Problem Statement

You are given a sequence of positive integers of length N: A=(A_1,A_2,\dots,A_N).

Find the sum of the odd-indexed elements of A. That is, find A_1 + A_3 + A_5 + \dots + A_m, where m is the largest odd number not exceeding N.

Constraints

• 1 \le N \le 100
• 1 \le A_i \le 100
• All input values are integers.

Sample Input 1

7
3 1 4 1 5 9 2

Sample Output 1

14

The sum of the odd-indexed elements of A is A_1+A_3+A_5+A_7=3+4+5+2=14.

Sample Input 2

1
100

Sample Output 2

100

Sample Input 3

14
100 10 1 10 100 10 1 10 100 10 1 10 100 10

Sample Output 3

403

Problem Statement

You are given a string S of length exactly 9 consisting of digits. One but all digits from 0 to 9 appear exactly once in S.

Print the only digit missing in S.

Constraints

• S is a string of length 9 consisting of digits.
• All characters in S are distinct.

Sample Input 1

023456789

Sample Output 1

1

The string 023456789 only lacks 1. Thus, 1 should be printed.

Sample Input 2

459230781

Sample Output 2

6

The string 459230781 only lacks 6. Thus, 6 should be printed.

Note that the digits in the string may not appear in increasing order.

Problem Statement

There is a grid with H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left.

Cell (i, j) is empty if C_{i, j} is ., and not empty if C_{i, j} is #.

Takahashi is currently at cell (S_i, S_j), and he will act according to the following rules for i = 1, 2, \ldots, |X| in order.

• If the i-th character of X is L, and the cell to the left of his current cell exists and is empty, he moves to the cell to the left. Otherwise, he stays in the current cell.
• If the i-th character of X is R, and the cell to the right of his current cell exists and is empty, he moves to the cell to the right. Otherwise, he stays in the current cell.
• If the i-th character of X is U, and the cell above his current cell exists and is empty, he moves to the cell above. Otherwise, he stays in the current cell.
• If the i-th character of X is D, and the cell below his current cell exists and is empty, he moves to the cell below. Otherwise, he stays in the current cell.

Print the cell where he is after completing the series of actions.

Constraints

• 1 \leq H, W \leq 50
• 1 \leq S_i \leq H
• 1 \leq S_j \leq W
• H, W, S_i, S_j are integers.
• C_{i, j} is . or #.
• C_{S_i, S_j} = .
• X is a string of length between 1 and 50, inclusive, consisting of L, R, U, D.

Sample Input 1

2 3
2 1
.#.
...
ULDRU

Sample Output 1

2 2

Takahashi starts at cell (2, 1). His series of actions are as follows:

• The 1st character of X is U, and the cell above (2, 1) exists and is an empty cell, so he moves to the cell above, which is (1, 1).
• The 2nd character of X is L, and the cell to the left of (1, 1) does not exist, so he stays at (1, 1).
• The 3rd character of X is D, and the cell below (1, 1) exists and is an empty cell, so he moves to the cell below, which is (2, 1).
• The 4th character of X is R, and the cell to the right of (2, 1) exists and is an empty cell, so he moves to the cell to the right, which is (2, 2).
• The 5th character of X is U, and the cell above (2, 2) exists but is not an empty cell, so he stays at (2, 2).

Therefore, after completing the series of actions, he is at cell (2, 2).

Sample Input 2

4 4
4 2
....
.#..
...#
....
DUUUURULRD

Sample Output 2

2 4

Sample Input 3

6 6
1 1
.#####
######
######
######
######
######
RURLDLULLRULRDL

Sample Output 3

1 1

Problem Statement

Find the N integer sequences A_0,\ldots,A_{N-1} defined as follows.

• For each i (0\leq i \leq N-1), the length of A_i is i+1.
• For each i and j (0\leq i \leq N-1, 0 \leq j \leq i), the (j+1)-th term of A_i, denoted by a_{i,j}, is defined as follows.
  • a_{i,j}=1, if j=0 or j=i.
  • a_{i,j} = a_{i-1,j-1} + a_{i-1,j}, otherwise.

Constraints

• 1 \leq N \leq 30
• N is an integer.

Sample Input 1

3

Sample Output 1

1
1 1
1 2 1

Sample Input 2

10

Sample Output 2

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1

Problem Statement

For an integer sequence A = (A_1, A_2, \ldots, A_{|A|}), we say that A is tilde-shaped if it satisfies all of the following four conditions:

• The length |A| is at least 4.
• A_1 < A_2.
• There exists exactly one integer i with 2 \leq i < |A| such that A_{i-1} < A_i > A_{i+1}.
• There exists exactly one integer i with 2 \leq i < |A| such that A_{i-1} > A_i < A_{i+1}.

You are given a permutation P = (P_1, P_2, \ldots, P_N) of (1, 2, \ldots, N). Find the number of (contiguous) subarrays of P that are tilde-shaped.

Constraints

• 4 \leq N \leq 3 \times 10^5
• P = (P_1, P_2, \ldots, P_N) is a permutation of (1, 2, \ldots, N).
• All input values are integers.

