Problem Statement

The versions of a certain OS in chronological order are "Ocelot", "Serval", "Lynx".
Determine whether version X is the same as or newer than version Y.

Constraints

• Each of X and Y is one of "Ocelot", "Serval", "Lynx" (without quotation marks).

Sample Input 1

Serval Ocelot

Sample Output 1

Yes

Version Serval is the same as or newer than version Ocelot. Therefore, print Yes.

Sample Input 2

Serval Lynx

Sample Output 2

No

Version Serval is not the same as nor newer than version Lynx. Therefore, print No.

Sample Input 3

Ocelot Ocelot

Sample Output 3

Yes

Version Ocelot itself is the same as or newer than version Ocelot. Therefore, print Yes.

Problem Statement

Given eight integers S_1,S_2,\dots, and S_8, print Yes if they satisfy all of the following three conditions, and No otherwise.

• The sequence (S_1,S_2,\dots,S_8) is monotonically non-decreasing. In other words, S_1 \leq S_2 \leq \dots \leq S_8.
• S_1,S_2,\dots, and S_8 are all between 100 and 675, inclusive.
• S_1,S_2,\dots, and S_8 are all multiples of 25.

Constraints

• 0\leq S_i \leq 1000
• All input values are integers.

Sample Input 1

125 175 250 300 400 525 600 650

Sample Output 1

Yes

They satisfy all of the three conditions.

Sample Input 2

100 250 300 400 325 575 625 675

Sample Output 2

No

They violate the first condition because S_4 > S_5.

Sample Input 3

0 23 24 145 301 413 631 632

Sample Output 3

No

They violate the second and third conditions.

Problem Statement

There is a grid with H rows and W columns. Each square has one integer written on it, and these integers are distinct. The square at the i-th row from the top and j-th column from the left has the integer A_{i,j} written on it.

Now, the host called out N distinct integers B_1, \dots, B_N.

If you find, for each row, how many of the integers called out by the host are contained in that row, what is the maximum value among these?

Constraints

• 1 \leq H \leq 3
• 1 \leq W \leq 5
• 1 \leq N \leq 90
• 1 \leq A_{i,j} \leq 90
• A_{i,j} are distinct.
• 1 \leq B_i \leq 90
• B_i are distinct.
• All input values are integers.

Sample Input 1

3 4 5
12 3 5 7
6 10 11 9
1 2 4 8
2
4
9
6
11

Sample Output 1

3

• Among the integers in the 1-st row from the top, 0 integers were called out by the host.
• Among the integers in the 2-nd row from the top, 3 integers 6,11,9 were called out by the host.
• Among the integers in the 3-rd row from the top, 2 integers 2,4 were called out by the host.

Thus, the answer is the maximum value among 0,3,2, which is 3.

Sample Input 2

3 5 2
81 63 31 16 15
30 3 6 54 24
26 41 48 64 66
44
79

Sample Output 2

0

Sample Input 3

3 5 12
78 19 70 58 83
12 30 80 20 27
48 71 8 43 82
82
30
43
8
80
70
20
78
12
71
19
48

Sample Output 3

5

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

Takahashi is going to read a manga series "Snuke-kun" in 10^9 volumes.
Initially, Takahashi has N books of this series. The i-th book is Volume a_i.

Takahashi may repeat the following operation any number of (possibly zero) times only before he begins to read:

• Do nothing if he has 1 or less books; otherwise, sell two of the books he has and buy one book of any volume instead.

Then, Takahashi reads Volume 1, Volume 2, Volume 3, \ldots, in order. However, when he does not have a book of the next volume to read, he stops reading the series (regardless of the other volumes he has).

Find the latest volume of the series that he can read up to. If he cannot read any, let the answer be 0.

Constraints

• 1 \leq N \leq 3 \times 10^5
• 1 \leq a_i \leq 10^9
• All values in the input are integers.

Sample Input 1

6
1 2 4 6 7 271

Sample Output 1

4

Before he begins to read the series, he may do the following operation: "sell books of Volumes 7 and 271 and buy one book of Volume 3 instead." Then, he has one book each of Volumes 1, 2, 3, 4, and 6.
If he then begins to read the series, he reads Volumes 1, 2, 3, and 4, then tries to read Volume 5. However, he does not have one, so he stops reading at this point.
Regardless of the choices in the operation, he cannot read Volume 5, so the answer is 4.

Sample Input 2

10
1 1 1 1 1 1 1 1 1 1

Sample Output 2

5

Takahashi may have multiple books of the same volume.
For this input, if he performs the following 4 operations before he begins to read the series, he can read up to Volume 5, which is the maximum:

• Sell two books of Volume 1 and buy a book of Volume 2 instead.
• Sell two books of Volume 1 and buy a book of Volume 3 instead.
• Sell two books of Volume 1 and buy a book of Volume 4 instead.
• Sell two books of Volume 1 and buy a book of Volume 5 instead.

Sample Input 3

1
5

Sample Output 3

0

Takahashi cannot read Volume 1.