Problem Statement

There is a 10^9-story building with N ladders.
Takahashi, who is on the 1-st (lowest) floor, wants to reach the highest floor possible by using ladders (possibly none).
The ladders are numbered from 1 to N, and ladder i connects the A_i-th and B_i-th floors. One can use ladder i in either direction to move from the A_i-th floor to the B_i-th floor or vice versa, but not between other floors.
Takahashi can freely move within the same floor, but cannot move between floors without using ladders.
What is the highest floor Takahashi can reach?

Constraints

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

Sample Input 1

4
1 4
4 3
4 10
8 3

Sample Output 1

10

He can reach the 10-th floor by using ladder 1 to get to the 4-th floor and then ladder 3 to get to the 10-th floor.

Sample Input 2

6
1 3
1 5
1 12
3 5
3 12
5 12

Sample Output 2

12

Sample Input 3

3
500000000 600000000
600000000 700000000
700000000 800000000

Sample Output 3

1

He may be unable to move between floors.

Problem Statement

We have two figures S and T on a two-dimensional grid with square cells.

S lies within a grid with N rows and N columns, and consists of the cells where S_{i,j} is #.
T lies within the same grid with N rows and N columns, and consists of the cells where T_{i,j} is #.

Determine whether it is possible to exactly match S and T by 90-degree rotations and translations.

Constraints

• 1 \leq N \leq 200
• Each of S and T consists of # and ..
• Each of S and T contains at least one #.

Sample Input 1

5
.....
..#..
.###.
.....
.....
.....
.....
....#
...##
....#

Sample Output 1

Yes

We can match S to T by rotating it 90-degrees counter-clockwise and translating it.

Sample Input 2

5
#####
##..#
#..##
#####
.....
#####
#..##
##..#
#####
.....

Sample Output 2

No

It is impossible to match them by 90-degree rotations and translations.

Sample Input 3

4
#...
..#.
..#.
....
#...
#...
..#.
....

Sample Output 3

Yes

Each of S and T may not be connected.

Sample Input 4

4
#...
.##.
..#.
....
##..
#...
..#.
....

Sample Output 4

No

Note that it is not allowed to rotate or translate just a part of a figure; it is only allowed to rotate or translate a whole figure.

Problem Statement

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

You will perform the following consecutive operations just once:

• Choose an integer x (0\leq x \leq N). If x is 0, do nothing. If x is 1 or greater, replace each of A_1,A_2,\ldots,A_x with L.

• Choose an integer y (0\leq y \leq N). If y is 0, do nothing. If y is 1 or greater, replace each of A_{N},A_{N-1},\ldots,A_{N-y+1} with R.

Print the minimum possible sum of the elements of A after the operations.

Constraints

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

Sample Input 1

5 4 3
5 5 0 6 3

Sample Output 1

14

If you choose x=2 and y=2, you will get A = (4,4,0,3,3), for the sum of 14, which is the minimum sum achievable.

Sample Input 2

4 10 10
1 2 3 4

Sample Output 2

10

If you choose x=0 and y=0, you will get A = (1,2,3,4), for the sum of 10, which is the minimum sum achievable.

Sample Input 3

10 -5 -3
9 -6 10 -1 2 10 -1 7 -15 5

Sample Output 3

-58

L, R, and A_i may be negative.

Problem Statement

A country has N cities and M power plants, which we collectively call places.
The places are numbered 1,2,\dots,N+M, among which Places 1,2,\dots,N are the cities and Places N+1,N+2,\dots,N+M are the power plants.

This country has E power lines. Power Line i (1 \le i \le E) connects Place U_i and Place V_i bidirectionally.
A city is said to be electrified if one can reach at least one of the power plants from the city using some power lines.

Now, Q events will happen. In the i-th (1 \le i \le Q) event, Power Line X_i breaks, making it unusable. Once a power line breaks, it remains broken in the succeeding events.

Find the number of electrified cities right after each events.

Constraints

• All values in input are integers.
• 1 \le N,M
• N+M \le 2 \times 10^5
• 1 \le Q \le E \le 5 \times 10^5
• 1 \le U_i < V_i \le N+M
• If i \neq j, then U_i \neq U_j or V_i \neq V_j.
• 1 \le X_i \le E
• X_i are distinct.

Sample Input 1

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

Sample Output 1

4
4
2
2
2
1

Initially, all cities are electrified.

• The 1-st event breaks Power Line 3 that connects Point 5 and Point 10.
  • Now City 5 is no longer electrified, while 4 cities remain electrified.
• The 2-nd event breaks Power Line 5 that connects Point 2 and Point 9.
• The 3-rd event breaks Power Line 8 that connects Point 3 and Point 6.
  • Now Cities 2 and 3 are no longer electrified, while 2 cities remain electrified.
• The 4-th event breaks Power Line 10 that connects Point 1 and Point 8.
• The 5-th event breaks Power Line 2 that connects Point 4 and Point 10.
• The 6-th event breaks Power Line 7 that connects Point 1 and Point 7.
  • Now City 1 is no longer electrified, while 1 city remains electrified.

Problem Statement

We have a grid with H horizontal rows and W vertical columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left. (i, j) contains an integer A_{i,j}.

Takahashi will depart (1, 1) and repeatedly move one square right or down until reaching (H, W). It is not allowed to exit the grid.

The cost of this travel is defined as:

the sum of the K greatest integers among the integers written on the H+W-1 squares traversed.

Find the minimum possible cost.

Constraints

• 1 \leq H,W \leq 30
• 1 \leq K < H+W
• 1 \leq A_{i,j} \leq 10^9
• All values in input are integers.

Sample Input 1

1 3 2
3 4 5

Sample Output 1

9

There is only one way to travel, where the traversed squares contain the integers 5, 4, 3 from largest to smallest, so we print 9(=5+4).

Sample Input 2

2 2 1
3 2
4 3

Sample Output 2

3

The minimum cost is achieved by traversing (1,1), (1,2), (2,2) in this order.

Sample Input 3

3 5 3
4 7 8 6 4
6 7 3 10 2
3 8 1 10 4

Sample Output 3

21