Problem Statement

You are given two different strings S and T.
If S is lexicographically smaller than T, print Yes; otherwise, print No.

Note that many major programming languages implement lexicographical comparison of strings as operators or functions in standard libraries. For more detail, see your language's reference.

Constraints

• S and T are different strings, each of which consists of lowercase English letters and has a length of between 1 and 10 (inclusive).

Sample Input 1

abc atcoder

Sample Output 1

Yes

abc and atcoder begin with the same character, but their second characters are different. Since b comes earlier than t in alphabetical order, we can see that abc is lexicographically smaller than atcoder.

Sample Input 2

arc agc

Sample Output 2

No

Sample Input 3

a aa

Sample Output 3

Yes

Problem Statement

Given integers A and B, print the value A^B.

Constraints

• 1 \leq A, B \leq 9
• All values in the input are integers.

Sample Input 1

4 3

Sample Output 1

64

4^3 = 64, so 64 should be printed.

Sample Input 2

5 5

Sample Output 2

3125

Sample Input 3

8 1

Sample Output 3

8

Problem Statement

We have 4 cards with an integer 1 written on it, 4 cards with 2, \ldots, 4 cards with N, for a total of 4N cards.

Takahashi shuffled these cards, removed one of them, and gave you a pile of the remaining 4N-1 cards. The i-th card (1 \leq i \leq 4N - 1) of the pile has an integer A_i written on it.

Find the integer written on the card removed by Takahashi.

Constraints

• 1 \leq N \leq 10^5
• 1 \leq A_i \leq N \, (1 \leq i \leq 4N - 1)
• For each k \, (1 \leq k \leq N), there are at most 4 indices i such that A_i = k.
• All values in input are integers.

Sample Input 1

3
1 3 2 3 3 2 2 1 1 1 2

Sample Output 1

3

Takahashi removed a card with 3 written on it.

Sample Input 2

1
1 1 1

Sample Output 2

1

Sample Input 3

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

Sample Output 3

2

Problem Statement

N participants, numbered 1 to N, will participate in a contest with M problems, numbered 1 to M.

For an integer i between 1 and N and an integer j between 1 and M, participant i can solve problem j if the j-th character of S_i is o, and cannot solve it if that character is x.

The participants must be in pairs. Print the number of ways to form a pair of participants who can collectively solve all the M problems.

More formally, print the number of pairs (x,y) of integers satisfying 1\leq x < y\leq N such that for any integer j between 1 and M, at least one of participant x and participant y can solve problem j.

Constraints

• N is an integer between 2 and 30, inclusive.
• M is an integer between 1 and 30, inclusive.
• S_i is a string of length M consisting of o and x.

Sample Input 1

5 5
ooooo
oooxx
xxooo
oxoxo
xxxxx

Sample Output 1

5

The following five pairs satisfy the condition: participants 1 and 2, participants 1 and 3, participants 1 and 4, participants 1 and 5, and participants 2 and 3.

On the other hand, the pair of participants 2 and 4, for instance, does not satisfy the condition because they cannot solve problem 4.

Sample Input 2

3 2
ox
xo
xx

Sample Output 2

1

Sample Input 3

2 4
xxxx
oxox

Sample Output 3

0

Problem Statement

We have a sequence of N positive integers: A=(A_1,\dots,A_N).
Let B be the concatenation of 10^{100} copies of A.

Consider summing up the terms of B from left to right. When does the sum exceed X for the first time?
In other words, find the minimum integer k such that:

\displaystyle{\sum_{i=1}^{k} B_i \gt X}.

Constraints

• 1 \leq N \leq 10^5
• 1 \leq A_i \leq 10^9
• 1 \leq X \leq 10^{18}
• All values in input are integers.

Sample Input 1

3
3 5 2
26

Sample Output 1

8

We have B=(3,5,2,3,5,2,3,5,2,\dots).
\displaystyle{\sum_{i=1}^{8} B_i = 28 \gt 26} holds, but the condition is not satisfied when k is 7 or less, so the answer is 8.

Sample Input 2

4
12 34 56 78
1000

Sample Output 2

23

Problem Statement

There are N people numbered 1, 2, \ldots, N on a two-dimensional plane, and person i is at the point represented by the coordinates (X_i,Y_i).

