Problem Statement

You are given a sequence of N integers: A=(A _ 1,A _ 2,\ldots,A _ N).

Print all even numbers in A without changing the order.

Constraints

• 1\leq N\leq 100
• 1\leq A _ i\leq 100\ (1\leq i\leq N)
• A contains at least one even number.
• All values in the input are integers.

Sample Input 1

5
1 2 3 5 6

Sample Output 1

2 6

We have A=(1,2,3,5,6). Among them are two even numbers, A _ 2=2 and A _ 5=6, so print 2 and 6 in this order, with a space in between.

Sample Input 2

5
2 2 2 3 3

Sample Output 2

2 2 2

A may contain equal elements.

Sample Input 3

10
22 3 17 8 30 15 12 14 11 17

Sample Output 3

22 8 30 12 14

Problem Statement

You are given an integer N between 1 and 9, inclusive, as input.

Concatenate N copies of the digit N and print the resulting string.

Constraints

• N is an integer between 1 and 9, inclusive.

Sample Input 1

3

Sample Output 1

333

Concatenate three copies of the digit 3 to yield the string 333.

Sample Input 2

9

Sample Output 2

999999999

Problem Statement

You are given a 4-digit PIN: X_1X_2X_3X_4, which may begin with a 0. The PIN is said to be weak when it satisfies one of the following conditions:

• All of the four digits are the same.
• For each integer i such that 1\leq i\leq 3, X_{i+1} follows X_i. Here, j+1 follows j for each 0\leq j\leq 8, and 0 follows 9.

If the given PIN is weak, print Weak; otherwise, print Strong.

Constraints

• 0 \leq X_1, X_2, X_3, X_4 \leq 9
• X_1, X_2, X_3, and X_4 are integers.

Sample Input 1

7777

Sample Output 1

Weak

All four digits are 7, satisfying the first condition, so this PIN is weak.

Sample Input 2

0112

Sample Output 2

Strong

The first and second digits differ, and the third digit does not follow the second digit, so neither condition is satisfied.

Sample Input 3

9012

Sample Output 3

Weak

Note that 0 follows 9.

Problem Statement

A string S is said to be a substring of a string T when there is a pair of integers i and j (1 \leq i \leq j \leq |T|) that satisfy the following condition.

• The extraction of the i-th through j-th characters of T without changing the order equals S.

Let T be the concatenation of 10^5 copies of oxx.
Given a string S, print Yes if S is a substring of T, and No otherwise.

Constraints

• S is a string consisting of o and x.
• The length of S is between 1 and 10 (inclusive).

Sample Input 1

xoxxoxxo

Sample Output 1

Yes

T begins like this: oxxoxxoxxoxx... Since the extraction of 3-rd through 10-th characters of T equals S, S is a substring of T, so Yes should be printed.

Sample Input 2

xxoxxoxo

Sample Output 2

No

Since there is no way to extract from T a string that equals S, S is not a substring of T, so No should be printed.

Sample Input 3

ox

Sample Output 3

Yes

Problem Statement

There are N creatures standing in a circle, called Snuke 1, 2, ..., N in counter-clockwise order.

When Snuke i (1 \leq i \leq N) receives a gem at time t, S_i units of time later, it will hand that gem to Snuke i+1 at time t+S_i. Here, Snuke N+1 is Snuke 1.

Additionally, Takahashi will hand a gem to Snuke i at time T_i.

For each i (1 \leq i \leq N), find the time when Snuke i receives a gem for the first time. Assume that it takes a negligible time to hand a gem.

Constraints

• 1 \leq N \leq 200000
• 1 \leq S_i,T_i \leq 10^9
• All values in input are integers.

Sample Input 1

3
4 1 5
3 10 100

Sample Output 1

3
7
8

We will list the three Snuke's and Takahashi's actions up to time 13 in chronological order.

Time 3: Takahashi hands a gem to Snuke 1.

Time 7: Snuke 1 hands a gem to Snuke 2.

Time 8: Snuke 2 hands a gem to Snuke 3.

Time 10: Takahashi hands a gem to Snuke 2.

Time 11: Snuke 2 hands a gem to Snuke 3.

Time 13: Snuke 3 hands a gem to Snuke 1.

After that, they will continue handing gems, though it will be irrelevant to the answer.

Sample Input 2

4
100 100 100 100
1 1 1 1

Sample Output 2

1
1
1
1

Note that the values S_i and T_i may not be distinct.

Sample Input 3

4
1 2 3 4
1 2 4 7

Sample Output 3

1
2
4
7

Note that a Snuke may perform multiple transactions simultaneously. Particularly, a Snuke may receive gems simultaneously from Takahashi and another Snuke.

Sample Input 4

8
84 87 78 16 94 36 87 93
50 22 63 28 91 60 64 27

Sample Output 4

50
22
63
28
44
60
64
27

Problem Statement

There is an N\times N grid with horizontal rows and vertical columns, where all squares are initially painted white. Let (i,j) denote the square at the i-th row and j-th column.

Takahashi has integers A and B, which are between 1 and N (inclusive). He will do the following operations.

• For every integer k such that \max(1-A,1-B)\leq k\leq \min(N-A,N-B), paint (A+k,B+k) black.
• For every integer k such that \max(1-A,B-N)\leq k\leq \min(N-A,B-1), paint (A+k,B-k) black.

In the grid after these operations, find the color of each square (i,j) such that P\leq i\leq Q and R\leq j\leq S.

Constraints

• 1 \leq N \leq 10^{18}
• 1 \leq A \leq N
• 1 \leq B \leq N
• 1 \leq P \leq Q \leq N
• 1 \leq R \leq S \leq N
• (Q-P+1)\times(S-R+1)\leq 3\times 10^5
• All values in input are integers.

