Problem Statement

In AtCoder, a user's rating is given as a positive integer, and based on this value, a certain number of ^ is displayed. Specifically, when the rating is between 1 and 399, inclusive, the display rules are as follows:

• When the rating is between 1 and 99, inclusive, ^ is displayed once.
• When the rating is between 100 and 199, inclusive, ^ is displayed twice.
• When the rating is between 200 and 299, inclusive, ^ is displayed three times.
• When the rating is between 300 and 399, inclusive, ^ is displayed four times.

Currently, Takahashi's rating is R. Here, it is guaranteed that R is an integer between 1 and 299, inclusive.
Find the minimum increase in rating required for him to increase the number of displayed ^.
It can be proved that under the constraints of this problem, he can increase the number of ^ without raising his rating to 400 or above.

Constraints

• 1 \leq R \leq 299
• R is an integer.

Sample Input 1

123

Sample Output 1

77

Takahashi's current rating is 123, and ^ is displayed twice.
By increasing his rating by 77, his rating will become 200, and ^ will be displayed three times. When the rating is 199 or below, ^ is displayed not more than twice, so print 77.

Sample Input 2

250

Sample Output 2

50

Problem Statement

You are given a string S consisting of uppercase and lowercase English letters.
Here, exactly one character of S is uppercase, and the others are all lowercase.
Find the integer x such that the x-th character of S is uppercase.
Here, the initial character of S is considered the 1-st one.

Constraints

• S is a string of length between 2 and 100, inclusive, consisting of uppercase and lowercase English letters.
• S has exactly one uppercase letter.

Sample Input 1

aBc

Sample Output 1

2

The 1-st character of aBc is a, the 2-nd is B, and the 3-rd is c; the 2-nd character is uppercase.
Thus, 2 should be printed.

Sample Input 2

xxxxxxXxxx

Sample Output 2

7

An uppercase letter X occurs as the 7-th character of S=xxxxxxXxxx, so 7 should be printed.

Sample Input 3

Zz

Sample Output 3

1

Problem Statement

You are given a positive integer N.

We have a grid with N rows and N columns, where the square at the i-th row from the top and j-th column from the left has a digit A_{i,j} written on it.

Assume that the upper and lower edges of this grid are connected, as well as the left and right edges. In other words, all of the following holds.

• (N,i) is just above (1,i), and (1,i) is just below (N,i). (1\le i\le N).
• (i,N) is just to the left of (i,1), and (i,1) is just to the right of (i,N). (1\le i\le N).

Takahashi will first choose one of the following eight directions: up, down, left, right, and the four diagonal directions. Then, he will start on a square of his choice and repeat moving one square in the chosen direction N-1 times.

In this process, Takahashi visits N squares. Find the greatest possible value of the integer that is obtained by arranging the digits written on the squares visited by Takahashi from left to right in the order visited by him.

Constraints

• 1 \le N \le 10
• 1 \le A_{i,j} \le 9
• All values in input are integers.

Sample Input 1

4
1161
1119
7111
1811

Sample Output 1

9786

If Takahashi starts on the square at the 2-nd row from the top and 4-th column from the left and goes down and to the right, the integer obtained by arranging the digits written on the visited squares will be 9786. It is impossible to make a value greater than 9786, so the answer is 9786.

Sample Input 2

10
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111

Sample Output 2

1111111111

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

Problem Statement

You are given a string S. Find the lexicographically smallest string S' obtained by permuting the characters of S.

Here, for different two strings s = s_1 s_2 \ldots s_n and t = t_1 t_2 \ldots t_m, s \lt t holds lexicographically when one of the conditions below is satisfied.

• There is an integer i\ (1 \leq i \leq \min(n,m)) such that s_i \lt t_i and s_j=t_j for all integers j\ (1 \leq j \lt i).
• s_i = t_i for all integers i\ (1 \leq i \leq \min(n,m)), and n \lt m.

Constraints

• S is a string of length between 1 and 2 \times 10^5 (inclusive) consisting of lowercase English letters.

Sample Input 1

aba

Sample Output 1

aab

Three strings can be obtained by permuting aba:

• aba
• aab
• baa

The lexicographically smallest among them is aab.

Sample Input 2

zzzz

Sample Output 2

zzzz

Problem Statement

The AtCoder Restaurant uses N types of ingredients numbered from 1 to N.

The restaurant offers M dishes numbered from 1 to M. Dish i uses K_i types of ingredients, namely A_{i,1}, A_{i,2}, \ldots, A_{i,K_i}.

