Problem Statement

You are given a 3-character string S, where the first character is a digit, the second character is the character x, and the third character is a digit.

Find the product of the two numbers in S.

Constraints

• S is a 3-character string where the first character is an integer between 1 and 9, inclusive, the second character is the character x, and the third character is an integer between 1 and 9, inclusive.

Sample Input 1

3x8

Sample Output 1

24

From 3 \times 8 = 24, print 24.

Sample Input 2

9x9

Sample Output 2

81

From 9 \times 9 = 81, print 81.

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

Consider an xy-plane. The positive direction of the x-axis is in the direction of east, and the positive direction of the y-axis is in the direction of north.
Takahashi is initially at point (x, y) = (0, 0) and facing east (in the positive direction of the x-axis).

You are given a string T = t_1t_2\ldots t_N of length N consisting of S and R. Takahashi will do the following move for each i = 1, 2, \ldots, N in this order.

• If t_i = S, Takahashi advances in the current direction by distance 1.
• If t_i = R, Takahashi turns 90 degrees clockwise without changing his position. As a result, Takahashi's direction changes as follows.
  • If he is facing east (in the positive direction of the x-axis) before he turns, he will face south (in the negative direction of the y-axis) after he turns.
  • If he is facing south (in the negative direction of the y-axis) before he turns, he will face west (in the negative direction of the x-axis) after he turns.
  • If he is facing west (in the negative direction of the x-axis) before he turns, he will face north (in the positive direction of the y-axis) after he turns.
  • If he is facing north (in the positive direction of the y-axis) before he turns, he will face east (in the positive direction of the x-axis) after he turns.

Print the coordinates Takahashi is at after all the steps above have been done.

Constraints

• 1 \leq N \leq 10^5
• N is an integer.
• T is a string of length N consisting of S and R.

Sample Input 1

4
SSRS

Sample Output 1

2 -1

Takahashi is initially at (0, 0) facing east. Then, he moves as follows.

1. t_1 = S, so he advances in the direction of east by distance 1, arriving at (1, 0).
2. t_2 = S, so he advances in the direction of east by distance 1, arriving at (2, 0).
3. t_3 = R, so he turns 90 degrees clockwise, resulting in facing south.
4. t_4 = S, so he advances in the direction of south by distance 1, arriving at (2, -1).

Thus, Takahashi's final position, (x, y) = (2, -1), should be printed.

Sample Input 2

20
SRSRSSRSSSRSRRRRRSRR

Sample Output 2

0 1

Problem Statement

On a non-empty string, a left shift moves the first character to the end of the string, and a right shift moves the last character to the beginning of the string.

For example, a left shift on abcde results in bcdea, and two right shifts on abcde result in deabc.

You are given a non-empty S consisting of lowercase English letters. Among the strings that can be obtained by performing zero or more left shifts and zero or more right shifts on S, find the lexicographically smallest string and the lexicographically largest string.

Constraints

• S consists of lowercase English letters.
• The length of S is between 1 and 1000 (inclusive).

Sample Input 1

aaba

Sample Output 1

aaab
baaa

By performing shifts, we can obtain four strings: aaab, aaba, abaa, baaa. The lexicographically smallest and largest among them are aaab and baaa, respectively.

Sample Input 2

z

Sample Output 2

z
z

Any sequence of operations results in z.

Sample Input 3

abracadabra

Sample Output 3

aabracadabr
racadabraab

Problem Statement

For a positive integer L, a level-L dango string is a string that satisfies the following conditions.

• It is a string of length L+1 consisting of o and -.
• Exactly one of the first character and the last character is -, and the other L characters are o.

For instance, ooo- is a level-3 dango string, but none of -ooo-, oo, and o-oo- is a dango string (more precisely, none of them is a level-L dango string for any positive integer L).

You are given a string S of length N consisting of the two characters o and -. Find the greatest positive integer X that satisfies the following condition.

• There is a contiguous substring of S that is a level-X dango string.

If there is no such integer, print -1.

Constraints

• 1\leq N\leq 2\times10^5
• S is a string of length N consisting of o and -.

Sample Input 1

10
o-oooo---o

Sample Output 1

4

For instance, the substring oooo- corresponding to the 3-rd through 7-th characters of S is a level-4 dango string. No substring of S is a level-5 dango string or above, so you should print 4.

Sample Input 2

1
-

Sample Output 2

-1

Only the empty string and - are the substrings of S. They are not dango strings, so you should print -1.

Sample Input 3

30
-o-o-oooo-oo-o-ooooooo--oooo-o

Sample Output 3

7

Problem Statement

Takahashi is standing at the coordinate 0 on a number line.

He will now perform N jumps. In the i-th jump (1 \leq i \leq N), he moves a_i or b_i in the positive direction.

Is it possible for him to be at the coordinate X after N jumps?

Constraints

• 1 \leq N \leq 100
• 1 \leq a_i \lt b_i \leq 100 \, (1 \leq i \leq N)
• 1 \leq X \leq 10000
• All values in input are integers.

Sample Input 1

2 10
3 6
4 5

Sample Output 1

Yes

By moving b_1 (= 6) in the first jump and a_2 (= 4) in the second jump, he can be at the coordinate X (= 10).

