Problem Statement

You are given a 3-character string S, which is a concatenation of integers a and b between 1 and 9 (inclusive) and the character x in this order: axb.

Find the product of a and b.

Constraints

• The length of S is 3.
• The 1-st and 3-rd characters are digits between 1 and 9 (inclusive).
• The 2-nd character is x.

Sample Input 1

3x7

Sample Output 1

21

We have 3 \times 7 = 21, which should be printed.

Sample Input 2

9x9

Sample Output 2

81

Sample Input 3

1x1

Sample Output 3

1

Problem Statement

The definition of an 11/22 string in this problem is the same as in Problems C and E.

A string T is called an 11/22 string when it satisfies all of the following conditions:

• |T| is odd. Here, |T| denotes the length of T.
• The 1-st through (\frac{|T|+1}{2} - 1)-th characters are all 1.
• The (\frac{|T|+1}{2})-th character is /.
• The (\frac{|T|+1}{2} + 1)-th through |T|-th characters are all 2.

For example, 11/22, 111/222, and / are 11/22 strings, but 1122, 1/22, 11/2222, 22/11, and //2/2/211 are not.

Given a string S of length N consisting of 1, 2, and /, determine whether S is an 11/22 string.

Constraints

• 1 \leq N \leq 100
• S is a string of length N consisting of 1, 2, and /.

Sample Input 1

5
11/22

Sample Output 1

Yes

11/22 satisfies the conditions for an 11/22 string in the problem statement.

Sample Input 2

1
/

Sample Output 2

Yes

/ satisfies the conditions for an 11/22 string.

Sample Input 3

4
1/22

Sample Output 3

No

1/22 does not satisfy the conditions for an 11/22 string.

Sample Input 4

5
22/11

Sample Output 4

No

Problem Statement

N examinees took an entrance exam.
The examinee numbered i scored A_i points in math and B_i points in English.

The admissions are determined as follows.

1. X examinees with the highest math scores are admitted.
2. Then, among the examinees who are not admitted yet, Y examinees with the highest English scores are admitted.
3. Then, among the examinees who are not admitted yet, Z examinees with the highest total scores in math and English are admitted.
4. Those examinees who are not admitted yet are rejected.

Here, in each of the steps 1. to 3., ties are broken by examinees' numbers: an examinee with the smaller examinee's number is prioritized. See also Sample Input and Output.

Print the examinees' numbers of the admitted examinees determined by the steps above in ascending order, separated by newlines.

Constraints

• All values in input are integers.
• 1 \le N \le 1000
• 0 \le X,Y,Z \le N
• 1 \le X+Y+Z \le N
• 0 \le A_i,B_i \le 100

Sample Input 1

6 1 0 2
80 60 80 60 70 70
40 20 50 90 90 80

Sample Output 1

1
4
5

• First, 1 examinee with the highest math score is admitted.
  • Examinee 1 is tied with Examinee 3, scoring the highest 80 points in math, and the tie is broken by the examinees' numbers, so Examinee 1 is admitted.
• Then, among the examinees who are not admitted yet, 0 examinees with the highest English scores are admitted.
  • Obviously, it does not affect the admissions.
• Then, among the examinees who are not admitted yet, 2 examinees with the highest total scores in math and English are admitted.
  • First, among the examinees who are not admitted yet, Examinee 5 is admitted, scoring the highest total score of 160 points.
  • Next, among the examinees who are not admitted yet, Examinee 4 is tied with Examinee 6, scoring a total score of 150 points. The tie is broken by the examinees' numbers, and Examinee 4 is admitted.

Therefore, the examinees' numbers of the admitted examinees are 1, 4, and 5. Print them in ascending order.

Sample Input 2

5 2 1 2
0 100 0 100 0
0 0 100 100 0

Sample Output 2

1
2
3
4
5

All examinees may be admitted.

Sample Input 3

15 4 3 2
30 65 20 95 100 45 70 85 20 35 95 50 40 15 85
0 25 45 35 65 70 80 90 40 55 20 20 45 75 100

Sample Output 3

2
4
5
6
7
8
11
14
15

Problem Statement

Given an integer X between -10^{18} and 10^{18}, inclusive, print \left\lceil \dfrac{X}{10} \right\rceil.
Here, \left\lceil a \right\rceil denotes the smallest integer not less than a.

