Problem Statement

You are given a sequence A=(A_1,A_2,\ldots,A_N) of length N and positive integers P,Q,R, and S.
Here, P,Q,R, and S satisfy 1\leq P\leq Q<R\leq S \leq N and Q-P=S-R.

Let B=(B_1, B_2,\ldots, B_N) be the sequence obtained by swapping the P-th through Q-th terms and the R-th through S-th terms of A.
Print the sequence B.

Constraints

• 1\leq N \leq 100
• 1\leq A_i\leq 100
• 1\leq P\leq Q<R\leq S \leq N
• Q-P=S-R
• All values in the input are integers.

Sample Input 1

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

Sample Output 1

5 6 7 4 1 2 3 8

Swapping the 1-st through 3-rd terms (1,2,3) and the 5-th through 7-th terms (5,6,7) of the sequence A=(1,2,3,4,5,6,7,8) results in B=(5,6,7,4,1,2,3,8), which should be printed with spaces in between.

Sample Input 2

5 2 3 4 5
2 2 1 1 1

Sample Output 2

2 1 1 2 1

The same integer may occur multiple times in the sequence.

Sample Input 3

2 1 1 2 2
50 100

Sample Output 3

100 50

Sample Input 4

10 2 4 7 9
22 75 26 45 72 81 47 29 97 2

Sample Output 4

22 47 29 97 72 81 75 26 45 2

Problem Statement

You are given a string S ending with er or ist.
If S ends with er, print er; if it ends with ist, print ist.

Constraints

• 2 \le |S| \le 20
• S consists of lowercase English letters.
• S ends with er or ist.

Sample Input 1

atcoder

Sample Output 1

er

S="atcoder" ends with er.

Sample Input 2

tourist

Sample Output 2

ist

Sample Input 3

er

Sample Output 3

er

Problem Statement

There is a grid with H rows from top to bottom and W columns from left to right. Let (i, j) denote the square at the i-th row from the top and j-th column from the left.
The squares are described by characters C_{i,j}. If C_{i,j} is ., (i, j) is empty; if it is #, (i, j) contains a box.

For integers j satisfying 1 \leq j \leq W, let the integer X_j defined as follows.

• X_j is the number of boxes in the j-th column. In other words, X_j is the number of integers i such that C_{i,j} is #.

Find all of X_1, X_2, \dots, X_W.

Constraints

• 1 \leq H \leq 1000
• 1 \leq W \leq 1000
• H and W are integers.
• C_{i, j} is . or #.

Sample Input 1

3 4
#..#
.#.#
.#.#

Sample Output 1

1 2 0 3

In the 1-st column, one square, (1, 1), contains a box. Thus, X_1 = 1.
In the 2-nd column, two squares, (2, 2) and (3, 2), contain a box. Thus, X_2 = 2.
In the 3-rd column, no squares contain a box. Thus, X_3 = 0.
In the 4-th column, three squares, (1, 4), (2, 4), and (3, 4), contain a box. Thus, X_4 = 3.
Therefore, the answer is (X_1, X_2, X_3, X_4) = (1, 2, 0, 3).

Sample Input 2

3 7
.......
.......
.......

Sample Output 2

0 0 0 0 0 0 0

There may be no square that contains a box.

Sample Input 3

8 3
.#.
###
.#.
.#.
.##
..#
##.
.##

Sample Output 3

2 7 4

Sample Input 4

5 47
.#..#..#####..#...#..#####..#...#...###...#####
.#.#...#.......#.#...#......##..#..#...#..#....
.##....#####....#....#####..#.#.#..#......#####
.#.#...#........#....#......#..##..#...#..#....
.#..#..#####....#....#####..#...#...###...#####

Sample Output 4

0 5 1 2 2 0 0 5 3 3 3 3 0 0 1 1 3 1 1 0 0 5 3 3 3 3 0 0 5 1 1 1 5 0 0 3 2 2 2 2 0 0 5 3 3 3 3

Problem Statement

You are given an H-by-W matrix A.
The element at the i-th row from the top and j-th column from the left of A is A_{i,j}.

