)
a(5)
a(6)
a(7)
a(8)
a(9)
a(10)

Problem Statement

We have N fuses connected in series. The i-th fuse from the left has a length of A_i centimeters and burns at a constant speed of B_i centimeters per second.

Consider igniting this object from left and right ends simultaneously. Find the distance between the position where the two flames will meet and the left end of the object.

Constraints

• 1 \leq N \leq 10^5
• 1 \leq A_i,B_i \leq 1000
• All values in input are integers.

Sample Input 1

3
1 1
2 1
3 1

Sample Output 1

3.000000000000000

The two flames will meet at 3 centimeters from the left end of the object.

Sample Input 2

3
1 3
2 2
3 1

Sample Output 2

3.833333333333333

Sample Input 3

5
3 9
1 2
4 6
1 5
5 3

Sample Output 3

8.916666666666668

Problem Statement

You are given a string S of length N consisting of 0 and 1.

A string T of length N consisting of 0 and 1 is a good string if and only if it satisfies the following condition:

• There is exactly one integer i such that 1 \leq i \leq N - 1 and the i-th and (i + 1)-th characters of T are the same.

For each i = 1,2,\ldots, N, you can choose whether or not to perform the following operation once:

• If the i-th character of S is 0, replace it with 1, and vice versa. The cost of this operation, if performed, is C_i.

Find the minimum total cost required to make S a good string.

Constraints

• 2 \leq N \leq 2 \times 10^5
• S is a string of length N consisting of 0 and 1.
• 1 \leq C_i \leq 10^9
• N and C_i are integers.

Sample Input 1

5
00011
3 9 2 6 4

Sample Output 1

7

Performing the operation for i = 1, 5 and not performing it for i = 2, 3, 4 makes S = 10010, which is a good string. The cost incurred in this case is 7, and it is impossible to make S a good string for less than 7, so print 7.

Sample Input 2

4
1001
1 2 3 4

Sample Output 2

0

Sample Input 3

11
11111100111
512298012 821282085 543342199 868532399 690830957 973970164 928915367 954764623 923012648 540375785 925723427

Sample Output 3

2286846953

Story

There is a long water tank with boards of different heights placed at equal intervals. Takahashi wants to know the time at which water reaches each section separated by the boards when water is poured from one end of the tank.

Problem Statement

You are given a sequence of positive integers of length N: H=(H _ 1,H _ 2,\dotsc,H _ N).

There is a sequence of non-negative integers of length N+1: A=(A _ 0,A _ 1,\dotsc,A _ N). Initially, A _ 0=A _ 1=\dotsb=A _ N=0.

Perform the following operations repeatedly on A:

1. Increase the value of A _ 0 by 1.
2. For i=1,2,\ldots,N in this order, perform the following operation:
   • If A _ {i-1}\gt A _ i and A _ {i-1}\gt H _ i, decrease the value of A _ {i-1} by 1 and increase the value of A _ i by 1.

For each i=1,2,\ldots,N, find the number of operations before A _ i>0 holds for the first time.

Constraints

• 1\leq N\leq2\times10 ^ 5
• 1\leq H _ i\leq10 ^ 9\ (1\leq i\leq N)
• All input values are integers.

Sample Input 1

5
3 1 4 1 5

Sample Output 1

4 5 13 14 26

The first five operations go as follows.

Here, each row corresponds to one operation, with the leftmost column representing step 1 and the others representing step 2.

From this diagram, A _ 1\gt0 holds for the first time after the 4th operation, and A _ 2\gt0 holds for the first time after the 5th operation.

Similarly, the answers for A _ 3, A _ 4, A _ 5 are 13, 14, 26, respectively.

Therefore, you should print 4 5 13 14 26.

Sample Input 2

6
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 2

1000000001 2000000001 3000000001 4000000001 5000000001 6000000001

Note that the values to be output may not fit within a 32-bit integer.

Sample Input 3

15
748 169 586 329 972 529 432 519 408 587 138 249 656 114 632

Sample Output 3

749 918 1921 2250 4861 5390 5822 6428 6836 7796 7934 8294 10109 10223 11373

Problem Statement

Given are M digits C_i.

Find the sum, modulo 998244353, of all integers between 1 and N (inclusive) that contain all of C_1, \ldots, C_M when written in base 10 without unnecessary leading zeros.

Constraints

• 1 \leq N < 10^{10^4}
• 1 \leq M \leq 10
• 0 \leq C_1 < \ldots < C_M \leq 9
• All values in input are integers.

Sample Input 1

104
2
0 1

Sample Output 1

520

Between 1 and 104, there are six integers that contain both 0 and 1 when written in base 10: 10,100,101,102,103,104.
The sum of them is 520.

Sample Input 2

999
4
1 2 3 4

Sample Output 2

0

Between 1 and 999, no integer contains all of 1, 2, 3, 4.

Sample Input 3

1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
5
0 2 4 6 8

Sample Output 3

397365274

Be sure to find the sum modulo 998244353.