Problem Statement

There are 2N people standing in a row, and the person at the i-th position from the left is wearing clothes of color A_i. Here, the clothes have N colors from 1 to N, and exactly two people are wearing clothes of each color.

Find how many of the integers i=1,2,\ldots,N satisfy the following condition:

• There is exactly one person between the two people wearing clothes of color i.

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq N
• Each integer from 1 through N appears exactly twice in A.
• All input values are integers.

Sample Input 1

3
1 2 1 3 2 3

Sample Output 1

2

There are two values of i that satisfy the condition: 1 and 3.

In fact, the people wearing clothes of color 1 are at the 1st and 3rd positions from the left, with exactly one person in between.

Sample Input 2

2
1 1 2 2

Sample Output 2

0

There may be no i that satisfies the condition.

Sample Input 3

4
4 3 2 3 2 1 4 1

Sample Output 3

3

Problem Statement

There is a grid with H horizontal rows and W vertical columns. Each cell has a lowercase English letter written on it. We denote by (i, j) the cell at the i-th row from the top and j-th column from the left.

The letters written on the grid are represented by H strings S_1,S_2,\ldots, S_H, each of length W. The j-th letter of S_i represents the letter written on (i, j).

There is a unique set of contiguous cells (going vertically, horizontally, or diagonally) in the grid with s, n, u, k, and e written on them in this order.
Find the positions of such cells and print them in the format specified in the Output section.

A tuple of five cells (A_1,A_2,A_3,A_4,A_5) is said to form a set of contiguous cells (going vertically, horizontally, or diagonally) with s, n, u, k, and e written on them in this order if and only if all of the following conditions are satisfied.

• A_1,A_2,A_3,A_4 and A_5 have letters s, n, u, k, and e written on them, respectively.
• For all 1\leq i\leq 4, cells A_i and A_{i+1} share a corner or a side.
• The centers of A_1,A_2,A_3,A_4, and A_5 are on a common line at regular intervals.

Constraints

• 5\leq H\leq 100
• 5\leq W\leq 100
• H and W are integers.
• S_i is a string of length W consisting of lowercase English letters.
• The given grid has a unique conforming set of cells.

Sample Input 1

6 6
vgxgpu
amkxks
zhkbpp
hykink
esnuke
zplvfj

Sample Output 1

5 2
5 3
5 4
5 5
5 6

Tuple (A_1,A_2,A_3,A_4,A_5)=((5,2),(5,3),(5,4),(5,5),(5,6)) satisfies the conditions.
Indeed, the letters written on them are s, n, u, k, and e;
for all 1\leq i\leq 4, cells A_i and A_{i+1} share a side;
and the centers of the cells are on a common line.

Sample Input 2

5 5
ezzzz
zkzzz
ezuzs
zzznz
zzzzs

Sample Output 2

5 5
4 4
3 3
2 2
1 1

Tuple (A_1,A_2,A_3,A_4,A_5)=((5,5),(4,4),(3,3),(2,2),(1,1)) satisfies the conditions.
However, for example, (A_1,A_2,A_3,A_4,A_5)=((3,5),(4,4),(3,3),(2,2),(3,1)) violates the third condition because the centers of the cells are not on a common line, although it satisfies the first and second conditions.

Sample Input 3

10 10
kseeusenuk
usesenesnn
kskekeeses
nesnusnkkn
snenuuenke
kukknkeuss
neunnennue
sknuessuku
nksneekknk
neeeuknenk

Sample Output 3

9 3
8 3
7 3
6 3
5 3

Problem Statement

Takahashi runs an SNS "Twidai," which has N users from user 1 through user N. In Twidai, users can follow or unfollow other users.

Q operations have been performed since Twidai was launched. The i-th (1\leq i\leq Q) operation is represented by three integers T_i, A_i, and B_i, whose meanings are as follows:

• If T_i = 1: it means that user A_i follows user B_i. If user A_i is already following user B_i at the time of this operation, it does not make any change.
• If T_i = 2: it means that user A_i unfollows user B_i. If user A_i is not following user B_i at the time of this operation, it does not make any change.
• If T_i = 3: it means that you are asked to determine if users A_i and B_i are following each other. You need to print Yes if user A_i is following user B_i and user B_i is following user A_i, and No otherwise.

When the service was launched, no users were following any users.

Print the correct answers for all operations such that T_i = 3 in ascending order of i.

Constraints

• 2 \leq N \leq 10 ^ 9
• 1 \leq Q \leq 2\times10 ^ 5
• T _ i=1,2,3\ (1\leq i\leq Q)
• 1 \leq A _ i \leq N\ (1\leq i\leq Q)
• 1 \leq B _ i \leq N\ (1\leq i\leq Q)
• A _ i\neq B _ i\ (1\leq i\leq Q)
• There exists i\ (1\leq i\leq Q) such that T _ i=3.
• All values in the input are integers.