Let B be a W-by-H matrix whose element at the i-th row from the top and j-th column from the left equals A_{j, i}.
That is, B is the transpose of A.

Print B.

Constraints

• 1\leq H,W \leq 10^5
• H \times W \leq 10^5
• 1 \leq A_{i,j} \leq 10^9
• All values in input are integers.

Sample Input 1

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

Sample Output 1

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

For example, we have A_{2,1}=4, so the element at the 1-st row from the top and 2-nd column from the left of the transpose B is 4.

Sample Input 2

2 2
1000000000 1000000000
1000000000 1000000000

Sample Output 2

1000000000 1000000000
1000000000 1000000000

Problem Statement

There are N giants, named 1 to N. When giant i stands on the ground, their shoulder height is A_i, and their head height is B_i.

You can choose a permutation (P_1, P_2, \ldots, P_N) of (1, 2, \ldots, N) and stack the N giants according to the following rules:

• First, place giant P_1 on the ground. The giant P_1's shoulder will be at a height of A_{P_1} from the ground, and their head will be at a height of B_{P_1} from the ground.

• For i = 1, 2, \ldots, N - 1 in order, place giant P_{i + 1} on the shoulders of giant P_i. If giant P_i's shoulders are at a height of t from the ground, then giant P_{i + 1}'s shoulders will be at a height of t + A_{P_{i + 1}} from the ground, and their head will be at a height of t + B_{P_{i + 1}} from the ground.

Find the maximum possible height of the head of the topmost giant P_N from the ground.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq A_i \leq B_i \leq 10^9
• All input values are integers.

Sample Input 1

3
4 10
5 8
2 9

Sample Output 1

18

If (P_1, P_2, P_3) = (2, 1, 3), then measuring from the ground, giant 2 has a shoulder height of 5 and a head height of 8, giant 1 has a shoulder height of 9 and a head height of 15, and giant 3 has a shoulder height of 11 and a head height of 18.

The head height of the topmost giant from the ground cannot be greater than 18, so print 18.

Sample Input 2

5
1 1
1 1
1 1
1 1
1 1

Sample Output 2

5

Sample Input 3

10
690830957 868532399
741145463 930111470
612846445 948344128
540375785 925723427
723092548 925021315
928915367 973970164
563314352 832796216
562681294 868338948
923012648 954764623
691107436 891127278

Sample Output 3

7362669937

Problem Statement

As KEYENCE headquarters have more and more workers, they decided to divide the departments in the headquarters into two groups and stagger their lunch breaks.

KEYENCE headquarters have N departments, and the number of people in the i-th department (1\leq i\leq N) is K_i.

When assigning each department to Group A or Group B, having each group take lunch breaks at the same time, and ensuring that the lunch break times of Group A and Group B do not overlap, find the minimum possible value of the maximum number of people taking a lunch break at the same time.
In other words, find the minimum possible value of the larger of the following: the total number of people in departments assigned to Group A, and the total number of people in departments assigned to Group B.

Constraints

• 2 \leq N \leq 20
• 1 \leq K_i \leq 10^8
• All input values are integers.

Sample Input 1

5
2 3 5 10 12

Sample Output 1

17

When assigning departments 1, 2, and 5 to Group A, and departments 3 and 4 to Group B, Group A has a total of 2+3+12=17 people, and Group B has a total of 5+10=15 people. Thus, the maximum number of people taking a lunch break at the same time is 17.

It is impossible to assign the departments so that both groups have 16 or fewer people, so print 17.

Sample Input 2

2
1 1

Sample Output 2

1

Multiple departments may have the same number of people.

Sample Input 3

6
22 25 26 45 22 31

Sample Output 3

89

For example, when assigning departments 1, 4, and 5 to Group A, and departments 2, 3, and 6 to Group B, the maximum number of people taking a lunch break at the same time is 89.

Problem Statement

The string 20230322 can be rearranged into 02320232, which is a repetition of 0232 twice.
Similarly, a string consisting of digits is said to be happy when it can be rearranged into (or already is) a repetition of some string twice.
You are given a string S consisting of digits. Find the number of pairs of integers (l,r) satisfying all of the following conditions.

