Problem Statement

There are four cards with integers A,B,C,D written on them.
Determine whether a Full House can be formed by adding one card.

A set of five cards is called a Full House if and only if the following condition is satisfied:

• For two distinct integers x and y, there are three cards with x written on them and two cards with y written on them.

Constraints

• All input values are integers.
• 1 \le A,B,C,D \le 13

Sample Input 1

7 7 7 1

Sample Output 1

Yes

Adding 1 to 7,7,7,1 forms a Full House.

Sample Input 2

13 12 11 10

Sample Output 2

No

Adding anything to 13,12,11,10 does not form a Full House.

Sample Input 3

3 3 5 5

Sample Output 3

Yes

Adding 3,3,5,5 to 3 forms a Full House.
Also, adding 5 forms a Full House.

Sample Input 4

8 8 8 8

Sample Output 4

No

Adding anything to 8,8,8,8 does not form a Full House.
Note that five identical cards do not form a Full House.

Sample Input 5

1 3 4 1

Sample Output 5

No

Problem Statement

You are given an integer K.

Print a string that is a concatenation of the first K uppercase English letters in ascending order, starting from A.

Constraints

• K is an integer between 1 and 26, inclusive.

Sample Input 1

3

Sample Output 1

ABC

The uppercase English letters in ascending order are A, B, C, ...

By concatenating the first three uppercase English letters, we get ABC.

Sample Input 2

1

Sample Output 2

A

Problem Statement

Takahashi is exploring a cave in a video game.

The cave consists of N rooms arranged in a row. The rooms are numbered Room 1,2,\ldots,N from the entrance.

Takahashi is initially in Room 1, and the time limit is T.
For each 1 \leq i \leq N-1, he may consume a time of A_i to move from Room i to Room (i+1). There is no other way to move between rooms. He cannot make a move that makes the time limit 0 or less.

There are M bonus rooms in the cave. The i-th bonus room is Room X_i; when he arrives at the room, the time limit increases by Y_i.

Can Takahashi reach Room N?

Constraints

• 2 \leq N \leq 10^5
• 0 \leq M \leq N-2
• 1 \leq T \leq 10^9
• 1 \leq A_i \leq 10^9
• 1 < X_1 < \ldots < X_M < N
• 1 \leq Y_i \leq 10^9
• All values in input are integers.

Sample Input 1

4 1 10
5 7 5
2 10

Sample Output 1

Yes

• Takahashi is initially in Room 1, and the time limit is 10.
• He consumes a time of 5 to move to Room 2. Now the time limit is 5. Then, the time limit increases by 10; it is now 15.
• He consumes a time of 7 to move to Room 3. Now the time limit is 8.
• He consumes a time of 5 to move to Room 4. Now the time limit is 3.

Sample Input 2

4 1 10
10 7 5
2 10

Sample Output 2

No

He cannot move from Room 1 to Room 2.

Problem Statement

Iroha has a sequence of positive integers A = (A_1, A_2, \dots, A_N) of length N (N \ge 1).
She generated a string S using A as follows:

• Start with S = |.
• For i = 1, 2, \dots, N, perform the following operations in order:
  • Append A_i copies of - to the end of S.
  • Then, append one | to the end of S.

Given the generated string S, reconstruct the sequence A.

Constraints

• S is a string of length between 3 and 100, inclusive, generated by the method in the problem statement.
• A is a sequence of positive integers of length at least 1.

Sample Input 1

|---|-|----|-|-----|

Sample Output 1

3 1 4 1 5

S = |---|-|----|-|-----| is generated by A = (3, 1, 4, 1, 5).

Sample Input 2

|----------|

Sample Output 2

10

Sample Input 3

|-|-|-|------|

Sample Output 3

1 1 1 6

Problem Statement

A non-negative integer n is called a good integer when it satisfies the following condition:

• All digits in the decimal notation of n are even numbers (0, 2, 4, 6, and 8).

For example, 0, 68, and 2024 are good integers.

You are given an integer N. Find the N-th smallest good integer.

Constraints

• 1 \leq N \leq 10^{12}
• N is an integer.

Sample Input 1

8

Sample Output 1

24

The good integers in ascending order are 0, 2, 4, 6, 8, 20, 22, 24, 26, 28, \dots.
The eighth smallest is 24, which should be printed.

Sample Input 2

133

Sample Output 2

2024

Sample Input 3

31415926535

Sample Output 3

2006628868244228

Problem Statement

You are given a sequence A=(A_1,A_2,\dots,A_{3N}) of length 3N where each of 1,2,\dots, and N occurs exactly three times.

For i=1,2,\dots,N, let f(i) be the index of the middle occurrence of i in A. Sort 1,2,\dots,N in ascending order of f(i).

Formally, f(i) is defined as follows.

• Suppose that those j such that A_j = i are j=\alpha,\beta,\gamma\ (\alpha < \beta < \gamma). Then, f(i) = \beta.

Constraints

• 1\leq N \leq 10^5
• 1 \leq A_j \leq N
• i occurs in A exactly three times, for each i=1,2,\dots,N.
• All input values are integers.

