Problem Statement

You are given an odd-length string S consisting of lowercase English letters.

Print the central character of S.

Constraints

• S is an odd-length string consisting of lowercase English letters.
• The length of S is between 1 and 99 (inclusive).

Sample Input 1

atcoder

Sample Output 1

o

The central character of atcoder is o.

Sample Input 2

a

Sample Output 2

a

Problem Statement

You are given an integer K.

Print a string that is a concatenation of the first K uppercase English letters in ascending order, starting from A.

Constraints

• K is an integer between 1 and 26, inclusive.

Sample Input 1

3

Sample Output 1

ABC

The uppercase English letters in ascending order are A, B, C, ...

By concatenating the first three uppercase English letters, we get ABC.

Sample Input 2

1

Sample Output 2

A

Problem Statement

There are N people numbered 1 to N.

Person i guessed the building area of KEYENCE headquarters building to be S_i square meters.

The shape of KEYENCE headquarters building is shown below, where a and b are some positive integers.
That is, the building area of the building can be represented as 4ab+3a+3b.

Based on just this information, how many of the N people are guaranteed to be wrong in their guesses?

Constraints

• 1 \leq N \leq 20
• 1 \leq S_i \leq 1000
• All values in input are integers.

Sample Input 1

3
10 20 39

Sample Output 1

1

The area would be 10 square meters if a=1,b=1, and 39 square meters if a=2,b=3.

However, no pair of positive integers a and b would make the area 20 square meters.

Thus, we can only be sure that Person 2 guessed wrong.

Sample Input 2

5
666 777 888 777 666

Sample Output 2

3

Problem Statement

There is a grid with H rows from top to bottom and W columns from left to right. Let (i, j) denote the square at the i-th row from the top and j-th column from the left.
The squares are described by characters C_{i,j}. If C_{i,j} is ., (i, j) is empty; if it is #, (i, j) contains a box.

For integers j satisfying 1 \leq j \leq W, let the integer X_j defined as follows.

• X_j is the number of boxes in the j-th column. In other words, X_j is the number of integers i such that C_{i,j} is #.

Find all of X_1, X_2, \dots, X_W.

Constraints

• 1 \leq H \leq 1000
• 1 \leq W \leq 1000
• H and W are integers.
• C_{i, j} is . or #.

Sample Input 1

3 4
#..#
.#.#
.#.#

Sample Output 1

1 2 0 3

In the 1-st column, one square, (1, 1), contains a box. Thus, X_1 = 1.
In the 2-nd column, two squares, (2, 2) and (3, 2), contain a box. Thus, X_2 = 2.
In the 3-rd column, no squares contain a box. Thus, X_3 = 0.
In the 4-th column, three squares, (1, 4), (2, 4), and (3, 4), contain a box. Thus, X_4 = 3.
Therefore, the answer is (X_1, X_2, X_3, X_4) = (1, 2, 0, 3).

Sample Input 2

3 7
.......
.......
.......

Sample Output 2

0 0 0 0 0 0 0

There may be no square that contains a box.

Sample Input 3

8 3
.#.
###
.#.
.#.
.##
..#
##.
.##

Sample Output 3

2 7 4

Sample Input 4

5 47
.#..#..#####..#...#..#####..#...#...###...#####
.#.#...#.......#.#...#......##..#..#...#..#....
.##....#####....#....#####..#.#.#..#......#####
.#.#...#........#....#......#..##..#...#..#....
.#..#..#####....#....#####..#...#...###...#####

Sample Output 4

0 5 1 2 2 0 0 5 3 3 3 3 0 0 1 1 3 1 1 0 0 5 3 3 3 3 0 0 5 1 1 1 5 0 0 3 2 2 2 2 0 0 5 3 3 3 3

Problem Statement

Takahashi is a cashier.

There is a cash register with 11 keys: 00, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The cash register initially displays 0. Whenever he types the key 00, the displayed number is multiplied by 100; whenever he types one of the others, the displayed number is multiplied by 10, and then added by the number written on the key.

Takahashi wants the cash register to display an integer S. At least how many keystrokes are required to make it display S?

Constraints

• 1\leq S\leq 10^{100000}
• S is an integer.

Sample Input 1

40004

Sample Output 1

4

For example, the following four keystrokes make the cash register display 40004. Initially, the cash register displays 0.

• Type the key 4. It now displays 4.
• Type the key 00. It now displays 400.
• Type the key 0. It now displays 4000.
• Type the key 4. It now displays 40004.

He cannot make it display 40004 with three or fewer keystrokes, so 4 should be printed.

Sample Input 2

1355506027

Sample Output 2

10

Sample Input 3

10888869450418352160768000001

Sample Output 3

27

Note that S may not fit into a 64-\operatorname{bit} integer type.

Problem Statement

There are N items in a shop. For each i = 1, 2, \ldots, N, the price of the i-th item is A_i yen (the currency of Japan).

Takahashi has K coupons.
Each coupon can be used on one item. You can use any number of coupons, possibly zero, on the same item. Using k coupons on an item with a price of a yen allows you to buy it for \max\lbrace a - kX, 0\rbrace yen.

