Problem Statement

There are four types of oysters, labeled 1, 2, 3, and 4. Exactly one of these types causes stomach trouble if eaten. The other types do not cause stomach trouble when eaten.

Takahashi ate oysters 1 and 2, and Aoki ate oysters 1 and 3. The information on whether each person got sick is given as two strings S_1 and S_2. Specifically, S_1 = sick means Takahashi got sick, and S_1 = fine means Takahashi did not get sick. Likewise, S_2 = sick means Aoki got sick, and S_2 = fine means Aoki did not get sick.

Based on the given information, find which type of oyster causes stomach trouble.

Constraints

• Each of S_1 and S_2 is sick or fine.

Sample Input 1

sick fine

Sample Output 1

2

Takahashi (who ate oysters 1 and 2) got sick, and Aoki (who ate oysters 1 and 3) did not get sick, so it can be concluded that oyster 2 causes stomach trouble.

Sample Input 2

fine fine

Sample Output 2

4

Neither Takahashi (who ate oysters 1 and 2) nor Aoki (who ate oysters 1 and 3) got sick, so it can be concluded that oyster 4 causes stomach trouble.

Problem Statement

You are given an integer sequence A=(A_1,A_2,A_3,A_4,A_5) obtained by permuting (1,2,3,4,5).

Determine whether A can be sorted in ascending order by performing exactly one operation of swapping two adjacent elements in A.

Constraints

• A is an integer sequence of length 5 obtained by permuting (1,2,3,4,5).

Sample Input 1

1 2 4 3 5

Sample Output 1

Yes

By swapping A_3 and A_4, A becomes (1,2,3,4,5), so it can be sorted in ascending order. Therefore, print Yes.

Sample Input 2

5 3 2 4 1

Sample Output 2

No

No matter what operation is performed, it is impossible to sort A in ascending order.

Sample Input 3

1 2 3 4 5

Sample Output 3

No

You must perform exactly one operation.

Sample Input 4

2 1 3 4 5

Sample Output 4

Yes

Problem Statement

You are given N strings S_1,S_2,\ldots,S_N consisting of lowercase English letters.
Determine if there are distinct integers i and j between 1 and N, inclusive, such that the concatenation of S_i and S_j in this order is a palindrome.

A string T of length M is a palindrome if and only if the i-th character and the (M+1-i)-th character of T are the same for every 1\leq i\leq M.

Constraints

• 2\leq N\leq 100
• 1\leq \lvert S_i\rvert \leq 50
• N is an integer.
• S_i is a string consisting of lowercase English letters.
• All S_i are distinct.

Sample Input 1

5
ab
ccef
da
a
fe

Sample Output 1

Yes

If we take (i,j)=(1,4), the concatenation of S_1=ab and S_4=a in this order is aba, which is a palindrome, satisfying the condition.
Thus, print Yes.

Here, we can also take (i,j)=(5,2), for which the concatenation of S_5=fe and S_2=ccef in this order is feccef, satisfying the condition.

Sample Input 2

3
a
b
aba

Sample Output 2

No

No two distinct strings among S_1, S_2, and S_3 form a palindrome when concatenated. Thus, print No.
Note that the i and j in the statement must be distinct.

Sample Input 3

2
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Sample Output 3

Yes

Problem Statement

There are N types of elements numbered 1, 2, \ldots, N.

Elements can be combined with each other. When elements i and j are combined, they transform into element A_{i, j} if i \geq j, and into element A_{j, i} if i < j.

Starting with element 1, combine it with elements 1, 2, \ldots, N in this order. Find the final element obtained.

Constraints

• 1 \leq N \leq 100
• 1 \leq A_{i, j} \leq N
• All input values are integers.

Sample Input 1

4
3
2 4
3 1 2
2 1 2 4

Sample Output 1

2

• Combining element 1 with element 1 results in element 3.

• Combining element 3 with element 2 results in element 1.

