Problem Statement

A positive integer x is called a 321-like Number when it satisfies the following condition.

• The digits of x are strictly decreasing from top to bottom.
• In other words, if x has d digits, it satisfies the following for every integer i such that 1 \le i < d:
  • (the i-th digit from the top of x) > (the (i+1)-th digit from the top of x).

Note that all one-digit positive integers are 321-like Numbers.

For example, 321, 96410, and 1 are 321-like Numbers, but 123, 2109, and 86411 are not.

You are given N as input. Print Yes if N is a 321-like Number, and No otherwise.

Constraints

• All input values are integers.
• 1 \le N \le 99999

Sample Input 1

321

Sample Output 1

Yes

For N=321, the following holds:

• The first digit from the top, 3, is greater than the second digit from the top, 2.
• The second digit from the top, 2, is greater than the third digit from the top, 1.

Thus, 321 is a 321-like Number.

Sample Input 2

123

Sample Output 2

No

For N=123, the following holds:

• The first digit from the top, 1, is not greater than the second digit from the top, 2.

Thus, 123 is not a 321-like Number.

Sample Input 3

1

Sample Output 3

Yes

Sample Input 4

86411

Sample Output 4

No

Problem Statement

Takahashi had his N-th birthday, when he was T centimeters tall.
Additionally, we know the following facts:

• In each year between Takahashi's birth (0-th birthday) and his X-th birthday, his height increased by D centimeters. More formally, for each i = 1, 2, \ldots, X, his height increased by D centimeters between his (i-1)-th birthday and his i-th birthday.
• Between Takahashi's X-th birthday and his N-th birthday, his height did not change.

Find Takahashi's height on his M-th birthday, in centimeters.

Constraints

• 0 \leq M \lt N \leq 100
• 1 \leq X \leq N
• 1 \leq T \leq 200
• 1 \leq D \leq 100
• Takahashi was at least 1 centimeter tall at his birth.
• All values in input are integers.

Sample Input 1

38 20 17 168 3

Sample Output 1

168

In this sample, Takahashi was 168 centimeters tall on his 38-th birthday. Also, his height did not change between his 17-th birthday and 38-th birthday.
From these facts, we find that he was 168 centimeters tall on his 20-th birthday, so the answer is 168.

Sample Input 2

1 0 1 3 2

Sample Output 2

1

In this sample, Takahashi was 1 centimeter tall on his 0(=M)-th birthday and 3(=T) centimeters tall on his 1(=N)-st birthday.

Sample Input 3

100 10 100 180 1

Sample Output 3

90

Problem Statement

You are given N integers A_1, A_2, \ldots, A_N. Find the largest among those integers that are not the largest.

The constraints of this problem guarantee that the answer exists.

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq 100
• It is not the case that all A_1, A_2, \ldots, A_N are equal.
• All input values are integers.

Sample Input 1

5
2 1 3 3 2

Sample Output 1

2

The largest integer among 2,1,3,3,2 is 3.

The integers that are not 3 among 2,1,3,3,2 are 2,1,2, among which the largest is 2.

Sample Input 2

4
4 3 2 1

Sample Output 2

3

Sample Input 3

8
22 22 18 16 22 18 18 22

Sample Output 3

18

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

There is a class with N students. The height of the i-th student (1 \leq i \leq N) is A_i.

For each j=1,2,\ldots,Q, answer the following question.

• How many of the N students have a height of at least x_j?

Constraints

• 1 \leq N,Q \leq 2 \times 10^5
• 1 \leq A_i \leq 10^9
• 1 \leq x_j \leq 10^9
• All values in input are integers.

Sample Input 1

3 1
100 160 130
120

Sample Output 1

2

The students with a height of at least 120 are the 2-nd and 3-rd ones.

Sample Input 2

5 5
1 2 3 4 5
6
5
4
3
2

Sample Output 2

0
1
2
3
4

Sample Input 3

5 5
804289384 846930887 681692778 714636916 957747794
424238336
719885387
649760493
596516650
189641422

Sample Output 3

5
3
5
5
5

Problem Statement

You are given an integer N. Consider permuting the digits in N and separate them into two positive integers.

For example, for the integer 123, there are six ways to separate it, as follows:

• 12 and 3,
• 21 and 3,
• 13 and 2,
• 31 and 2,
• 23 and 1,
• 32 and 1.

Here, the two integers after separation must not contain leading zeros. For example, it is not allowed to separate the integer 101 into 1 and 01. Additionally, since the resulting integers must be positive, it is not allowed to separate 101 into 11 and 0, either.

What is the maximum possible product of the two resulting integers, obtained by the optimal separation?