Sample Input 1

3
1 1 3 2 3 2 2 3 1

Sample Output 1

1 3 2

• 1 occurs in A at A_1,A_2,A_9, so f(1) = 2.
• 2 occurs in A at A_4,A_6,A_7, so f(2) = 6.
• 3 occurs in A at A_3,A_5,A_8, so f(3) = 5.

Thus, f(1) < f(3) < f(2), so 1,3, and 2 should be printed in this order.

Sample Input 2

1
1 1 1

Sample Output 2

1

Sample Input 3

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

Sample Output 3

3 4 1 2

Problem Statement

There is a grid with N \times N squares. We denote by (i, j) the square at the i-th row from the top and j-th column from the left.

Initially, a piece is placed on (1, 1). You may repeat the following operation any number of times:

• Let (i, j) be the square the piece is currently on. Move the piece to the square whose distance from (i, j) is exactly \sqrt{M}.

Here, we define the distance between square (i, j) and square (k, l) as \sqrt{(i-k)^2+(j-l)^2}.

For all squares (i, j), determine if the piece can reach (i, j). If it can, find the minimum number of operations required to do so.

Constraints

• 1 \le N \le 400
• 1 \le M \le 10^6
• All values in the input are integers.

Sample Input 1

3 1

Sample Output 1

0 1 2
1 2 3
2 3 4

You can move the piece to four adjacent squares.

For example, we can move the piece to (2,2) with two operations as follows.

• The piece is now on (1,1). The distance between (1,1) and (1,2) is exactly \sqrt{1}, so move the piece to (1,2).
• The piece is now on (1,2). The distance between (1,2) and (2,2) is exactly \sqrt{1}, so move the piece to (2,2).

Sample Input 2

10 5

Sample Output 2

0 3 2 3 2 3 4 5 4 5
3 4 1 2 3 4 3 4 5 6
2 1 4 3 2 3 4 5 4 5
3 2 3 2 3 4 3 4 5 6
2 3 2 3 4 3 4 5 4 5
3 4 3 4 3 4 5 4 5 6
4 3 4 3 4 5 4 5 6 5
5 4 5 4 5 4 5 6 5 6
4 5 4 5 4 5 6 5 6 7
5 6 5 6 5 6 5 6 7 6

Problem Statement

You are given a weighted undirected graph G with N vertices, numbered 1 to N. Initially, G has no edges.

You will perform M operations to add edges to G. The i-th operation (1 \leq i \leq M) is as follows:

• You are given a subset of vertices S_i=\lbrace A_{i,1},A_{i,2},\dots,A_{i,K_i}\rbrace consisting of K_i vertices. For every pair u, v such that u, v \in S_i and u < v, add an edge between vertices u and v with weight C_i.

After performing all M operations, determine whether G is connected. If it is, find the total weight of the edges in a minimum spanning tree of G.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq M \leq 2 \times 10^5
• 2 \leq K_i \leq N
• \sum_{i=1}^{M} K_i \leq 4 \times 10^5
• 1 \leq A_{i,1} < A_{i,2} < \dots < A_{i,K_i} \leq N
• 1 \leq C_i \leq 10^9
• All input values are integers.

Sample Input 1

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

Sample Output 1

9

The left diagram shows G after all M operations, and the right diagram shows a minimum spanning tree of G (the numbers next to the edges indicate their weights).

The total weight of the edges in the minimum spanning tree is 3 + 2 + 4 = 9.

Sample Input 2

3 2
2 1
1 2
2 1
1 2

Sample Output 2

-1

G is not connected even after all M operations.

Sample Input 3

10 5
6 158260522
1 3 6 8 9 10
10 877914575
1 2 3 4 5 6 7 8 9 10
4 602436426
2 6 7 9
6 24979445
2 3 4 5 8 10
4 861648772
2 4 8 9

Sample Output 3

1202115217

Problem Statement

You are given N strings S_1,\ldots,S_N consisting of digits.

Find the maximum possible value, when interpreted as a decimal integer (after removing extra leading zeros), of a string obtained by choosing exactly K of these strings and concatenating them in any order of your choice.

Here, the value obtained by interpreting a string consisting entirely of the character 0 as a decimal integer after removing extra leading zeros is defined to be 0.

Constraints

• 1 \leq K \leq N \leq 10^5
• S_i is a string of length between 1 and 10 (inclusive) consisting of digits.
• N and K are integers.

Sample Input 1

3 2
123
45
6

Sample Output 1

45123

There are six strings obtained by choosing two of 123, 45, 6 and concatenating them: 12345, 1236, 45123, 456, 6123, 645.

Among these, the maximum value when interpreted as a decimal integer is 45123.

Sample Input 2

5 3
00000
00
1
0000
000

Sample Output 2

1000000000

Sample Input 3

9 9
0000000001
000000002
00000003
0000004
000005
00006
0007
008
09

Sample Output 3

90080007000060000050000004000000030000000020000000001

The answer must be output without extra leading zeros.