Problem Statement

We have a grid with 2 horizontal rows and 2 vertical columns.
Each of the squares is black or white, and there are at least 2 black squares.
The colors of the squares are given to you as strings S_1 and S_2, as follows.

• If the j-th character of S_i is #, the square at the i-th row from the top and j-th column from the left is black.
• If the j-th character of S_i is ., the square at the i-th row from the top and j-th column from the left is white.

You can travel between two different black squares if and only if they share a side.
Determine whether it is possible to travel from every black square to every black square (directly or indirectly) by only passing black squares.

Constraints

• Each of S_1 and S_2 is a string with two characters consisting of # and ..
• S_1 and S_2 have two or more #s in total.

Sample Input 1

##
.#

Sample Output 1

Yes

It is possible to directly travel between the top-left and top-right black squares and between top-right and bottom-right squares.
These two moves enable us to travel from every black square to every black square, so the answer is Yes.

Sample Input 2

.#
#.

Sample Output 2

No

It is impossible to travel between the top-right and bottom-left black squares, so the answer is No.

Problem Statement

You are given two integers A and B, each between 0 and 9, inclusive.

Print any integer between 0 and 9, inclusive, that is not equal to A + B.

Constraints

• 0 \leq A \leq 9
• 0 \leq B \leq 9
• A + B \leq 9
• A and B are integers.

Sample Input 1

2 5

Sample Output 1

2

When A = 2, B = 5, we have A + B = 7. Thus, printing any of 0, 1, 2, 3, 4, 5, 6, 8, 9 is correct.

Sample Input 2

0 0

Sample Output 2

9

Sample Input 3

7 1

Sample Output 3

4

Problem Statement

There were N participants in a contest. The participant ranked i-th had the nickname S_i.
Print the nicknames of the top K participants in lexicographical order.

Constraints

• 1 \leq K \leq N \leq 100
• K and N are integers.
• S_i is a string of length 10 consisting of lowercase English letters.
• S_i \neq S_j if i \neq j.

Sample Input 1

5 3
abc
aaaaa
xyz
a
def

Sample Output 1

aaaaa
abc
xyz

This contest had five participants. The participants ranked first, second, third, fourth, and fifth had the nicknames abc, aaaaa, xyz, a, and def, respectively.

The nicknames of the top three participants were abc, aaaaa, xyz, so print these in lexicographical order: aaaaa, abc, xyz.

Sample Input 2

4 4
z
zyx
zzz
rbg

Sample Output 2

rbg
z
zyx
zzz

Sample Input 3

3 1
abc
arc
agc

Sample Output 3

abc

Problem Statement

You are given an integer B.
If there exists a positive integer A such that A^A = B, print its value; otherwise, output -1.

Constraints

• 1 \leq B \leq 10^{18}
• B is an integer.

Sample Input 1

27

Sample Output 1

3

3^3 = 27, so print 3.

Sample Input 2

100

Sample Output 2

-1

There is no A such that A^A = B.

Sample Input 3

10000000000

Sample Output 3

10

Problem Statement

The AtCoder Restaurant uses N types of ingredients numbered from 1 to N.

The restaurant offers M dishes numbered from 1 to M. Dish i uses K_i types of ingredients, namely A_{i,1}, A_{i,2}, \ldots, A_{i,K_i}.

Snuke currently dislikes all N ingredients. He cannot eat any dish that uses one or more ingredients he dislikes, and he can eat a dish that uses none of the disliked ingredients.

Over the next N days, he will overcome his dislikes one ingredient per day. On day i, he overcomes ingredient B_i, and from then on he no longer dislikes it.

For each i=1,2,\ldots,N, find:

• the number of dishes at the AtCoder Restaurant that he can eat immediately after overcoming ingredient B_i on day i.

Constraints

• 1 \leq N \leq 3 \times 10^{5}
• 1 \leq M \leq 3 \times 10^{5}
• 1 \leq K_i \leq N (1 \leq i \leq M)
• The sum of K_i is at most 3 \times 10^{5}.
• 1 \leq A_{i,j} \leq N (1 \leq i \leq M, 1 \leq j \leq K_i)
• A_{i,j} \neq A_{i,k} (1 \leq i \leq M, j \neq k)
• 1 \leq B_i \leq N (1 \leq i \leq N)
• B_i \neq B_j (i \neq j )
• All input values are integers.

Sample Input 1

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

Sample Output 1

0
1
2
3
4

Snuke overcomes his disliked ingredients as follows:

• Day 1: He overcomes ingredient 1. At this time, every dish still uses a disliked ingredient, so print 0.
• Day 2: He overcomes ingredient 3. Dish 4 no longer uses any disliked ingredient and becomes edible; all other dishes still use disliked ingredients, so print 1.
• Day 3: He overcomes ingredient 2. Dish 1 no longer uses any disliked ingredient and becomes edible; all dishes except 1 and 4 still use disliked ingredients, so print 2.
• Day 4: He overcomes ingredient 5. Dish 3 no longer uses any disliked ingredient and becomes edible; all dishes except 1, 3, and 4 still use disliked ingredients, so print 3.
• Day 5: He overcomes ingredient 4. Dish 2 no longer uses any disliked ingredient and becomes edible; now all dishes have no disliked ingredients, so print 4.

Sample Input 2

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

Sample Output 2

0
0
1
1
1
2
4
6
8