Constraints

• -10^{18} \leq X \leq 10^{18}
• X is an integer.

Sample Input 1

27

Sample Output 1

3

The integers not less than \frac{27}{10} = 2.7 are 3, 4, 5, \dots. Among these, the smallest is 3, so \left \lceil \frac{27}{10} \right \rceil = 3.

Sample Input 2

-13

Sample Output 2

-1

The integers not less than \frac{-13}{10} = -1.3 are all positive integers, 0, and -1. Among these, the smallest is -1, so \left \lceil \frac{-13}{10} \right \rceil = -1.

Sample Input 3

40

Sample Output 3

4

The smallest integer not less than \frac{40}{10} = 4 is 4 itself.

Sample Input 4

-20

Sample Output 4

-2

Sample Input 5

123456789123456789

Sample Output 5

12345678912345679

Problem Statement

There are N pigeons numbered from 1 to N, and there are N nests numbered from 1 to N. Initially, pigeon i is in nest i for 1\leq i\leq N.

You are given Q queries, which you must process in order. There are two types of queries, each given in one of the following formats:

• 1 P H : Move pigeon P to nest H.
• 2 : Output the number of nests that contain more than one pigeon.

Constraints

• 2 \leq N \leq 10^6
• 1 \leq Q \leq 3\times 10^5
• 1 \leq P, H \leq N
• For a query of the first type, pigeon P is not in nest H before the move.
• All input values are integers.

Sample Input 1

4 7
2
1 1 2
2
1 3 2
2
1 3 4
2

Sample Output 1

0
1
1
2

Initially, pigeons 1,2,3,4 are in nests 1,2,3,4, respectively.

• For the 1st query, the counts of pigeons in nests 1,2,3,4 are 1,1,1,1. No nests contain multiple pigeons, output 0.
• For the 2nd query, move pigeon 1 to nest 2.
• For the 3rd query, the counts become 0,2,1,1, respectively. One nest (nest 2) contains multiple pigeons, so output 1.
• For the 4th query, move pigeon 3 to nest 2.
• For the 5th query, the counts become 0,3,0,1, respectively. One nest (nest 2) contains multiple pigeons, so output 1.
• For the 6th query, move pigeon 3 to nest 4.
• For the 7th query, the counts become 0,2,0,2, respectively. Two nests (nests 2 and 4) contain multiple pigeons, so output 2.

Sample Input 2

5 10
2
1 4 3
1 4 5
2
1 3 1
2
1 2 3
1 2 5
1 1 3
2

Sample Output 2

0
1
2
1

Problem Statement

You are given N strings S_1,S_2,\dots,S_N consisting of lowercase English alphabets.

Consider choosing some number of strings from S_1,S_2,\dots,S_N.

Find the maximum number of distinct alphabets that satisfy the following condition: "the alphabet is contained in exactly K of the chosen strings."

Constraints

• 1 \le N \le 15
• 1 \le K \le N
• N and K are integers.
• S_i is a non-empty string consisting of lowercase English alphabets.
• For each integer i such that 1 \le i \le N, S_i does not contain two or more same alphabets.
• If i \neq j, then S_i \neq S_j.

Sample Input 1

4 2
abi
aef
bc
acg

Sample Output 1

3

When S_1,S_3, and S_4 are chosen, a,b, and c occur in exactly two of the strings.

There is no way to choose strings so that 4 or more alphabets occur in exactly 2 of the strings, so the answer is 3.

Sample Input 2

2 2
a
b

Sample Output 2

0

You cannot choose the same string more than once.

Sample Input 3

5 2
abpqxyz
az
pq
bc
cy

Sample Output 3

7

Problem Statement

The Republic of AtCoder has N cities numbered 1 through N and N-1 roads numbered 1 through N-1. Road i connects City A_i and City B_i bidirectionally. It is guaranteed that one can travel between every pair of cities using roads.

Takahashi will depart City 1 and have a journey by repeating the following.

• If there are unvisited cities that are directly connected to the city Takahashi is in now, he goes to the city with the smallest number among those cities.
• Otherwise,
  • if he is in City 1, he ends the journey;
  • otherwise, he goes to the city he was in just before visiting the current city for the first time.