Snuke currently dislikes all N ingredients. He cannot eat any dish that uses one or more ingredients he dislikes, and he can eat a dish that uses none of the disliked ingredients.

Over the next N days, he will overcome his dislikes one ingredient per day. On day i, he overcomes ingredient B_i, and from then on he no longer dislikes it.

For each i=1,2,\ldots,N, find:

• the number of dishes at the AtCoder Restaurant that he can eat immediately after overcoming ingredient B_i on day i.

Constraints

• 1 \leq N \leq 3 \times 10^{5}
• 1 \leq M \leq 3 \times 10^{5}
• 1 \leq K_i \leq N (1 \leq i \leq M)
• The sum of K_i is at most 3 \times 10^{5}.
• 1 \leq A_{i,j} \leq N (1 \leq i \leq M, 1 \leq j \leq K_i)
• A_{i,j} \neq A_{i,k} (1 \leq i \leq M, j \neq k)
• 1 \leq B_i \leq N (1 \leq i \leq N)
• B_i \neq B_j (i \neq j )
• All input values are integers.

Sample Input 1

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

Sample Output 1

0
1
2
3
4

Snuke overcomes his disliked ingredients as follows:

• Day 1: He overcomes ingredient 1. At this time, every dish still uses a disliked ingredient, so print 0.
• Day 2: He overcomes ingredient 3. Dish 4 no longer uses any disliked ingredient and becomes edible; all other dishes still use disliked ingredients, so print 1.
• Day 3: He overcomes ingredient 2. Dish 1 no longer uses any disliked ingredient and becomes edible; all dishes except 1 and 4 still use disliked ingredients, so print 2.
• Day 4: He overcomes ingredient 5. Dish 3 no longer uses any disliked ingredient and becomes edible; all dishes except 1, 3, and 4 still use disliked ingredients, so print 3.
• Day 5: He overcomes ingredient 4. Dish 2 no longer uses any disliked ingredient and becomes edible; now all dishes have no disliked ingredients, so print 4.

Sample Input 2

9 8
1 4
5 6 9 7 4 3
4 2 4 1 3
1 1
5 7 9 8 1 5
2 9 8
1 2
1 1
6 5 2 7 8 4 1 9 3

Sample Output 2

0
0
1
1
1
2
4
6
8

Problem Statement

There is a 3\times3 grid with numbers between 1 and 9, inclusive, written in each square. The square at the i-th row from the top and j-th column from the left (1\leq i\leq3,1\leq j\leq3) contains the number c _ {i,j}.

The same number may be written in different squares, but not in three consecutive cells vertically, horizontally, or diagonally. More precisely, it is guaranteed that c _ {i,j} satisfies all of the following conditions.

• c _ {i,1}=c _ {i,2}=c _ {i,3} does not hold for any 1\leq i\leq3.
• c _ {1,j}=c _ {2,j}=c _ {3,j} does not hold for any 1\leq j\leq3.
• c _ {1,1}=c _ {2,2}=c _ {3,3} does not hold.
• c _ {3,1}=c _ {2,2}=c _ {1,3} does not hold.

Takahashi will see the numbers written in each cell in random order. He will get disappointed when there is a line (vertical, horizontal, or diagonal) that satisfies the following condition.

• The first two squares he sees contain the same number, but the last square contains a different number.

Find the probability that Takahashi sees the numbers in all the squares without getting disappointed.

Constraints

• c _ {i,j}\in\lbrace1,2,3,4,5,6,7,8,9\rbrace\ (1\leq i\leq3,1\leq j\leq3)
• c _ {i,1}=c _ {i,2}=c _ {i,3} does not hold for any 1\leq i\leq3.
• c _ {1,j}=c _ {2,j}=c _ {3,j} does not hold for any 1\leq j\leq3.
• c _ {1,1}=c _ {2,2}=c _ {3,3} does not hold.
• c _ {3,1}=c _ {2,2}=c _ {1,3} does not hold.

Sample Input 1

3 1 9
2 5 6
2 7 1

Sample Output 1

0.666666666666666666666666666667

For example, if Takahashi sees c _ {3,1}=2,c _ {2,1}=2,c _ {1,1}=3 in this order, he will get disappointed.

On the other hand, if Takahashi sees c _ {1,1},c _ {1,2},c _ {1,3},c _ {2,1},c _ {2,2},c _ {2,3},c _ {3,1},c _ {3,2},c _ {3,3} in this order, he will see all numbers without getting disappointed.

The probability that Takahashi sees all the numbers without getting disappointed is \dfrac 23. Your answer will be considered correct if the absolute error from the true value is at most 10 ^ {-8}, so outputs such as 0.666666657 and 0.666666676 would also be accepted.

