Problem Statement

Print how many distinct integers there are in given five integers A, B, C, D, and E.

Constraints

• 0 \leq A, B, C, D, E \leq 100
• All values in input are integers.

Sample Input 1

31 9 24 31 24

Sample Output 1

3

In the given five integers 31, 9, 24, 31, and 24, there are three distinct integers 9, 24, and 31. Thus, 3 should be printed.

Sample Input 2

0 0 0 0 0

Sample Output 2

1

Problem Statement

You are given a three-digit integer N where each digit is an integer between 1 and 9, inclusive.

Let a, b, c be the hundreds, tens, ones digits of N, respectively. Print an integer formed by arranging b, c, a in this order, and an integer formed by arranging c, a, b in this order.

Constraints

• N is a three-digit integer where each digit is an integer between 1 and 9, inclusive.

Sample Input 1

379

Sample Output 1

793 937

The hundreds, tens, ones digits of 379 are 3, 7, 9, respectively, so print 793 and 937.

Sample Input 2

919

Sample Output 2

199 991

The hundreds, tens, ones digits of 919 are 9, 1, 9, respectively, so print 199 and 991.

Problem Statement

You are given a positive integer N. If there are integers x and y such that N=2^x3^y, print Yes; otherwise, print No.

Constraints

• 1\leq N\leq10^{18}
• N is an integer.

Sample Input 1

324

Sample Output 1

Yes

For x=2,y=4, we have 2^x3^y=2^23^4=4\times81=324, so the condition is satisfied. Thus, you should print Yes.

Sample Input 2

5

Sample Output 2

No

There are no integers x and y such that 2^x3^y=5. Thus, you should print No.

Sample Input 3

32

Sample Output 3

Yes

For x=5,y=0, we have 2^x3^y=32\times1=32, so you should print Yes.

Sample Input 4

37748736

Sample Output 4

Yes

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

You are given a simple undirected graph with N vertices numbered 1 to N and M edges numbered 1 to M. Edge i connects vertex u_i and vertex v_i.
Find the number of connected components in this graph.

Notes

A simple undirected graph is a graph that is simple and has undirected edges.
A graph is simple if and only if it has no self-loop or multi-edge.

A subgraph of a graph is a graph formed from some of the vertices and edges of that graph.
A graph is connected if and only if one can travel between every pair of vertices via edges.
A connected component is a connected subgraph that is not part of any larger connected subgraph.

Constraints

• 1 \leq N \leq 100
• 0 \leq M \leq \frac{N(N - 1)}{2}
• 1 \leq u_i, v_i \leq N
• The given graph is simple.
• All values in the input are integers.

Sample Input 1

5 3
1 2
1 3
4 5

Sample Output 1

2

The given graph contains the following two connected components:

• a subgraph formed from vertices 1, 2, 3, and edges 1, 2;
• a subgraph formed from vertices 4, 5, and edge 3.

Sample Input 2

5 0

Sample Output 2

5

Sample Input 3

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

Sample Output 3

1

Problem Statement

You are given an integer X. The following action on this integer is called an operation.

• Choose and do one of the following.
  • Add 1 to X.
  • Subtract 1 from X.

The terms in the arithmetic progression S with N terms whose initial term is A and whose common difference is D are called good numbers.
Consider performing zero or more operations to make X a good number. Find the minimum number of operations required to do so.

Constraints

• All values in input are integers.
• -10^{18} \le X,A \le 10^{18}
• -10^6 \le D \le 10^6
• 1 \le N \le 10^{12}

Sample Input 1

6 2 3 3

Sample Output 1

1

Since A=2,D=3,N=3, we have S=(2,5,8).
You can subtract 1 from X once to make X=6 a good number.
It is impossible to make X good in zero operations.

Sample Input 2

0 0 0 1

Sample Output 2

0

We might have D=0. Additionally, no operation might be required.

Sample Input 3

998244353 -10 -20 30

Sample Output 3

998244363

Sample Input 4

-555555555555555555 -1000000000000000000 1000000 1000000000000

Sample Output 4

444445

Problem Statement

You are given a sequence A = (A_1, A_2, \dots, A_N) of length N consisting of positive integers, and integers x and y.
Determine whether it is possible to place N+1 points p_1, p_2, \dots, p_N, p_{N+1} in the xy-coordinate plane to satisfy all of the following conditions. (It is allowed to place two or more points at the same coordinates.)

• p_1 = (0, 0).
• p_2 = (A_1, 0).
• p_{N+1} = (x, y).
• The distance between the points p_i and p_{i+1} is A_i. (1 \leq i \leq N)
• The segments p_i p_{i+1} and p_{i+1} p_{i+2} form a 90 degree angle. (1 \leq i \leq N - 1)

Constraints

• 2 \leq N \leq 10^3
• 1 \leq A_i \leq 10
• |x|, |y| \leq 10^4
• All values in the input are integers.