• Combining element 1 with element 3 results in element 3.

• Combining element 3 with element 4 results in element 2.

Therefore, the value to be printed is 2.

Sample Input 2

5
5
5 5
5 5 5
5 5 5 5
5 5 5 5 5

Sample Output 2

5

Sample Input 3

6
2
1 5
1 6 3
2 6 1 4
2 1 1 1 6
5 6 1 2 2 5

Sample Output 3

5

Problem Statement

You are given a matrix A with H_1 rows and W_1 columns, and a matrix B with H_2 rows and W_2 columns.

• For all integer pairs (i, j) such that 1 \leq i \leq H_1 and 1 \leq j \leq W_1, the element at the i-th row and j-th column of matrix A is A_{i, j}.
• For all integer pairs (i, j) such that 1 \leq i \leq H_2 and 1 \leq j \leq W_2, the element at the i-th row and j-th column of matrix B is B_{i, j}.

You may perform the following operations on the matrix A any number of (possibly 0) times in any order:

• Choose an arbitrary row of A and remove it.
• Choose an arbitrary column of A and remove it.

Determine if it is possible to make the matrix A equal the matrix B.

Constraints

• 1 \leq H_2 \leq H_1 \leq 10
• 1 \leq W_2 \leq W_1 \leq 10
• 1 \leq A_{i, j} \leq 10^9
• 1 \leq B_{i, j} \leq 10^9
• All values in input are integers.

Sample Input 1

4 5
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
2 3
6 8 9
16 18 19

Sample Output 1

Yes

Removing the 2-nd column from the initial A results in:

1 3 4 5
6 8 9 10
11 13 14 15
16 18 19 20

Then, removing the 3-rd row from A results in:

1 3 4 5
6 8 9 10
16 18 19 20

Then, removing the 1-st row from A results in:

6 8 9 10
16 18 19 20

Then, removing the 4-th column from A results in:

6 8 9
16 18 19

Now the matrix equals the matrix B.
Thus, we can make the matrix A equal the matrix B by repeating the operations, so Yes should be printed.

Sample Input 2

3 3
1 1 1
1 1 1
1 1 1
1 1
2

Sample Output 2

No

Regardless of how we perform the operations, we cannot make the matrix A equal the matrix B, so No should be printed.

Problem Statement

There is a grid with H rows and W columns. Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.
Initially, there was one cookie on each square inside a rectangle whose height and width were at least 2 squares long, and no cookie on the other squares.
Formally, there was exactly one quadruple of integers (a,b,c,d) that satisfied all of the following conditions.

• 1 \leq a \lt b \leq H
• 1 \leq c \lt d \leq W
• There was one cookie on each square (i, j) such that a \leq i \leq b, c \leq j \leq d, and no cookie on the other squares.

However, Snuke took and ate one of the cookies on the grid.
The square that contained that cookie is now empty.

As the input, you are given the state of the grid after Snuke ate the cookie.
The state of the square (i, j) is given as the character S_{i,j}, where # means a square with a cookie, and . means a square without one.
Find the square that contained the cookie eaten by Snuke. (The answer is uniquely determined.)

Constraints

• 2 \leq H, W \leq 500
• S_{i,j} is # or ..

Sample Input 1

5 6
......
..#.#.
..###.
..###.
......

Sample Output 1

2 4

Initially, cookies were on the squares inside the rectangle with (2, 3) as the top-left corner and (4, 5) as the bottom-right corner, and Snuke ate the cookie on (2, 4). Thus, you should print (2, 4).

Sample Input 2

3 2
#.
##
##

Sample Output 2

1 2

Initially, cookies were placed on the squares inside the rectangle with (1, 1) as the top-left corner and (3, 2) as the bottom-right corner, and Snuke ate the cookie at (1, 2).

