Problem Statement

You are given a simple undirected graph with N vertices and M edges. The vertices are numbered 1, \dots, N, and the i-th (1 \leq i \leq M) edge connects Vertex U_i and Vertex V_i.

Find the number of tuples of integers a, b, c that satisfy all of the following conditions:

• 1 \leq a \lt b \lt c \leq N
• There is an edge connecting Vertex a and Vertex b.
• There is an edge connecting Vertex b and Vertex c.
• There is an edge connecting Vertex c and Vertex a.

Constraints

• 3 \leq N \leq 100
• 1 \leq M \leq \frac{N(N - 1)}{2}
• 1 \leq U_i \lt V_i \leq N \, (1 \leq i \leq M)
• (U_i, V_i) \neq (U_j, V_j) \, (i \neq j)
• All values in input are integers.

Sample Input 1

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

Sample Output 1

2

(a, b, c) = (1, 4, 5), (2, 3, 5) satisfy the conditions.

Sample Input 2

3 1
1 2

Sample Output 2

0

Sample Input 3

7 10
1 7
5 7
2 5
3 6
4 7
1 5
2 4
1 3
1 6
2 7

Sample Output 3

4

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

There are N people numbered 1, 2, \ldots, N on a two-dimensional plane, and person i is at the point represented by the coordinates (X_i,Y_i).

Person 1 has been infected with a virus. The virus spreads to people within a distance of D from an infected person.

Here, the distance is defined as the Euclidean distance, that is, for two points (a_1, a_2) and (b_1, b_2), the distance between these two points is \sqrt {(a_1-b_1)^2 + (a_2-b_2)^2}.

After a sufficient amount of time has passed, that is, when all people within a distance of D from person i are infected with the virus if person i is infected, determine whether person i is infected with the virus for each i.

Constraints

• 1 \leq N, D \leq 2000
• -1000 \leq X_i, Y_i \leq 1000
• (X_i, Y_i) \neq (X_j, Y_j) if i \neq j.
• All input values are integers.

Sample Input 1

4 5
2 -1
3 1
8 8
0 5

Sample Output 1

Yes
Yes
No
Yes

The distance between person 1 and person 2 is \sqrt 5, so person 2 gets infected with the virus.
Also, the distance between person 2 and person 4 is 5, so person 4 gets infected with the virus.
Person 3 has no one within a distance of 5, so they will not be infected with the virus.

Sample Input 2

3 1
0 0
-1000 -1000
1000 1000

Sample Output 2

Yes
No
No

Sample Input 3

9 4
3 2
6 -1
1 6
6 5
-2 -3
5 3
2 -3
2 1
2 6

Sample Output 3

Yes
No
No
Yes
Yes
Yes
Yes
Yes
No

Problem Statement

The definition of an 11/22 string in this problem is the same as in Problems A and E.

A string T is called an 11/22 string when it satisfies all of the following conditions:

• |T| is odd. Here, |T| denotes the length of T.
• The 1-st through (\frac{|T|+1}{2} - 1)-th characters are all 1.
• The (\frac{|T|+1}{2})-th character is /.
• The (\frac{|T|+1}{2} + 1)-th through |T|-th characters are all 2.

For example, 11/22, 111/222, and / are 11/22 strings, but 1122, 1/22, 11/2222, 22/11, and //2/2/211 are not.

You are given a string S of length N consisting of 1, 2, and /, where S contains at least one /.
Find the maximum length of a (contiguous) substring of S that is an 11/22 string.

Constraints

• 1 \leq N \leq 2 \times 10^5
• S is a string of length N consisting of 1, 2, and /.
• S contains at least one /.

Sample Input 1

8
211/2212

Sample Output 1

5

The substring from the 2-nd to 6-th character of S is 11/22, which is an 11/22 string. Among all substrings of S that are 11/22 strings, this is the longest. Therefore, the answer is 5.

Sample Input 2

5
22/11

Sample Output 2

1

Sample Input 3

22
/1211/2///2111/2222/11

Sample Output 3

7

Problem Statement

There are three Takahashis numbered 1, 2 and 3, and three hats colored red, green, and blue. Each Takahashi is wearing one hat. The color of the hat that Takahashi i is currently wearing is represented by a character S_i. Here, R corresponds to red, G to green, and B to blue. Now, they will do the following operation exactly 10^{18} times.

Operation

• Choose two out of the three Takahashis. The two exchange the hats they are wearing.

Is it possible to make Takahashi i wearing the hat of color corresponding to character T_i after the 10^{18} repetitions?

Constraints

• S_1, S_2, S_3 are a permutation of R, G, B.
• T_1, T_2, T_3 are a permutation of R, G, B.

Sample Input 1

R G B
R G B

Sample Output 1

Yes

For example, the objective can be achieved by repeating 10^{18} times the operation of swapping the hats of Takahashi 1 and Takahashi 2.