Problem Statement

You are given a 6-digit positive integer N.
Determine whether N satisfies all of the following conditions.

• Among the digits of N, the digit 1 appears exactly once.
• Among the digits of N, the digit 2 appears exactly twice.
• Among the digits of N, the digit 3 appears exactly three times.

Constraints

• N is an integer satisfying 100000 \le N \le 999999.

Sample Input 1

123233

Sample Output 1

Yes

123233 satisfies the conditions in the problem statement, so print Yes.

Sample Input 2

123234

Sample Output 2

No

123234 does not satisfy the conditions in the problem statement, so print No.

Sample Input 3

323132

Sample Output 3

Yes

Sample Input 4

500000

Sample Output 4

No

Problem Statement

There is one humidifier in the AtCoder company office. The current time is 0, and the humidifier has no water inside.

You will add water to this humidifier N times. The i-th addition of water (1 \leq i \leq N) takes place at time T_i, and you add V_i liters of water. It is guaranteed that T_i < T_{i+1} for all 1 \leq i \leq N-1.

However, the humidifier has a leak, and as long as there is water inside, the amount of water decreases by 1 liter per unit time.

Find the amount of water remaining in the humidifier immediately after you finish adding water at time T_N.

Constraints

• 1 \leq N \leq 100
• 1 \leq T_i \leq 100 (1 \leq i \leq N)
• 1 \leq V_i \leq 100 (1 \leq i \leq N)
• T_i < T_{i+1} (1 \leq i \leq N-1)
• All input values are integers.

Sample Input 1

4
1 3
3 1
4 4
7 1

Sample Output 1

3

At each point in time, water is added as follows:

• Time 1: Before adding, the humidifier has 0 liters. After adding 3 liters, it has 3 liters.
• Time 3: Before adding, it has 1 liter. After adding 1 liter, it has 2 liters total.
• Time 4: Before adding, it has 1 liter. After adding 4 liters, it has 5 liters total.
• Time 7: Before adding, it has 2 liters. After adding 1 liter, it has 3 liters total.

After finishing the addition at time 7, the humidifier contains 3 liters. Thus, the answer is 3.

Sample Input 2

3
1 8
10 11
21 5

Sample Output 2

5

Sample Input 3

10
2 1
22 10
26 17
29 2
45 20
47 32
72 12
75 1
81 31
97 7

Sample Output 3

57

Problem Statement

There is a simple undirected graph G with N vertices labeled with numbers 1, 2, \ldots, N.

You are given the adjacency matrix (A_{i,j}) of G. That is, G has an edge connecting vertices i and j if and only if A_{i,j} = 1.

For each i = 1, 2, \ldots, N, print the numbers of the vertices directly connected to vertex i in ascending order.

Here, vertices i and j are said to be directly connected if and only if there is an edge connecting vertices i and j.

Constraints

• 2 \leq N \leq 100
• A_{i,j} \in \lbrace 0,1 \rbrace
• A_{i,i} = 0
• A_{i,j} = A_{j,i}
• All input values are integers.

Sample Input 1

4
0 1 1 0
1 0 0 1
1 0 0 0
0 1 0 0

Sample Output 1

2 3
1 4
1
2

Vertex 1 is directly connected to vertices 2 and 3. Thus, the first line should contain 2 and 3 in this order.

Similarly, the second line should contain 1 and 4 in this order, the third line should contain 1, and the fourth line should contain 2.

Sample Input 2

2
0 0
0 0

Sample Output 2

G may have no edges.

Sample Input 3

5
0 1 0 1 1
1 0 0 1 0
0 0 0 0 1
1 1 0 0 1
1 0 1 1 0

Sample Output 3

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

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

You are given a sequence of N numbers: A=(A_1,\ldots,A_N).

Determine whether there is a pair (i,j) with 1\leq i,j \leq N such that A_i-A_j=X.

Constraints

• 2 \leq N \leq 2\times 10^5
• -10^9 \leq A_i \leq 10^9
• -10^9 \leq X \leq 10^9
• All values in the input are integers.

Sample Input 1

6 5
3 1 4 1 5 9

Sample Output 1

Yes

We have A_6-A_3=9-4=5.

Sample Input 2

6 -4
-2 -7 -1 -8 -2 -8

Sample Output 2

No

There is no pair (i,j) such that A_i-A_j=-4.

Sample Input 3

2 0
141421356 17320508

Sample Output 3

Yes

We have A_1-A_1=0.