Sample Input 1

6
1 3 6 4 2 5

Sample Output 1

2

Among the subarrays of (1, 3, 6, 4, 2, 5), exactly two are tilde-shaped: (3, 6, 4, 2, 5) and (1, 3, 6, 4, 2, 5).

Sample Input 2

6
1 2 3 4 5 6

Sample Output 2

0

Sample Input 3

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

Sample Output 3

4

Problem Statement

There are N boxes numbered 1 to N and N items numbered 1 to N. Item i (1 \leq i \leq N) is in box A_i and has a weight of W_i.

You can repeatedly perform the operation of choosing an item and moving it to another box zero or more times. If the weight of the item being moved is w, the cost of the operation is w.

Find the minimum total cost required to make each box contain exactly one item.

Constraints

• 1 \leq N \leq 10^{5}
• 1 \leq A_i \leq N (1 \leq i \leq N)
• 1 \leq W_i \leq 10^{4} (1 \leq i \leq N)
• All input values are integers.

Sample Input 1

5
2 2 3 3 5
33 40 2 12 16

Sample Output 1

35

With the following two moves, you can make each box contain exactly one item:

• Move item 1 from box 2 to box 1. The cost is 33.
• Move item 3 from box 3 to box 4. The cost is 2.

The total cost of these two moves is 35. It is impossible to make each box contain exactly one item with a cost less than 35, so print 35.

Sample Input 2

12
3 6 7 4 12 4 8 11 11 1 8 11
3925 9785 9752 3587 4013 1117 3937 7045 6437 6208 3391 6309

Sample Output 2

17254

Problem Statement

We have a string S. Initially, S= 1.
Process Q queries in the following formats in order.

• 1 x : Append a digit x at the end of S.
• 2 : Delete the digit at the beginning of S.
• 3 : Print the number represented by S in decimal, modulo 998244353.

Constraints

• 1 \leq Q \leq 6 \times 10^5
• For each query in the first format, x \in \{1,2,3,4,5,6,7,8,9\}.
• A query in the second format is given only if S has a length of 2 or greater.
• There is at least one query in the third format.

Sample Input 1

3
3
1 2
3

Sample Output 1

1
12

In the first query, S is 1, so you should print 1 modulo 998244353, that is, 1.
In the second query, S becomes 12.
In the third query, S is 12, so you should print 12 modulo 998244353, that is, 12.

Sample Input 2

3
1 5
2
3

Sample Output 2

5

Sample Input 3

11
1 9
1 9
1 8
1 2
1 4
1 4
1 3
1 5
1 3
2
3

Sample Output 3

0

Be sure to print numbers modulo 998244353.

Problem Statement

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

Find \displaystyle \sum_{i=1}^{N-1}\sum_{j=i+1}^{N}\left\lfloor\frac{\max(A_i,A_j)}{\min(A_i,A_j)}\right\rfloor.

Here, \lfloor x \rfloor represents the greatest integer not greater than x. For example, \lfloor 3.14 \rfloor=3 and \lfloor 2 \rfloor=2.

Constraints

• 2 \leq N \leq 2\times 10^5
• 1 \leq A_i \leq 10^6
• All input values are integers.

Sample Input 1

3
3 1 4

Sample Output 1

8

The sought value is

\left\lfloor\frac{\max(3,1)}{\min(3,1)}\right\rfloor + \left\lfloor\frac{\max(3,4)}{\min(3,4)}\right\rfloor + \left\lfloor\frac{\max(1,4)}{\min(1,4)}\right\rfloor\\ =\left\lfloor\frac{3}{1}\right\rfloor + \left\lfloor\frac{4}{3}\right\rfloor + \left\lfloor\frac{4}{1}\right\rfloor\\ =3+1+4\\ =8.

Sample Input 2

6
2 7 1 8 2 8

Sample Output 2

53

Sample Input 3

12
3 31 314 3141 31415 314159 2 27 271 2718 27182 271828

Sample Output 3

592622

Problem Statement

You are given a sequence P = (p_1,p_2,\ldots,p_N) that contains 1,2,\ldots,N exactly once each.
You may perform the following operations between 0 and K times in total in any order:

• Choose one term of P and remove it.
• Move the last term of P to the head.

Find the lexicographically smallest P that can be obtained as a result of the operations.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 0 \leq K \leq N-1
• 1 \leq p_i \leq N
• (p_1,p_2,\ldots,p_N) contains 1,2,\ldots,N exactly once each.
• All values in input are integers.

Sample Input 1

5 3
4 5 2 3 1

Sample Output 1

1 2 3

The following operations make P equal (1,2,3).

• Removing the first term makes P equal (5,2,3,1).
• Moving the last term to the head makes P equal (1,5,2,3).
• Removing the second term makes P equal (1,2,3).

There is no way to obtain P lexicographically smaller than (1,2,3), so this is the answer.

Sample Input 2

3 0
3 2 1

Sample Output 2

3 2 1

You may be unable to perform operations.

Sample Input 3

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

Sample Output 3

1 3 4 7 2 8 11 9