Problem Statement

You are given two strings S and T. Determine whether it is possible to make S and T equal by doing the following operation at most once:

• choose two adjacent characters in S and swap them.

Note that it is allowed to choose not to do the operation.

Constraints

• Each of S and T is a string of length between 2 and 100 (inclusive) consisting of lowercase English letters.
• S and T have the same length.

Sample Input 1

abc
acb

Sample Output 1

Yes

You can swap the 2-nd and 3-rd characters of S to make S and T equal.

Sample Input 2

aabb
bbaa

Sample Output 2

No

There is no way to do the operation to make S and T equal.

Sample Input 3

abcde
abcde

Sample Output 3

Yes

S and T are already equal.

Problem Statement

You are given N sequences numbered 1 to N.
Sequence i has a length of L_i and its j-th element (1 \leq j \leq L_i) is a_{i,j}.

Sequence i and Sequence j are considered the same when L_i = L_j and a_{i,k} = a_{j,k} for every k (1 \leq k \leq L_i).
How many different sequences are there among Sequence 1 through Sequence N?

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq L_i \leq 2 \times 10^5 (1 \leq i \leq N)
• 0 \leq a_{i,j} \leq 10^{9} (1 \leq i \leq N, 1 \leq j \leq L_i)
• The total number of elements in the sequences, \sum_{i=1}^N L_i, does not exceed 2 \times 10^5.
• All values in input are integers.

Sample Input 1

4
2 1 2
2 1 1
2 2 1
2 1 2

Sample Output 1

3

Sample Input 1 contains four sequences:

• Sequence 1 : (1, 2)
• Sequence 2 : (1, 1)
• Sequence 3 : (2, 1)
• Sequence 4 : (1, 2)

Except that Sequence 1 and Sequence 4 are the same, these sequences are pairwise different, so we have three different sequences.

Sample Input 2

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

Sample Output 2

4

Sample Input 2 contains five sequences:

• Sequence 1 : (1)
• Sequence 2 : (1)
• Sequence 3 : (2)
• Sequence 4 : (1, 1)
• Sequence 5 : (1, 1, 1)

Sample Input 3

1
1 1

Sample Output 3

1

Problem Statement

There is a slot machine with N reels.
The placement of symbols on the i-th reel is represented by a string S_i of length 10 containing each of 0, 1, \ldots, 9 exactly once.

Each reel has a corresponding button. For each non-negative integer t, Takahashi can press one of the buttons of his choice (or do nothing) t seconds after the reels start spinning.
If the button for the i-th reel is pressed t seconds after the start of the spin, the i-th reel will stop to display the ((t\bmod{10})+1)-th character of S_i.
Here, t\bmod{10} denotes the remainder when t is divided by 10.

Takahashi wants to stop all reels to make them display the same character.
Find the minimum number of seconds needed to achieve his objective after the start of the spin.

Constraints

• 2\leq N\leq 100
• N is an integer.
• S_i is a string of length 10 containing each of 0, 1, \ldots, 9 exactly once.

Sample Input 1

3
1937458062
8124690357
2385760149

Sample Output 1

6

Takahashi can make all reels display 8 in 6 seconds after the start of the spin by stopping them as follows.

• 0 seconds after the start of the spin, press the button for the 2-nd reel, making it stop to display the ((0\bmod{10})+1=1)-st character of S_2, 8.
• 2 seconds after the start of the spin, press the button for the 3-rd reel, making it stop to display the ((2\bmod{10})+1=3)-rd character of S_3, 8.
• 6 seconds after the start of the spin, press the button for the 1-st reel, making it stop to display the ((6\bmod{10})+1=7)-th character of S_1, 8.

There is no way to make all reels display the same character in five seconds or less, so the answer is 6.

Sample Input 2

5
0123456789
0123456789
0123456789
0123456789
0123456789

Sample Output 2

40

Note that he must stop all reels to make them display the same character.

Problem Statement

On an xy-coordinate plane, is there a lattice point whose distances from two lattice points (x_1, y_1) and (x_2, y_2) are both \sqrt{5}?

Notes

A point on an xy-coordinate plane whose x and y coordinates are both integers is called a lattice point.
The distance between two points (a, b) and (c, d) is defined to be the Euclidean distance between them, \sqrt{(a - c)^2 + (b-d)^2}.

The following figure illustrates an xy-plane with a black circle at (0, 0) and white circles at the lattice points whose distances from (0, 0) are \sqrt{5}. (The grid shows where either x or y is an integer.)

Constraints

• -10^9 \leq x_1 \leq 10^9
• -10^9 \leq y_1 \leq 10^9
• -10^9 \leq x_2 \leq 10^9
• -10^9 \leq y_2 \leq 10^9
• (x_1, y_1) \neq (x_2, y_2)
• All values in input are integers.

Sample Input 1

0 0 3 3

Sample Output 1

Yes

• The distance between points (2,1) and (x_1, y_1) is \sqrt{(0-2)^2 + (0-1)^2} = \sqrt{5};
• the distance between points (2,1) and (x_2, y_2) is \sqrt{(3-2)^2 + (3-1)^2} = \sqrt{5};
• point (2, 1) is a lattice point,

so point (2, 1) satisfies the condition. Thus, Yes should be printed.
One can also assert in the same way that (1, 2) also satisfies the condition.

Sample Input 2

0 1 2 3

Sample Output 2

No

No lattice point satisfies the condition, so No should be printed.

Sample Input 3

1000000000 1000000000 999999999 999999999

Sample Output 3

Yes

Point (10^9 + 1, 10^9 - 2) and point (10^9 - 2, 10^9 + 1) satisfy the condition.

Problem Statement

You are given positive integers A and B.

You will repeat the following operation until A=B:

• compare A and B to perform one of the following two:
  • if A > B, replace A with A-B;
  • if A < B, replace B with B-A.

How many times will you repeat it until A=B? It is guaranteed that a finite repetition makes A=B.

Constraints

• 1 \le A,B \le 10^{18}
• All values in the input are integers.

Sample Input 1

3 8

Sample Output 1

4

Initially, A=3 and B=8. You repeat the operation as follows:

• A<B, so replace B with B-A=5, making A=3 and B=5.
• A<B, so replace B with B-A=2, making A=3 and B=2.
• A>B, so replace A with A-B=1, making A=1 and B=2.
• A<B, so replace B with B-A=1, making A=1 and B=1.

Thus, you repeat it four times.

Sample Input 2

1234567890 1234567890

Sample Output 2

0

Note that the input may not fit into a 32-bit integer type.

Sample Input 3

1597 987

Sample Output 3

15