Sample Input 1

3 -1 1
2 1 3

Sample Output 1

Yes

The figure below shows a placement where p_1 = (0, 0), p_2 = (2, 0), p_3 = (2, 1), and p_4 = (-1, 1). All conditions in the Problem Statement are satisfied.

Sample Input 2

5 2 0
2 2 2 2 2

Sample Output 2

Yes

Letting p_1 = (0, 0), p_2 = (2, 0), p_3 = (2, 2), p_4 = (0, 2), p_5 = (0, 0), and p_6 = (2, 0) satisfies all the conditions. Note that multiple points may be placed at the same coordinates.

Sample Input 3

4 5 5
1 2 3 4

Sample Output 3

No

Sample Input 4

3 2 7
2 7 4

Sample Output 4

No

Sample Input 5

10 8 -7
6 10 4 1 5 9 8 6 5 1

Sample Output 5

Yes

Problem Statement

Takahashi is initially at his house and is about to visit Aoki's house.

There are N bus stops numbered 1 to N between the two houses, and Takahashi can move between them in the following ways:

• He can walk from his house to bus stop 1 in X units of time.
• For each i = 1, 2, \ldots, N-1, a bus departs from bus stop i at each time that is a multiple of P_i, and by taking this bus, he can get to bus stop (i+1) in T_i units of time. Here, the constraints guarantee that 1 \leq P_i \leq 8.
• Takahashi can walk from bus stop N to Aoki's house in Y units of time.

For each i = 1, 2, \ldots, Q, process the following query.

Find the earliest time that Takahashi can arrive at Aoki's house when he leaves his house at time q_i.

Note that if he arrives at a bus stop exactly at the departure time of a bus, he can take that bus.

Constraints

• 2 \leq N \leq 10^5
• 1 \leq X, Y \leq 10^9
• 1 \leq P_i \leq 8
• 1 \leq T_i \leq 10^9
• 1 \leq Q \leq 2 \times 10^5
• 0 \leq q_i \leq 10^9
• All input values are integers.

Sample Input 1

4 2 3
5 4
6 6
3 1
7
13
0
710511029
136397527
763027379
644706927
447672230

Sample Output 1

34
22
710511052
136397548
763027402
644706946
447672250

For the first query, Takahashi can move as follows to arrive at Aoki's house at time 34.

• Leave his house at time 13.
• Walk from his house and arrive at bus stop 1 at time 15.
• Take the bus departing from bus stop 1 at time 15 and arrive at bus stop 2 at time 19.
• Take the bus departing from bus stop 2 at time 24 and arrive at bus stop 3 at time 30.
• Take the bus departing from bus stop 3 at time 30 and arrive at bus stop 4 at time 31.
• Walk from bus stop 4 and arrive at Aoki's house at time 34.

For the second query, Takahashi can move as follows and arrive at Aoki's house at time 22.

• Leave his house at time 0.
• Walk from his house and arrive at bus stop 1 at time 2.
• Take the bus departing from bus stop 1 at time 5 and arrive at bus stop 2 at time 9.
• Take the bus departing from bus stop 2 at time 12 and arrive at bus stop 3 at time 18.
• Take the bus departing from bus stop 3 at time 18 and arrive at bus stop 4 at time 19.
• Walk from bus stop 4 and arrive at Aoki's house at time 22.

Problem Statement

You are given a connected simple undirected graph G with N vertices numbered 1 to N and N edges. The i-th edge connects Vertex u_i and Vertex v_i bidirectionally.

Answer the following Q queries.

• Determine whether there is a unique simple path from Vertex x_i to Vertex y_i (a simple path is a path without repetition of vertices).

Constraints

• 3 \leq N \leq 2 \times 10^5
• 1 \leq u_i < v_i\leq N
• (u_i,v_i) \neq (u_j,v_j) if i \neq j.
• G is a connected simple undirected graph with N vertices and N edges.
• 1 \leq Q \leq 2 \times 10^5
• 1 \leq x_i < y_i\leq N
• All values in input are integers.

Sample Input 1

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

Sample Output 1

No
Yes
No

The simple paths from Vertex 1 to 2 are (1,2) and (1,3,2), which are not unique, so the answer to the first query is No.

The simple path from Vertex 1 to 4 is (1,4), which is unique, so the answer to the second query is Yes.

The simple paths from Vertex 1 to 5 are (1,2,5) and (1,3,2,5), which are not unique, so the answer to the third query is No.

Sample Input 2

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

Sample Output 2

Yes
No
Yes
Yes
No
No
Yes
No
Yes
No