Sample Input 1

5 3 2
1 5 1 5

Sample Output 1

...#.
#.#..
.#...
#.#..
...#.

The first operation paints the four squares (2,1), (3,2), (4,3), (5,4) black, and the second paints the four squares (4,1), (3,2), (2,3), (1,4) black.
Thus, the above output should be printed, since P=1, Q=5, R=1, S=5.

Sample Input 2

5 3 3
4 5 2 5

Sample Output 2

#.#.
...#

The operations paint the nine squares (1,1), (1,5), (2,2), (2,4), (3,3), (4,2), (4,4), (5,1), (5,5).
Thus, the above output should be printed, since P=4, Q=5, R=2, S=5.

Sample Input 3

1000000000000000000 999999999999999999 999999999999999999
999999999999999998 1000000000000000000 999999999999999998 1000000000000000000

Sample Output 3

#.#
.#.
#.#

Note that the input may not fit into a 32-bit integer type.

Problem Statement

There is a deck consisting of N face-down cards with an integer from 1 through N written on them. The integer on the i-th card from the top is P_i.

Using this deck, you will perform N moves, each consisting of the following steps:

• Draw the topmost card from the deck. Let X be the integer written on it.
• Stack the drawn card, face up, onto the card with the smallest integer among the face-up topmost cards on the table with an integer greater than or equal to X written on them. If there is no such card on the table, put the drawn card on the table, face up, without stacking it onto any card.
• Then, if there is a pile consisting of K face-up cards on the table, eat all those cards. The eaten cards all disappear from the table.

For each card, find which of the N moves eats it. If the card is not eaten until the end, report that fact.

Constraints

• All values in input are integers.
• 1 \le K \le N \le 2 \times 10^5
• P is a permutation of (1,2,\dots,N) (i.e. a sequence obtained by rearranging (1,2,\dots,N)).

Sample Input 1

5 2
3 5 2 1 4

Sample Output 1

4
3
3
-1
4

In this input, P=(3,5,2,1,4) and K=2.

• In the 1-st move, the card with 3 written on it is put on the table, face up, without stacked onto any card.
• In the 2-nd move, the card with 5 written on it is put on the table, face up, without stacked onto any card.
• In the 3-rd move, the card with 2 written on it is stacked, face up, onto the card with 3 written on it.
  • Now there is a pile consisting of K=2 face-up cards, on which 2 and 3 from the top are written, so these cards are eaten.
• In the 4-th move, the card with 1 written on it is stacked, face up, onto the card with 5 written on it.
  • Now there is a pile consisting of K=2 face-up cards, on which 1 and 5 from the top are written, so these cards are eaten.
• In the 5-th move, the card with 4 written on it is put on the table, face up, without stacked onto any card.
• The card with 4 written on it was not eaten until the end.

Sample Input 2

5 1
1 2 3 4 5

Sample Output 2

1
2
3
4
5

If K=1, every card is eaten immediately after put on the table within a single move.

Sample Input 3

15 3
3 14 15 9 2 6 5 13 1 7 10 11 8 12 4

Sample Output 3

9
9
9
15
15
6
-1
-1
6
-1
-1
-1
-1
6
15

Problem Statement

Takahashi participated in N contests and earned a performance P_i in the i-th contest.
He wants to choose some (at least one) contests from these and maximize his rating calculated from the results of those contests.

Find the maximum possible rating he can achieve by optimally choosing the contests.

Here, Takahashi's rating R is calculated as the following, where k is the number of chosen contests and (Q_1, Q_2, \ldots, Q_k) are the performances in the chosen contests in the order he participated:

Constraints

• 1\leq N\leq 5000
• 1\leq P_i\leq 5000
• All input values are integers.

Sample Input 1

3
1000 600 1200

Sample Output 1

256.735020470879931

If Takahashi chooses the first and third contests, his rating will be:

\displaystyle R=\frac{0.9\times 1000+ 1.0\times 1200}{0.9+1.0}-\frac{1200}{\sqrt{2}}=256.73502....

This is the maximum possible rating.

Sample Input 2

3
600 1000 1200

Sample Output 2

261.423219407873376

The rating is maximized when all the first, second, and third contests are selected.

Sample Input 3

1
100

Sample Output 3

-1100.000000000000000

The rating can also be negative.

Problem Statement

Given is a tree with N vertices. The vertices are numbered 1, 2, \ldots, N, and for each 1\leq i\leq N-1, the i-th edge connects Vertex U_i and Vertex V_i. Let D be the diameter of the tree. Find the number, modulo 998244353, of ways to choose two or more of the vertices and paint them red so that all distances between two red vertices are D.

Here, the distance between two vertices is the minimum number of edges that must be traversed to travel from one vertex to the other, and the diameter of the tree is the maximum distance between two vertices.

Constraints

• 2 \leq N \leq 2\times 10^5
• 1 \leq U_i,V_i \leq N
• U_i \neq V_i
• All values in input are integers.
• The given graph is a tree.

Sample Input 1

5
1 2
1 3
1 4
4 5

Sample Output 1

2

The given tree has five vertices and a diameter of 3.
There are just two pairs of vertices whose distance is 3: (2,5) and (3,5), so there are two ways to paint the tree to satisfy the condition: \lbrace 2,5\rbrace and \lbrace 3,5\rbrace .
Note that painting 2,3,5 does not satisfy the condition since the distance between Vertex 2 and Vertex 3 is 2.

Sample Input 2

4
1 2
1 3
1 4

Sample Output 2

4

The diameter is 2, and the four ways to paint the tree to satisfy the condition are: \lbrace 2,3\rbrace , \lbrace 2,4\rbrace , \lbrace 3,4\rbrace , \lbrace 2,3,4\rbrace .