Find the sequence of cities visited by Takahashi in the order he visits them.

Constraints

• 2 \leq N \leq 2\times 10^5
• 1\leq A_i,B_i \leq N
• It is possible to travel between every pair of cities using roads.

Sample Input 1

4
1 2
4 2
3 1

Sample Output 1

1 2 4 2 1 3 1

His journey will be as follows.

• Start in City 1.
• The unvisited cities directly connected to City 1 are City 2 and 3. Go to the city with the smaller number, that is, City 2.
• The unvisited city directly connected to City 2 is City 4. Go there.
• There is no unvisited city directly connected to City 4. Go back to City 2.
• There is no unvisited city directly connected to City 2. Go to City 1, where he was in just before visiting City 2 for the first time.
• The unvisited city directly connected to City 1 is City 3. Go there.
• There is no unvisited city directly connected to City 3. Go back to City 1.
• There is no unvisited city directly connected to City 1. End the journey.

Sample Input 2

5
1 2
1 3
1 4
1 5

Sample Output 2

1 2 1 3 1 4 1 5 1

Problem Statement

This problem is an interactive problem (in which your program and the judge system communicate via input and output).

You are given a tree G with N vertices numbered 1 to N. The i-th edge connects vertices U_i and V_i.

You will play a game with Takahashi using this tree G. First, you decide who is first and who is second. Then, starting from the first player, take turns performing the following operation:

• Choose a pair of integers (i,j) with 1 \leq i < j \leq N that satisfies both of the following conditions, then add an edge connecting vertices i and j to G.
  • G does not already have an edge connecting vertices i and j.
  • Adding an edge connecting vertices i and j does not create an odd cycle.

A player who cannot perform this operation loses, and the other player wins. Play this game against Takahashi and win.

Constraints

• 2 \leq N \leq 100
• 1 \leq U_i < V_i \leq N
• The given graph is a tree.
• All input values are integers.

Interaction

This is an interactive problem (in which your program and the judge system communicate via input and output).

First, read N and the edges of G from Standard Input, given in the following format:

N
U_1 V_1
U_2 V_2
\vdots
U_{N-1} V_{N-1}

Then, decide whether you go first or second. If you choose first, print First; if second, print Second.

Then, the game begins.

On your turn, output the chosen pair (i,j) by printing two integers i and j in this order, separated by a space:

i j

On Takahashi's turn, two integers i,j will be given in order, separated by a space, via Standard Input:

i j

If (i,j)=(-1,-1), it means he can no longer make a move and you win. Immediately terminate your program in this case.
Otherwise, (i,j) is the pair of integers he has chosen.

Notes

• After each output, be sure to print a newline and flush Standard Output. Otherwise, you may get TLE.
• If you produce output in an incorrect format or your program ends prematurely, the judge result is indeterminate.
• Once the game finishes, terminate your program immediately. Otherwise, the judge result is indeterminate.

Sample Interaction

Problem Statement

You are given a positive integer N, a positive integer M, and an integer sequence A=(A_1,A_2,\ldots,A_N) of length N. It is guaranteed that each element of A is between 0 and M-1, inclusive.

You can perform the following operation on the integer sequence A any number of times, possibly zero:

• Choose a pair of integers (l,r) satisfying 1\le l\le r\le N, and replace A_i with (A_i+1) \bmod M for each i=l,l+1,\ldots,r.

Find the minimum number of operations required to make A a palindrome.

Here, A is a palindrome if A_i=A_{N+1-i} holds for i=1,2,\ldots,N.

You are given T test cases; solve each of them.

Constraints

• 1\le T
• 1\le N\le 2\times 10^5
• 1\le M\le 10^9
• 0\le A_i < M
• The sum of N over all test cases is at most 2\times 10^5.
• All input values are integers.

Sample Input 1

3
4 5
0 3 1 2
1 20260418
454
7 12
3 1 4 1 5 9 2

Sample Output 1

3
0
5

Consider the first test case.

You can make A a palindrome in three operations as follows:

• Choose (l,r)=(2,4). A becomes (0,4,2,3).
• Choose (l,r)=(3,4). A becomes (0,4,3,4).
• Choose (l,r)=(3,4). A becomes (0,4,4,0).

It is impossible to make A a palindrome in fewer than three operations, so output 3.