Print the minimum amount of money Takahashi needs to buy all the items.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq K, X \leq 10^9
• 1 \leq A_i \leq 10^9
• All values in input are integers.

Sample Input 1

5 4 7
8 3 10 5 13

Sample Output 1

12

By using 1 coupon on the 1-st item, 1 coupon on the 3-rd item, and 2 coupons on the 5-th item, Takahashi can:

• buy the 1-st item for \max\lbrace A_1-X, 0 \rbrace = 1 yen,
• buy the 2-nd item for \max\lbrace A_2, 0 \rbrace = 3 yen,
• buy the 3-rd item for \max\lbrace A_3-X, 0 \rbrace = 3 yen,
• buy the 4-th item for \max\lbrace A_4, 0 \rbrace = 5 yen,
• buy the 5-th item for \max\lbrace A_5-2X, 0 \rbrace = 0 yen,

for a total of 1 + 3 + 3 + 5 + 0 = 12 yen, which is the minimum possible.

Sample Input 2

5 100 7
8 3 10 5 13

Sample Output 2

0

Sample Input 3

20 815 60
2066 3193 2325 4030 3725 1669 1969 763 1653 159 5311 5341 4671 2374 4513 285 810 742 2981 202

Sample Output 3

112

Problem Statement

You are given an integer sequence of length N, A = (A_1, A_2, \ldots, A_N), and a positive integer K.

For each i = 1, 2, \ldots, Q, determine whether a contiguous subsequence of A, (A_{l_i}, A_{l_i+1}, \ldots, A_{r_i}), is a good sequence.

Here, a sequence of length n, X = (X_1, X_2, \ldots, X_n), is good if and only if there is a way to perform the operation below some number of times (possibly zero) to make all elements of X equal 0.

Choose an integer i such that 1 \leq i \leq n-K+1 and an integer c (possibly negative). Add c to each of the K elements X_{i}, X_{i+1}, \ldots, X_{i+K-1}.

It is guaranteed that r_i - l_i + 1 \geq K for every i = 1, 2, \ldots, Q.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq K \leq \min\lbrace 10, N \rbrace
• -10^9 \leq A_i \leq 10^9
• 1 \leq Q \leq 2 \times 10^5
• 1 \leq l_i, r_i \leq N
• r_i-l_i+1 \geq K
• All values in the input are integers.

Sample Input 1

7 3
3 -1 1 -2 2 0 5
2
1 6
2 7

Sample Output 1

Yes
No

The sequence X \coloneqq (A_1, A_2, A_3, A_4, A_5, A_6) = (3, -1, 1, -2, 2, 0) is good. Indeed, you can do the following to make all elements equal 0.

• First, do the operation with i = 2, c = 4, making X = (3, 3, 5, 2, 2, 0).
• Next, do the operation with i = 3, c = -2, making X = (3, 3, 3, 0, 0, 0).
• Finally, do the operation with i = 1, c = -3, making X = (0, 0, 0, 0, 0, 0).

Thus, the first line should contain Yes.

On the other hand, for the sequence (A_2, A_3, A_4, A_5, A_6, A_7) = (-1, 1, -2, 2, 0, 5), there is no way to make all elements equal 0, so it is not a good sequence. Thus, the second line should contain No.

Sample Input 2

20 4
-19 -66 -99 16 18 33 32 28 26 11 12 0 -16 4 21 21 37 17 55 -19
5
13 16
4 11
3 12
13 18
4 10

Sample Output 2

No
Yes
No
Yes
No

Problem Statement

There is a length-N sequence A=(A_1,\ldots,A_N) that is a permutation of 1,\ldots,N.

While you do not know A, you know that A_{X_i}<A_{Y_i} for M pairs of integers (X_i,Y_i).

Can A be uniquely determined? If it is possible, find A.

Constraints

• 2 \leq N \leq 2\times 10^5
• 1 \leq M \leq 2\times 10^5
• 1\leq X_i,Y_i \leq N
• All values in the input are integers.
• There is an A consistent with the input.

Sample Input 1

3 2
3 1
2 3

Sample Output 1

Yes
3 1 2

We can uniquely determine that A=(3,1,2).

Sample Input 2

3 2
3 1
3 2

Sample Output 2

No

Two sequences (2,3,1) and (3,2,1) can be A.

Sample Input 3

4 6
1 2
1 2
2 3
2 3
3 4
3 4

Sample Output 3

Yes
1 2 3 4

Problem Statement

Given is a string S. How many different strings can be obtained as a permutation of a non-empty, not necessarily contiguous subsequence of S?

Since the count can be enormous, print it modulo 998244353.

Constraints

• S is a string of length 1 and 5000 (inclusive) consisting of lowercase English letters.

Sample Input 1

aab

Sample Output 1

8

There are 8 different strings that can be obtained as a permutation of a subsequence of S: a, b, aa, ab, ba, aab, aba, baa.

Sample Input 2

aaa

Sample Output 2

3

Sample Input 3

abcdefghijklmnopqrstuvwxyz

Sample Output 3

149621752

Be sure to print the count modulo 998244353.