Problem Statement

The definition of an 11/22 string in this problem is the same as in Problems C and E.

A string T is called an 11/22 string when it satisfies all of the following conditions:

• |T| is odd. Here, |T| denotes the length of T.
• The 1-st through (\frac{|T|+1}{2} - 1)-th characters are all 1.
• The (\frac{|T|+1}{2})-th character is /.
• The (\frac{|T|+1}{2} + 1)-th through |T|-th characters are all 2.

For example, 11/22, 111/222, and / are 11/22 strings, but 1122, 1/22, 11/2222, 22/11, and //2/2/211 are not.

Given a string S of length N consisting of 1, 2, and /, determine whether S is an 11/22 string.

Constraints

• 1 \leq N \leq 100
• S is a string of length N consisting of 1, 2, and /.

Sample Input 1

5
11/22

Sample Output 1

Yes

11/22 satisfies the conditions for an 11/22 string in the problem statement.

Sample Input 2

1
/

Sample Output 2

Yes

/ satisfies the conditions for an 11/22 string.

Sample Input 3

4
1/22

Sample Output 3

No

1/22 does not satisfy the conditions for an 11/22 string.

Sample Input 4

5
22/11

Sample Output 4

No

Problem Statement

This is the 214-th AtCoder Beginner Contest (ABC).

The ABCs so far have had the following number of problems.

• The 1-st through 125-th ABCs had 4 problems each.
• The 126-th through 211-th ABCs had 6 problems each.
• The 212-th through 214-th ABCs have 8 problems each.

Find the number of problems in the N-th ABC.

Constraints

• 1 \leq N \leq 214
• All values in input are integers.

Sample Input 1

214

Sample Output 1

8

Sample Input 2

1

Sample Output 2

4

Sample Input 3

126

Sample Output 3

6

Problem Statement

N people labeled from 1 to N participated in a certain contest. The score of person i (1 \leq i \leq N) was P_i.

In this contest, the rank of each of the N people is determined by the following procedure:

1. Prepare a variable r, and initialize r = 1. Initially, the ranks of the N people are all undetermined.
2. Repeat the following operation until the ranks of all N people are determined:
   • Let x be the maximum score among the people whose ranks are currently undetermined, and let k be the number of people whose score is x. Determine the rank of those k people with score x to be r, and then add k to r.

Print the rank of each of the N people.

Constraints

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

Sample Input 1

4
3 12 9 9

Sample Output 1

4
1
2
2

The ranks of the N\ (=4) people are determined as follows:

1. Prepare a variable r and initialize r=1. At first, the ranks of all 4 people are undetermined.
2. Currently, persons 1, 2, 3, 4 have undetermined ranks. The maximum score among them is P_2\ (=12). Therefore, determine the rank of person 2 to be r\ (=1), and then add 1 to r, making r=2.
3. Currently, persons 1, 3, 4 have undetermined ranks. The maximum score among them is P_3=P_4\ (=9). Therefore, determine the ranks of persons 3 and 4 to be r\ (=2), and then add 2 to r, making r=4.
4. Currently, person 1 has an undetermined rank. The maximum score among them is P_1\ (=3). Therefore, determine the rank of person 1 to be r\ (=4), and then add 1 to r, making r=5.
5. The ranks of all 4 people are now determined, so the process ends.

Sample Input 2

3
3 9 6

Sample Output 2

3
1
2

Sample Input 3

4
100 100 100 100

Sample Output 3

1
1
1
1

Sample Input 4

8
87 87 87 88 41 38 41 38

Sample Output 4

2
2
2
1
5
7
5
7

Problem Statement

Given a non-negative integer X, perform the following operation for i=1,2,\dots,K in this order and find the resulting X.

• Round X off to the nearest 10^i.
  • Formally, replace X with Y that is "the largest multiple of 10^i that minimizes |Y-X|."
  • Here are some examples:
    • Rounding 273 off to the nearest 10^2 yields 300.
    • Rounding 999 off to the nearest 10^3 yields 1000.
    • Rounding 100 off to the nearest 10^{10} yields 0.
    • Rounding 1015 off to the nearest 10^1 yields 1020.

Constraints

• X and K are integers.
• 0 \le X < 10^{15}
• 1 \le K \le 15

Sample Input 1

2048 2

Sample Output 1

2100

X changes as 2048 \rightarrow 2050 \rightarrow 2100 by the operations.

Sample Input 2

1 15

Sample Output 2

0

Sample Input 3

999 3

Sample Output 3

1000

Sample Input 4

314159265358979 12

Sample Output 4

314000000000000

X may not fit into a 32-bit integer type.

Problem Statement

The AtCoder company office is represented as a grid of 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.

The state of each cell is represented by a character S_{i,j}. If S_{i,j} is #, that cell has a wall; if S_{i,j} is ., that cell is a floor; if S_{i,j} is H, that cell has a humidifier placed on a floor cell.

A certain cell is considered humidified if it can be reached from at least one humidifier cell by at most D moves up, down, left, or right without passing through a wall. Note that any cell with a humidifier is always humidified.

Find the number of humidified floor cells.

Constraints

• 1 \leq H \leq 1000
• 1 \leq W \leq 1000
• 0 \leq D \leq H\times W
• S_{i,j} is #, ., or H. (1 \leq i \leq H, 1 \leq j \leq W)
• All input numbers are integers.

Sample Input 1

3 4 1
H...
#..H
.#.#

Sample Output 1

5

Five cells (1,1), (1,2), (1,4), (2,3), (2,4) are humidified.

Sample Input 2

5 6 2
##...H
H.....
..H.#.
.HH...
.###..

Sample Output 2

21

Sample Input 3

1 6 3
...#..

Sample Output 3

0

It is possible that no cells are humidified.