Problem Statement

Keyence has N bases worldwide, numbered 1 to N. Base i has W_i employees, and at 0 o'clock in Coordinated Universal Time (UTC), it is X_i o'clock at base i.

You want to hold a one-hour meeting across the entire company. Each employee can only participate in the meeting if the meeting time is completely within the 9:00-18:00 time slot at their base. Find the maximum number of employees who can participate when deciding the meeting time to allow as many employees as possible to participate.

Constraints

• 1\leq N \leq 1000
• 1\leq W_i \leq 10^6
• 0\leq X_i < 24
• All input values are integers.

Sample Input 1

3
5 0
3 3
2 18

Sample Output 1

8

Consider holding the meeting from 14:00 to 15:00 in UTC.

• The meeting is held from 14:00 to 15:00 at base 1, so the 5 employees at base 1 can participate in the meeting.
• The meeting is held from 17:00 to 18:00 at base 2, so the 3 employees at base 2 can participate in the meeting.
• The meeting is held from 8:00 to 9:00 at base 3, so the 2 employees at base 3 cannot participate in the meeting.

Thus, a total of 5+3=8 employees can participate in the meeting. No meeting time allows more employees to participate.

Sample Input 2

2
1 10
1000000 20

Sample Output 2

1000000

Sample Input 3

6
31 3
20 8
11 5
4 3
47 14
1 18

Sample Output 3

67

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

You have N socks. The color of the i-th sock is A_i.

You want to perform the following operation as many times as possible. How many times can it be performed at most?

• Choose two same-colored socks that are not paired yet, and pair them.

Constraints

• 1\leq N \leq 5\times 10^5
• 1\leq A_i \leq 10^9
• All values in the input are integers.

Sample Input 1

6
4 1 7 4 1 4

Sample Output 1

2

You can do the operation twice as follows.

• Choose two socks with the color 1 and pair them.
• Choose two socks with the color 4 and pair them.

Then, you will be left with one sock with the color 4 and another with the color 7, so you can no longer do the operation. There is no way to do the operation three or more times, so you should print 2.

Sample Input 2

1
158260522

Sample Output 2

0

Sample Input 3

10
295 2 29 295 29 2 29 295 2 29

Sample Output 3

4

Problem Statement

You are given a sequence A=(A_1,A_2,\ldots,A_N) of length N consisting of non-negative integers.

Determine if there is an even number represented as the sum of two different elements of A. If it exists, find the maximum such number.

Constraints

• 2\leq N \leq 2\times 10^5
• 0\leq A_i\leq 10^9
• The elements of A are distinct.
• All values in the input are integers.

Sample Input 1

3
2 3 4

Sample Output 1

6

The values represented as the sum of two distinct elements of A are 5, 6, and 7. We have an even number here, and the maximum is 6.

Sample Input 2

2
1 0

Sample Output 2

-1

The value represented as the sum of two distinct elements of A is 1. We have no even number here, so -1 should be printed.

Problem Statement

There is an N \times M grid and a player standing on it.
Let (i,j) denote the square at the i-th row from the top and j-th column from the left of this grid.
Each square of this grid is ice or rock, which is represented by N strings S_1,S_2,\dots,S_N of length M as follows:

• if the j-th character of S_i is ., square (i,j) is ice;
• if the j-th character of S_i is #, square (i,j) is rock.

The outer periphery of this grid (all squares in the 1-st row, N-th row, 1-st column, M-th column) is rock.

Initially, the player rests on the square (2,2), which is ice.
The player can make the following move zero or more times.

• First, specify the direction of movement: up, down, left, or right.
• Then, keep moving in that direction until the player bumps against a rock. Formally, keep doing the following:
  • if the next square in the direction of movement is ice, go to that square and keep moving;
  • if the next square in the direction of movement is rock, stay in the current square and stop moving.

Find the number of ice squares the player can touch (pass or rest on).

Constraints

• 3 \le N,M \le 200
• S_i is a string of length M consisting of # and ..
• Square (i, j) is rock if i=1, i=N, j=1, or j=M.
• Square (2,2) is ice.

Sample Input 1

6 6
######
#....#
#.#..#
#..#.#
#....#
######

Sample Output 1

12

For instance, the player can rest on (5,5) by moving as follows:

• (2,2) \rightarrow (5,2) \rightarrow (5,5).

The player can pass (2,4) by moving as follows:

• (2,2) \rightarrow (2,5), passing (2,4) in the process.

The player cannot pass or rest on (3,4).

Sample Input 2

21 25
#########################
#..............###...####
#..............#..#...###
#........###...#...#...##
#........#..#..#........#
#...##...#..#..#...#....#
#..#..#..###...#..#.....#
#..#..#..#..#..###......#
#..####..#..#...........#
#..#..#..###............#
#..#..#.................#
#........##.............#
#.......#..#............#
#..........#....#.......#
#........###...##....#..#
#..........#..#.#...##..#
#.......#..#....#..#.#..#
##.......##.....#....#..#
###.............#....#..#
####.................#..#
#########################

Sample Output 2

215