Constraints

• N is an integer between 1 and 10^9 (inclusive).
• N contains two or more digits that are not 0.

Sample Input 1

123

Sample Output 1

63

As described in Problem Statement, there are six ways to separate it:

• 12 and 3,
• 21 and 3,
• 13 and 2,
• 31 and 2,
• 23 and 1,
• 32 and 1.

The products of these pairs, in this order, are 36, 63, 26, 62, 23, 32, with 63 being the maximum.

Sample Input 2

1010

Sample Output 2

100

There are two ways to separate it:

• 100 and 1,
• 10 and 10.

In either case, the product is 100.

Sample Input 3

998244353

Sample Output 3

939337176

Problem Statement

You are given an integer sequence A = (A_1, \dots, A_N) of length N.

Find the number of triplets of integers (i, j, k) satisfying all of the conditions below.

• 1 \leq i, j, k \leq N
• \frac{A_i}{A_j} = A_k

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq A_i \leq 2 \times 10^5 \, (1 \leq i \leq N)
• All values in input are integers.

Sample Input 1

3
6 2 3

Sample Output 1

2

(i, j, k) = (1, 2, 3), (1, 3, 2) satisfy the conditions.

Sample Input 2

1
2

Sample Output 2

0

Sample Input 3

10
1 3 2 4 6 8 2 2 3 7

Sample Output 3

62

Problem Statement

You are given a simple directed graph with N vertices numbered 1 to N and M edges numbered 1 to M. Edge i is a directed edge from vertex u_i to vertex v_i.

You may perform the following operation zero or more times.

• Choose distinct vertices x and y such that there is no directed edge from vertex x to vertex y, and add a directed edge from vertex x to vertex y.

Find the minimum number of times you need to perform the operation to make the graph satisfy the following condition.

• For every triple of distinct vertices a, b, and c, if there are directed edges from vertex a to vertex b and from vertex b to vertex c, there is also a directed edge from vertex a to vertex c.

Constraints

• 3 \leq N \leq 2000
• 0 \leq M \leq 2000
• 1 \leq u_i ,v_i \leq N
• u_i \neq v_i
• (u_i,v_i) \neq (u_j,v_j) if i \neq j.
• All values in the input are integers.

Sample Input 1

4 3
2 4
3 1
4 3

Sample Output 1

3

Initially, the condition is not satisfied because, for instance, for vertices 2, 4, and 3, there are directed edges from vertex 2 to vertex 4 and from vertex 4 to vertex 3, but not from vertex 2 to vertex 3.

You can make the graph satisfy the condition by adding the following three directed edges:

• one from vertex 2 to vertex 3,
• one from vertex 2 to vertex 1, and
• one from vertex 4 to vertex 1.

On the other hand, the condition cannot be satisfied by adding two or fewer edges, so the answer is 3.

Sample Input 2

292 0

Sample Output 2

0

Sample Input 3

5 8
1 2
2 1
1 3
3 1
1 4
4 1
1 5
5 1

Sample Output 3

12

Problem Statement

On a blackboard, there are N sets S_1,S_2,\dots,S_N consisting of integers between 1 and M. Here, S_i = \lbrace S_{i,1},S_{i,2},\dots,S_{i,A_i} \rbrace.

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

• choose two sets X and Y with at least one common element. Erase them from the blackboard, and write X\cup Y on the blackboard instead.

Here, X\cup Y denotes the set consisting of the elements contained in at least one of X and Y.

Determine if one can obtain a set containing both 1 and M. If it is possible, find the minimum number of operations required to obtain it.

Constraints

• 1 \le N \le 2 \times 10^5
• 2 \le M \le 2 \times 10^5
• 1 \le \sum_{i=1}^{N} A_i \le 5 \times 10^5
• 1 \le S_{i,j} \le M(1 \le i \le N,1 \le j \le A_i)
• S_{i,j} \neq S_{i,k}(1 \le j < k \le A_i)
• All values in the input are integers.

Sample Input 1

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

Sample Output 1

2

First, choose and remove \lbrace 1,2 \rbrace and \lbrace 2,3 \rbrace to obtain \lbrace 1,2,3 \rbrace.

Then, choose and remove \lbrace 1,2,3 \rbrace and \lbrace 3,4,5 \rbrace to obtain \lbrace 1,2,3,4,5 \rbrace.

Thus, one can obtain a set containing both 1 and M with two operations. Since one cannot achieve the objective by performing the operation only once, the answer is 2.

Sample Input 2

1 2
2
1 2

Sample Output 2

0

S_1 already contains both 1 and M, so the minimum number of operations required is 0.

Sample Input 3

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

Sample Output 3

-1

Sample Input 4

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

Sample Output 4

2