Sample Input 2

7 7 6
8 6 8
7 7 6

Sample Output 2

0.004982363315696649029982363316

Sample Input 3

3 6 7
1 9 7
5 7 5

Sample Output 3

0.4

Problem Statement

There are N ropes numbered 1 through N. One end of each rope is painted red, and the other is painted blue.

You are going to perform M operations of tying ropes. In the i-th operation, you tie the end of rope A_i painted B_i with the end of rope C_i painted D_i, where R means red and B means blue. For each rope, an end with the same color is not tied multiple times.

Find the number of groups of connected ropes that form cycles, and the number of those that do not, after all the operations.

Here, a group of connected ropes \lbrace v_0, v_1, \ldots, v_{x-1} \rbrace is said to form a cycle if one can rearrange the elements of v so that, for each 0 \leq i < x, rope v_i is tied to rope v_{(i+1) \bmod x}.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 0 \leq M \leq 2 \times 10^5
• 1 \leq A_i, C_i \leq N
• (A_i, B_i) \neq (A_j, B_j), (C_i, D_i) \neq (C_j, D_j) (i \neq j)
• (A_i, B_i) \neq (C_j, D_j)
• N, M, A_i, and C_i are integers.
• B_i is R or B, and so is D_i.

Sample Input 1

5 3
3 R 5 B
5 R 3 B
4 R 2 B

Sample Output 1

1 2

There are three groups of connected ropes: \lbrace 1 \rbrace, \lbrace 2,4 \rbrace, and \lbrace 3,5 \rbrace.

The group of ropes \lbrace 3,5 \rbrace forms a cycle, while the groups of rope \lbrace 1 \rbrace and ropes \lbrace 2,4 \rbrace do not. Thus, X = 1 and Y = 2.

Sample Input 2

7 0

Sample Output 2

0 7

Sample Input 3

7 6
5 R 3 R
7 R 4 R
4 B 1 R
2 R 3 B
2 B 5 B
1 B 7 B

Sample Output 3

2 1

Problem Statement

There are N servers numbered from 1 to N and M cables numbered from 1 to M.
Cable i connects servers A_i and B_i bidirectionally.

By performing the following operation some number of times (possibly zero), make all servers connected via cables.

• Operation: Choose one cable and reconnect one of its ends to a different server.

Find the minimum number of operations required and output an operation sequence achieving this minimum.

Constraints

• 2 \leq N \leq 2\times 10^5
• N-1 \leq M \leq 2\times 10^5
• 1 \leq A_i, B_i \leq N
• All input values are integers.

Sample Input 1

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

Sample Output 1

1
1 1 3

By reconnecting the end of cable 1 that is connected to server 1 to server 3, the servers can be connected via cables.

Operations such as reconnecting the end of cable 5 that is connected to server 4 to server 1, or reconnecting the end of cable 2 that is connected to server 2 to server 3, will also result in all servers being connected and are considered correct.

Sample Input 2

4 3
3 4
4 1
1 2

Sample Output 2

0

No operation may be necessary.

Sample Input 3

5 4
3 3
3 3
3 3
3 3

Sample Output 3

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

Problem Statement

You are given N strings S_i consisting of lowercase English letters.

For all possible permutations P=(P_1,P_2,\dots,P_N) of (1,2,\dots,N), write down the string generated as follows:

• Concatenate S_{P_1},S_{P_2},\dots,S_{P_N} in this order.

Let A_1,A_2,\dots,A_{N!} be the sequence of the N! written strings sorted in lexicographical order.
Output A_2.

You are given T test cases; solve each of them.

Constraints

• 1 \le T \le 1.5 \times 10^5
• 2 \le N \le 3 \times 10^5
• T,N are integers.
• S_i is a string consisting of lowercase English letters with length between 1 and 10^6-1, inclusive.
• For a single input, the sum of N does not exceed 3 \times 10^5.
• For a single input, the sum of |S_i| does not exceed 10^6.

Sample Input 1

3
3
abc
ac
ahc
4
aaa
a
aaaa
a
15
ks
sy
k
ysk
yks
ky
ksy
sk
syk
s
kys
sky
ys
yk
y

Sample Output 1

abcahcac
aaaaaaaaa
kksksykykysskskyssyksyyksykyskyys

This input contains three test cases.

For the first test case, S=( abc, ac, ahc ).
We have A=( abcacahc, abcahcac, acabcahc, acahcabc, ahcabcac, ahcacabc ), so output A_2= abcahcac.