Sample Input 3

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

Sample Output 3

2 5

Problem Statement

There is an online game with N registered players.
Today, which is the 10^{100}-th day since its launch, the developer Takahashi examined the users' login history. It turned out that the i-th player logged in for B_i consecutive days from Day A_i, where Day 1 is the launch day, and did not log in for the other days. In other words, the i-th player logged in on Day A_i, A_i+1, \ldots, A_i+B_i-1, and only on those days.
For each integer k such that 1\leq k\leq N, find the number of days on which exactly k players logged in.

Constraints

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

Sample Input 1

3
1 2
2 3
3 1

Sample Output 1

2 2 0

The first player logged in on Day 1, 2, the second player logged in on Day 2, 3, 4, and the third player logged in on Day 3 only.

Thus, we can see that Day 1, 4 had 1 player logged in, Day 2, 3 had 2 players logged in, and the other days had no players logged in.

The answer is: there were 2 days with exactly 1 player logged in, 2 days with exactly 2 players logged in, and 0 days with exactly 3 players logged in.

Sample Input 2

2
1000000000 1000000000
1000000000 1000000000

Sample Output 2

0 1000000000

There may be two or more players who logged in during the same period.

Problem Statement

We have an empty sequence A. You will be given Q queries, which should be processed in the order they are given. Each query is of one of the three kinds below:

• 1 x : Append x to the end of A.
• 2 : Print the element at the beginning of A. Then, delete that element. It is guaranteed that A will not empty when this query is given.
• 3 : Sort A in ascending order.

Constraints

• 1 \leq Q \leq 2 \times 10^5
• 0 \leq x \leq 10^9
• A will not be empty when a query 2 is given.
• All values in input are integers.

Sample Input 1

8
1 4
1 3
1 2
1 1
3
2
1 0
2

Sample Output 1

1
2

The i-th line below shows the contents of A after the i-th query is processed in Sample Input 1.

• (4)
• (4, 3)
• (4, 3, 2)
• (4, 3, 2, 1)
• (1, 2, 3, 4)
• (2, 3, 4)
• (2, 3, 4, 0)
• (3, 4, 0)

Sample Input 2

9
1 5
1 5
1 3
2
3
2
1 6
3
2

Sample Output 2

5
3
5

The i-th line below shows the contents of A after the i-th query is processed in Sample Input 2.

• (5)
• (5, 5)
• (5, 5, 3)
• (5, 3)
• (3, 5)
• (5)
• (5, 6)
• (5, 6)
• (6)

Problem Statement

There are N buildings, building 1, building 2, \ldots, building N, arranged in this order in a straight line from west to east. Building 1 is the westernmost, and building N is the easternmost. The height of building i\ (1\leq i\leq N) is H_i.

For a pair of integers (i,j)\ (1\leq i\lt j\leq N), building j can be seen from building i if the following condition is satisfied.

• There is no building taller than building j between buildings i and j. In other words, there is no integer k\ (i\lt k\lt j) such that H_k > H_j.

You are given Q queries. In the i-th query, given a pair of integers (l_i,r_i)\ (l_i\lt r_i), find the number of buildings to the east of building r_i (that is, buildings r_i + 1, r_i + 2, \ldots, N) that can be seen from both buildings l_i and r_i.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq Q \leq 2 \times 10^5
• 1 \leq H_i \leq N
• H_i\neq H_j\ (i\neq j)
• 1 \leq l_i < r_i \leq N
• All input values are integers.

Sample Input 1

5 3
2 1 4 3 5
1 2
3 5
1 4

Sample Output 1

2
0
1

• For the first query, among the buildings to the east of building 2, buildings 3 and 5 can be seen from both buildings 1 and 2, so the answer is 2.
• For the second query, there are no buildings to the east of building 5.
• For the third query, among the buildings to the east of building 4, building 5 can be seen from both buildings 1 and 4, so the answer is 1.

Sample Input 2

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

Sample Output 2

1
3
1
2
1
0
1
1
0
0