Person 1 has been infected with a virus. The virus spreads to people within a distance of D from an infected person.

Here, the distance is defined as the Euclidean distance, that is, for two points (a_1, a_2) and (b_1, b_2), the distance between these two points is \sqrt {(a_1-b_1)^2 + (a_2-b_2)^2}.

After a sufficient amount of time has passed, that is, when all people within a distance of D from person i are infected with the virus if person i is infected, determine whether person i is infected with the virus for each i.

Constraints

• 1 \leq N, D \leq 2000
• -1000 \leq X_i, Y_i \leq 1000
• (X_i, Y_i) \neq (X_j, Y_j) if i \neq j.
• All input values are integers.

Sample Input 1

4 5
2 -1
3 1
8 8
0 5

Sample Output 1

Yes
Yes
No
Yes

The distance between person 1 and person 2 is \sqrt 5, so person 2 gets infected with the virus.
Also, the distance between person 2 and person 4 is 5, so person 4 gets infected with the virus.
Person 3 has no one within a distance of 5, so they will not be infected with the virus.

Sample Input 2

3 1
0 0
-1000 -1000
1000 1000

Sample Output 2

Yes
No
No

Sample Input 3

9 4
3 2
6 -1
1 6
6 5
-2 -3
5 3
2 -3
2 1
2 6

Sample Output 3

Yes
No
No
Yes
Yes
Yes
Yes
Yes
No

Problem Statement

How many positive integers no greater than N can be represented as a^2 \times b \times c^2 with three primes a,b, and c such that a<b<c?

Constraints

• N is an integer satisfying 300 \le N \le 10^{12}.

Sample Input 1

1000

Sample Output 1

3

The conforming integers no greater than 1000 are the following three.

• 300 = 2^2 \times 3 \times 5^2
• 588 = 2^2 \times 3 \times 7^2
• 980 = 2^2 \times 5 \times 7^2

Sample Input 2

1000000000000

Sample Output 2

2817785

Problem Statement

There are N squares called Square 1 though Square N. You start on Square 1.

Each of the squares from Square 1 through Square N-1 has a die on it. The die on Square i is labeled with the integers from 0 through A_i, each occurring with equal probability. (Die rolls are independent of each other.)

Until you reach Square N, you will repeat rolling a die on the square you are on. Here, if the die on Square x rolls the integer y, you go to Square x+y.

Find the expected value, modulo 998244353, of the number of times you roll a die.

Notes

It can be proved that the sought expected value is always a rational number. Additionally, if that value is represented \frac{P}{Q} using two coprime integers P and Q, there is a unique integer R such that R \times Q \equiv P\pmod{998244353} and 0 \leq R \lt 998244353. Find this R.

Constraints

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

Sample Input 1

3
1 1

Sample Output 1

4

The sought expected value is 4, so 4 should be printed.

Here is one possible scenario until reaching Square N:

• Roll 1 on Square 1, and go to Square 2.
• Roll 0 on Square 2, and stay there.
• Roll 1 on Square 2, and go to Square 3.

This scenario occurs with probability \frac{1}{8}.

Sample Input 2

5
3 1 2 1

Sample Output 2

332748122

Problem Statement

For a string S of length N and an integer i\ (0\leq i\leq N), let us define the string f_i(S) as the concatenation of:

• the first i characters of S,
• the reversal of S, and
• the last (N-i) characters of S,

in this order. For instance, if S= abc and i=2, we have f_i(S)= abcbac.

You are given a string T of length 2N. Find a pair of a string S of length N and an integer i\ (0\leq i\leq N) such that f_i(S)=T. If no such pair of S and i exists, report that fact.

Constraints

• 1\leq N \leq 10^6
• N is an integer.
• T is a string of length 2N consisting of lowercase English letters.

Sample Input 1

3
abcbac

Sample Output 1

abc
2

As mentioned in the problem statement, if S= abc and i=2, we have f_i(S)= abcbac, which equals T, so you should print abc and 2.

Sample Input 2

4
abababab

Sample Output 2

abab
1

S= abab and i=3 also satisfy the condition.

Sample Input 3

3
agccga

Sample Output 3

cga
0

S= agc and i=3 also satisfy the condition.

Sample Input 4

4
atcodeer

Sample Output 4

-1

If no pair of S and i satisfies the condition, print -1.