Sample Input 1

3 9
1 1 2
3 1 2
1 2 1
3 1 2
1 2 3
1 3 2
3 1 3
2 1 2
3 1 2

Sample Output 1

No
Yes
No
No

Twidai has three users. The nine operations are as follows.

• User 1 follows user 2. No other users are following or followed by any users.
• Determine if users 1 and 2 are following each other. User 1 is following user 2, but user 2 is not following user 1, so No is the correct answer to this operation.
• User 2 follows user 1.
• Determine if users 1 and 2 are following each other. User 1 is following user 2, and user 2 is following user 1, so Yes is the correct answer to this operation.
• User 2 follows user 3.
• User 3 follows user 2.
• Determine if users 1 and 3 are following each other. User 1 is not following user 3, and user 3 is not following user 1, so No is the correct answer to this operation.
• User 1 unfollows user 2.
• Determine if users 1 and 2 are following each other. User 2 is following user 1, but user 1 is not following user 2, so No is the correct answer to this operation.

Sample Input 2

2 8
1 1 2
1 2 1
3 1 2
1 1 2
1 1 2
1 1 2
2 1 2
3 1 2

Sample Output 2

Yes
No

A user may follow the same user multiple times.

Sample Input 3

10 30
3 1 6
3 5 4
1 6 1
3 1 7
3 8 4
1 1 6
2 4 3
1 6 5
1 5 6
1 1 8
1 8 1
2 3 10
1 7 6
3 5 6
1 6 7
3 6 7
1 9 5
3 8 6
3 3 8
2 6 9
1 7 1
3 10 8
2 9 2
1 10 9
2 6 10
2 6 8
3 1 6
3 1 8
2 8 5
1 9 10

Sample Output 3

No
No
No
No
Yes
Yes
No
No
No
Yes
Yes

Problem Statement

Planning to place many PCs in his room, Takahashi has decided to write a code that finds how many PCs he can place in his room.

You are given H strings S_1,S_2,\ldots,S_H, each of length W, consisting of . and T.

Takahashi may perform the following operation any number of times (possibly zero):

• Choose integers satisfying 1\leq i \leq H and 1 \leq j \leq W-1 such that the j-th and (j+1)-th characters of S_i are both T. Replace the j-th character of S_i with P, and (j+1)-th with C.

He tries to maximize the number of times he performs the operation. Find possible resulting S_1,S_2,\ldots,S_H.

Constraints

• 1\leq H \leq 100
• 2\leq W \leq 100
• H and W are integers.
• S_i is a string of length W consisting of . and T.

Sample Input 1

2 3
TTT
T.T

Sample Output 1

PCT
T.T

He can perform the operation at most once.

For example, an operation with (i,j)=(1,1) makes S_1 PCT.

Sample Input 2

3 5
TTT..
.TTT.
TTTTT

Sample Output 2

PCT..
.PCT.
PCTPC

Problem Statement

Takahashi and Aoki are competing in an election.
There are N electoral districts. The i-th district has X_i + Y_i voters, of which X_i are for Takahashi and Y_i are for Aoki. (X_i + Y_i is always an odd number.)
In each district, the majority party wins all Z_i seats in that district. Then, whoever wins the majority of seats in the N districts as a whole wins the election. (\displaystyle \sum_{i=1}^N Z_i is odd.)
At least how many voters must switch from Aoki to Takahashi for Takahashi to win the election?

Constraints

• 1 \leq N \leq 100
• 0 \leq X_i, Y_i \leq 10^9
• X_i + Y_i is odd.
• 1 \leq Z_i
• \displaystyle \sum_{i=1}^N Z_i \leq 10^5
• \displaystyle \sum_{i=1}^N Z_i is odd.

Sample Input 1

1
3 8 1

Sample Output 1

3

Since there is only one district, whoever wins the seat in that district wins the election.
If three voters for Aoki in the district switch to Takahashi, there will be six voters for Takahashi and five for Aoki, and Takahashi will win the seat.

Sample Input 2

2
3 6 2
1 8 5

Sample Output 2

4

Since there are more seats in the second district than in the first district, Takahashi must win a majority in the second district to win the election.
If four voters for Aoki in the second district switch sides, Takahashi will win five seats. In this case, Aoki will win two seats, so Takahashi will win the election.

Sample Input 3

3
3 4 2
1 2 3
7 2 6

Sample Output 3

0

If Takahashi will win the election even if zero voters switch sides, the answer is 0.

Sample Input 4

10
1878 2089 16
1982 1769 13
2148 1601 14
2189 2362 15
2268 2279 16
2394 2841 18
2926 2971 20
3091 2146 20
3878 4685 38
4504 4617 29

Sample Output 4

86