Problem Statement

You are given an integer N and a sequence S=(S_1,\ldots,S_N) of length N.

Find a sequence A=(A_1,\ldots,A_N) of length N that satisfies the following condition for all k=1,\ldots,N:

• A_1+A_2+\ldots+A_k = S_k.

Such a sequence A always exists and is unique.

Constraints

• 1 \leq N \leq 10
• -10^9\leq S_i \leq 10^9
• All values in the input are integers.

Sample Input 1

3
3 4 8

Sample Output 1

3 1 4

The sequence in the output actually satisfies all the conditions:

• A_1=3=S_1;
• A_1+A_2=3+1=4=S_2;
• A_1+A_2+A_3=3+1+4=8=S_3.

Sample Input 2

10
314159265 358979323 846264338 -327950288 419716939 -937510582 97494459 230781640 628620899 -862803482

Sample Output 2

314159265 44820058 487285015 -1174214626 747667227 -1357227521 1035005041 133287181 397839259 -1491424381

Problem Statement

N examinees took an entrance exam.
The examinee numbered i scored A_i points in math and B_i points in English.

The admissions are determined as follows.

1. X examinees with the highest math scores are admitted.
2. Then, among the examinees who are not admitted yet, Y examinees with the highest English scores are admitted.
3. Then, among the examinees who are not admitted yet, Z examinees with the highest total scores in math and English are admitted.
4. Those examinees who are not admitted yet are rejected.

Here, in each of the steps 1. to 3., ties are broken by examinees' numbers: an examinee with the smaller examinee's number is prioritized. See also Sample Input and Output.

Print the examinees' numbers of the admitted examinees determined by the steps above in ascending order, separated by newlines.

Constraints

• All values in input are integers.
• 1 \le N \le 1000
• 0 \le X,Y,Z \le N
• 1 \le X+Y+Z \le N
• 0 \le A_i,B_i \le 100

Sample Input 1

6 1 0 2
80 60 80 60 70 70
40 20 50 90 90 80

Sample Output 1

1
4
5

• First, 1 examinee with the highest math score is admitted.
  • Examinee 1 is tied with Examinee 3, scoring the highest 80 points in math, and the tie is broken by the examinees' numbers, so Examinee 1 is admitted.
• Then, among the examinees who are not admitted yet, 0 examinees with the highest English scores are admitted.
  • Obviously, it does not affect the admissions.
• Then, among the examinees who are not admitted yet, 2 examinees with the highest total scores in math and English are admitted.
  • First, among the examinees who are not admitted yet, Examinee 5 is admitted, scoring the highest total score of 160 points.
  • Next, among the examinees who are not admitted yet, Examinee 4 is tied with Examinee 6, scoring a total score of 150 points. The tie is broken by the examinees' numbers, and Examinee 4 is admitted.

Therefore, the examinees' numbers of the admitted examinees are 1, 4, and 5. Print them in ascending order.

Sample Input 2

5 2 1 2
0 100 0 100 0
0 0 100 100 0

Sample Output 2

1
2
3
4
5

All examinees may be admitted.

Sample Input 3

15 4 3 2
30 65 20 95 100 45 70 85 20 35 95 50 40 15 85
0 25 45 35 65 70 80 90 40 55 20 20 45 75 100

Sample Output 3

2
4
5
6
7
8
11
14
15

Problem Statement

For two strings A and B, let A+B denote the concatenation of A and B in this order.

You are given N strings S_1,\ldots,S_N. Modify and print them as follows, in the order i=1, \ldots, N:

• if none of S_1,\ldots,S_{i-1} is equal to S_i, print S_i;
• if X (X>0) of S_1,\ldots,S_{i-1} are equal to S_i, print S_i+ ( +X+ ), treating X as a string.

Constraints

• 1 \leq N \leq 2\times 10^5
• S_i is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.

Sample Input 1

5
newfile
newfile
newfolder
newfile
newfolder

Sample Output 1

newfile
newfile(1)
newfolder
newfile(2)
newfolder(1)

Sample Input 2

11
a
a
a
a
a
a
a
a
a
a
a

Sample Output 2

a
a(1)
a(2)
a(3)
a(4)
a(5)
a(6)
a(7)
a(8)
a(9)
a(10)

Problem Statement

Takahashi and Aoki each have a toy made by attaching M cords to N balls.

In Takahashi's toy, the balls are numbered 1, \dots, N, and the i-th cord ties Ball A_i and B_i.

Similarly, in Aoki's toy, the balls are numbered 1, \dots, N, and the i-th cord ties Ball C_i and D_i.

In each toy, no cord ties a ball to itself, and no two balls are tied by two or more different cords.

Snuke is wondering whether the two toys have the same shape.
Here, they are said to have the same shape when there is a sequence P that satisfies the conditions below.

• P is a permutation of (1, \dots, N).
• For every pair of integers i, j between 1 and N (inclusive), the following holds.
  • Balls i and j in Takahashi's toy are tied by a cord if and only if Balls P_i and P_j in Aoki's toy are tied by a cord.

If the two toys have the same shape, print Yes; otherwise, print No.

Constraints

• 1 \leq N \leq 8
• 0 \leq M \leq \frac{N(N - 1)}{2}
• 1 \leq A_i \lt B_i \leq N \, (1 \leq i \leq M)
• (A_i, B_i) \neq (A_j, B_j) \, (i \neq j)
• 1 \leq C_i \lt D_i \leq N \, (1 \leq i \leq M)
• (C_i, D_i) \neq (C_j, D_j) \, (i \neq j)
• All values in input are integers.

Sample Input 1

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

Sample Output 1

Yes

Takahashi's toy is illustrated on the left in the figure below, and Aoki's is illustrated on the right.

The following figure shows that the two toys have the same shape. The condition in the statement is satisfied when P = (3, 2, 1, 4), for example.

Sample Input 2

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

Sample Output 2

No

The two toys do not have the same shape.

Sample Input 3

8 0

Sample Output 3

Yes

Problem Statement

You are given a simple undirected graph G with N vertices and M edges (a simple graph does not contain self-loops or multi-edges). For i = 1, 2, \ldots, M, the i-th edge connects vertex u_i and vertex v_i.

Print the number of pairs of integers (u, v) that satisfy 1 \leq u \lt v \leq N and both of the following conditions.

• The graph G does not have an edge connecting vertex u and vertex v.
• Adding an edge connecting vertex u and vertex v in the graph G results in a bipartite graph.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 0 \leq M \leq \min \lbrace 2 \times 10^5, N(N-1)/2 \rbrace
• 1 \leq u_i, v_i \leq N
• The graph G is simple.
• All values in the input are integers.

Sample Input 1

5 4
4 2
3 1
5 2
3 2

Sample Output 1

2

We have two pairs of integers (u, v) that satisfy the conditions in the problem statement: (1, 4) and (1, 5). Thus, you should print 2.
The other pairs do not satisfy the conditions. For instance, for (1, 3), the graph G has an edge connecting vertex 1 and vertex 3; for (4, 5), adding an edge connecting vertex 4 and vertex 5 in the graph G does not result in a bipartite graph.

Sample Input 2

4 3
3 1
3 2
1 2

Sample Output 2

0

Note that the given graph may not be bipartite or connected.

Sample Input 3

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

Sample Output 3

9