• 1 \le l \le r \le |S|. (|S| is the length of S.)
• The (contiguous) substring formed of the l-th through r-th characters of S is happy.

Constraints

• S is a string consisting of digits whose length is between 1 and 5 \times 10^5, inclusive.

Sample Input 1

20230322

Sample Output 1

4

We have S= 20230322.

Here are the four pairs of integers (l,r) that satisfy the condition: (1,6), (1,8), (2,7), and (7,8).

Sample Input 2

0112223333444445555556666666777777778888888889999999999

Sample Output 2

185

S may begin with 0.

Sample Input 3

3141592653589793238462643383279502884197169399375105820974944

Sample Output 3

9

Problem Statement

You are given an undirected graph consisting of N vertices and M edges.
For i = 1, 2, \ldots, M, the i-th edge is an undirected edge connecting vertex u_i and v_i that is initially passable if a_i = 1 and initially impassable if a_i = 0. Additionally, there are switches on K of the vertices: vertex s_1, vertex s_2, \ldots, vertex s_K.

Takahashi is initially on vertex 1, and will repeat performing one of the two actions below, Move or Hit Switch, which he may choose each time, as many times as he wants.

• Move: Choose a vertex adjacent to the vertex he is currently on via an edge, and move to that vertex.
• Hit Switch: If there is a switch on the vertex he is currently on, hit it. This will invert the passability of every edge in the graph. That is, a passable edge will become impassable, and vice versa.

Determine whether Takahashi can reach vertex N, and if he can, print the minimum possible number of times he performs Move before reaching vertex N.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq M \leq 2 \times 10^5
• 0 \leq K \leq N
• 1 \leq u_i, v_i \leq N
• u_i \neq v_i
• a_i \in \lbrace 0, 1\rbrace
• 1 \leq s_1 \lt s_2 \lt \cdots \lt s_K \leq N
• All values in the input are integers.

Sample Input 1

5 5 2
1 3 0
2 3 1
5 4 1
2 1 1
1 4 0
3 4

Sample Output 1

5

Takahashi can reach vertex N as follows.

• Move from vertex 1 to vertex 2.
• Move from vertex 2 to vertex 3.
• Hit the switch on vertex 3. This inverts the passability of every edge in the graph.
• Move from vertex 3 to vertex 1.
• Move from vertex 1 to vertex 4.
• Hit the switch on vertex 4. This again inverts the passability of every edge in the graph.
• Move from vertex 4 to vertex 5.

Here, Move is performed five times, which is the minimum possible number.

Sample Input 2

4 4 2
4 3 0
1 2 1
1 2 0
2 1 1
2 4

Sample Output 2

-1

The given graph may be disconnected or contain multi-edges. In this sample input, there is no way for Takahashi to reach vertex N, so you should print -1.

Problem Statement

The Republic of Atcoder has N towns numbered 1 through N, and M highways numbered 1 through M.
Highway i connects Town A_i and Town B_i bidirectionally.

King Takahashi is going to construct (N-M-1) new highways so that the following two conditions are satisfied:

• One can travel between every pair of towns using some number of highways
• For each i=1,\ldots,N, exactly D_i highways are directly connected to Town i

Determine if there is such a way of construction. If it exists, print one.

Constraints

• 2 \leq N \leq 2\times 10^5
• 0 \leq M \lt N-1
• 1 \leq D_i \leq N-1
• 1\leq A_i \lt B_i \leq N
• If i\neq j, then (A_i, B_i) \neq (A_j,B_j).
• All values in input are integers.

Sample Input 1

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

Sample Output 1

6 2
5 6
4 5

As in the Sample Output, the conditions can be satisfied by constructing highways connecting Towns 6 and 2, Towns 5 and 6, and Towns 4 and 5, respectively.

Another example to satisfy the conditions is to construct highways connecting Towns 6 and 4, Towns 5 and 6, and Towns 2 and 5, respectively.

Sample Input 2

5 1
1 1 1 1 4
2 3

Sample Output 2

-1

Sample Input 3

4 0
3 3 3 3

Sample Output 3

-1