Sample Input 2

2 10
10 100
10 100

Sample Output 2

No

He can be at the coordinate X (= 10) after the first jump, but not after all jumps.

Sample Input 3

4 12
1 8
5 7
3 4
2 6

Sample Output 3

Yes

Problem Statement

You are given an N \times N grid. Let (i,j) denote the cell in the i-th row from the top and the j-th column from the left.
The states of the cells are given by N strings of length N, S_1, S_2, \dots, S_N, in the following format:

• If the j-th character of S_i is o, there is an o written in cell (i,j).
• If the j-th character of S_i is x, there is an x written in cell (i,j).

Find the number of triples of cells that satisfy all of the following conditions:

• The three cells in the triple are distinct.
• All three cells have an o written in them.
• Exactly two of the cells are in the same row.
• Exactly two of the cells are in the same column.

Here, two triples are considered different if and only if some cell is contained in exactly one of the triples.

Constraints

• N is an integer between 2 and 2000, inclusive.
• S_i is a string of length N consisting of o and x.

Sample Input 1

3
ooo
oxx
xxo

Sample Output 1

4

The following four triples satisfy the conditions:

• (1,1),(1,2),(2,1)
• (1,1),(1,3),(2,1)
• (1,1),(1,3),(3,3)
• (1,2),(1,3),(3,3)

Sample Input 2

4
oxxx
xoxx
xxox
xxxo

Sample Output 2

0

Sample Input 3

15
xooxxooooxxxoox
oxxoxoxxxoxoxxo
oxxoxoxxxoxoxxx
ooooxooooxxoxxx
oxxoxoxxxoxoxxx
oxxoxoxxxoxoxxo
oxxoxooooxxxoox
xxxxxxxxxxxxxxx
xooxxxooxxxooox
oxxoxoxxoxoxxxo
xxxoxxxxoxoxxoo
xooxxxooxxoxoxo
xxxoxxxxoxooxxo
oxxoxoxxoxoxxxo
xooxxxooxxxooox

Sample Output 3

2960

Problem Statement

You are given a connected undirected graph with N vertices and M edges without self-loops, where vertices are numbered from 1 to N and edges are numbered from 1 to M. Edge i connects vertices u_i and v_i bidirectionally and has a label w_i.

Among the simple paths (paths that do not visit the same vertex more than once) from vertex 1 to vertex N, find the minimum possible value of the bitwise \mathrm{OR} of all labels on edges included in the path.

Constraints

• 2\le N\le 2\times 10^5
• N-1\le M\le 2\times 10^5
• 1\le u_i < v_i\le N
• 0\le w_i< 2^{30}
• The given graph is connected.
• All input values are integers.

Sample Input 1

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

Sample Output 1

3

By traversing edges 1,3,5 in order and visiting vertices 1,2,3,4 in order, the total bitwise \mathrm{OR} is 1\ \mathrm{OR}\ 2\ \mathrm{OR}\ 3=3.

It is impossible to make the total bitwise \mathrm{OR} smaller than 3, so output 3.

Sample Input 2

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

Sample Output 2

4

The graph may contain multi-edges.

Sample Input 3

8 12
4 5 16691344
5 7 129642441
2 7 789275447
3 8 335307651
3 5 530163333
5 6 811293773
3 8 333712701
1 2 2909941
2 3 160265478
5 7 465414272
1 3 903373004
6 7 408299562

Sample Output 3

468549631

Problem Statement

There are N towns numbered 1,\ldots,N and M roads numbered 1,\ldots,M.

Road i connects towns A_i and B_i. When you use a road, your score changes as follows:

• when you move from town A_i to town B_i using road i, your score increases by C_i; when you move from town B_i to town A_i using road i, your score decreases by C_i.

Your score may become negative.

Answer the following Q questions.

• If you start traveling from town X_i with initial score 0, find the maximum possible score when you are at town Y_i.
  Here, if you cannot get from town X_i to town Y_i, print nan instead; if you can have as large a score as you want when you are at town Y_i, print inf instead.

Constraints

• 2\leq N \leq 10^5
• 0\leq M \leq 10^5
• 1\leq Q \leq 10^5
• 1\leq A_i,B_i,X_i,Y_i \leq N
• 0\leq C_i \leq 10^9
• All values in the input are integers.

Sample Input 1

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

Sample Output 1

-2
inf
nan

For the first question, if you use road 5 to move from town 5 to town 3, you can have a score -2 when you are at town 3.
Since you cannot make the score larger, the answer is -2.

For the second question, you can have as large a score as you want when you are at town 2 if you travel as follows: repeatedly "use road 2 to move from town 1 to town 2 and then use road 1 to move from town 2 to town 1" as many times as you want, and finally use road 2 to move from town 1 to town 2.

For the third question, you cannot get from town 3 to town 1.

Sample Input 2

2 1 1
1 1 1
1 1

Sample Output 2

inf

The endpoints of a road may be the same, and so may the endpoints given in a question.

Sample Input 3

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

Sample Output 3

inf
nan
nan
inf
-9