Problem Statement

In a certain programming contest, T-shirts are awarded to participants according to the following rules.

• All participants who ranked A-th or higher get a T-shirt.
• Additionally, from the participants who ranked between (A+1)-th and B-th (inclusive), C participants chosen uniformly at random get a T-shirt.

There were 1000 participants in this contest, and all of them got different ranks.
Iroha-chan, who participated in this contest, ranked X-th.
Find the probability that she gets a T-shirt.

Constraints

• All values in input are integers.
• 1 \le A < B \le 1000
• 1 \le C \le B-A
• 1 \le X \le 1000

Sample Input 1

30 500 20 103

Sample Output 1

0.042553191489

Iroha-chan ranked 103-rd.
She will get a T-shirt if she is among the 20 participants chosen uniformly at random from the 470 participants who ranked between 31-st and 500-th, which happens with probability \frac{20}{470}=0.04255319\dots.

Sample Input 2

50 500 100 1

Sample Output 2

1.000000000000

Iroha-chan ranked 1-st. This time, she is guaranteed to get a T-shirt.

Sample Input 3

1 2 1 1000

Sample Output 3

0.000000000000

Iroha-chan ranked 1000-th. This time, she will never get a T-shirt.

Problem Statement

You are given a non-empty string S consisting of uppercase and lowercase English letters. Determine whether the following condition is satisfied:

• The first character of S is uppercase, and all other characters are lowercase.

Constraints

• 1 \leq |S| \leq 100 (|S| is the length of the string S.)
• Each character of S is an uppercase or lowercase English letter.

Sample Input 1

Capitalized

Sample Output 1

Yes

The first character C of Capitalized is uppercase, and all other characters apitalized are lowercase, so you should print Yes.

Sample Input 2

AtCoder

Sample Output 2

No

AtCoder contains an uppercase letter C that is not at the beginning, so you should print No.

Sample Input 3

yes

Sample Output 3

No

The first character y of yes is not uppercase, so you should print No.

Sample Input 4

A

Sample Output 4

Yes

Problem Statement

There are N players numbered 1 to N, who have played a round-robin tournament. For every match in this tournament, one player won and the other lost.

The results of the matches are given as N strings S_1,S_2,\ldots,S_N of length N each, in the following format:

• If i\neq j, the j-th character of S_i is o or x. o means that player i won against player j, and x means that player i lost to player j.

• If i=j, the j-th character of S_i is -.

The player with more wins ranks higher. If two players have the same number of wins, the player with the smaller player number ranks higher. Report the player numbers of the N players in descending order of rank.

Constraints

• 2\leq N\leq 100
• N is an integer.
• S_i is a string of length N consisting of o, x, and -.
• S_1,\ldots,S_N conform to the format described in the problem statement.

Sample Input 1

3
-xx
o-x
oo-

Sample Output 1

3 2 1

Player 1 has 0 wins, player 2 has 1 win, and player 3 has 2 wins. Thus, the player numbers in descending order of rank are 3,2,1.

Sample Input 2

7
-oxoxox
x-xxxox
oo-xoox
xoo-ooo
ooxx-ox
xxxxx-x
oooxoo-

Sample Output 2

4 7 3 1 5 2 6

Both players 4 and 7 have 5 wins, but player 4 ranks higher because their player number is smaller.

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

You are given a positive integer D.

Find the minimum value of |x^2+y^2-D| for non-negative integers x and y.

Constraints

• 1\leq D \leq 2\times 10^{12}
• All input values are integers.

Sample Input 1

21

Sample Output 1

1

For x=4 and y=2, we have |x^2+y^2-D| = |16+4-21|=1.

There are no non-negative integers x and y such that |x^2+y^2-D|=0, so the answer is 1.

Sample Input 2

998244353

Sample Output 2

0

Sample Input 3

264428617

Sample Output 3

32