Problem Statement

You are given a string S consisting of lowercase English letters.

Swap the a-th and b-th characters from the beginning of S and print the resulting string.

Constraints

• S is a string consisting of lowercase English letters.
• The length of S, |S|, satisfies 2 \leq |S| \leq 10.
• 1 \leq a < b \leq |S|
• a and b are integers.

Sample Input 1

chokudai
3 5

Sample Output 1

chukodai

After swapping the 3-rd character o and 5-th character u of chokudai, we have chukodai.

Sample Input 2

aa
1 2

Sample Output 2

aa

In this sample, after swapping the 1-st and 2-nd characters of S, we have the same string as S.

Sample Input 3

aaaabbbb
1 8

Sample Output 3

baaabbba

Problem Statement

Takahashi turns on the light of his room at S o'clock (on the 24-hour clock) every day and turns it off at T o'clock every day.
The date may change while the light is on.

Determine whether the light is on at 30 minutes past X o'clock.

Constraints

• 0 \leq S, T, X \leq 23
• S \neq T
• All values in input are integers.

Sample Input 1

7 20 12

Sample Output 1

Yes

The light is on between 7 o'clock and 20 o'clock. At 30 minutes past 12 o'clock, it is on, so we print Yes.

Sample Input 2

20 7 12

Sample Output 2

No

The light is on between 0 o'clock and 7 o'clock, and between 20 o'clock and 0 o'clock (on the next day). At 30 minutes past 12 o'clock, it is off, so we print No.

Sample Input 3

23 0 23

Sample Output 3

Yes

Problem Statement

Keyence has N bases worldwide, numbered 1 to N. Base i has W_i employees, and at 0 o'clock in Coordinated Universal Time (UTC), it is X_i o'clock at base i.

You want to hold a one-hour meeting across the entire company. Each employee can only participate in the meeting if the meeting time is completely within the 9:00-18:00 time slot at their base. Find the maximum number of employees who can participate when deciding the meeting time to allow as many employees as possible to participate.

Constraints

• 1\leq N \leq 1000
• 1\leq W_i \leq 10^6
• 0\leq X_i < 24
• All input values are integers.

Sample Input 1

3
5 0
3 3
2 18

Sample Output 1

8

Consider holding the meeting from 14:00 to 15:00 in UTC.

• The meeting is held from 14:00 to 15:00 at base 1, so the 5 employees at base 1 can participate in the meeting.
• The meeting is held from 17:00 to 18:00 at base 2, so the 3 employees at base 2 can participate in the meeting.
• The meeting is held from 8:00 to 9:00 at base 3, so the 2 employees at base 3 cannot participate in the meeting.

Thus, a total of 5+3=8 employees can participate in the meeting. No meeting time allows more employees to participate.

Sample Input 2

2
1 10
1000000 20

Sample Output 2

1000000

Sample Input 3

6
31 3
20 8
11 5
4 3
47 14
1 18

Sample Output 3

67

Problem Statement

There is an infinitely long piano keyboard. Is there a continuous segment within this keyboard that consists of W white keys and B black keys?

Let S be the string formed by infinitely repeating the string wbwbwwbwbwbw.

Is there a substring of S that consists of W occurrences of w and B occurrences of b?

Constraints

• W and B are integers.
• 0\leq W,B \leq 100
• W+B \geq 1

Sample Input 1

3 2

Sample Output 1

Yes

The first 15 characters of S are wbwbwwbwbwbwwbw. You can take the 11-th through 15-th characters to form the string bwwbw, which is a substring consisting of three occurrences of w and two occurrences of b.

Sample Input 2

3 0

Sample Output 2

No

The only string consisting of three occurrences of w and zero occurrences of b is www, which is not a substring of S.

Sample Input 3

92 66

Sample Output 3

Yes

Problem Statement

You are given N strings S_1,S_2,\dots,S_N, each of length M, consisting of lowercase English letter. Here, S_i are pairwise distinct.

Determine if one can rearrange these strings to obtain a new sequence of strings T_1,T_2,\dots,T_N such that:

• for all integers i such that 1 \le i \le N-1, one can alter exactly one character of T_i to another lowercase English letter to make it equal to T_{i+1}.

Constraints

• 2 \le N \le 8
• 1 \le M \le 5
• S_i is a string of length M consisting of lowercase English letters. (1 \le i \le N)
• S_i are pairwise distinct.

Sample Input 1

4 4
bbed
abcd
abed
fbed

Sample Output 1

Yes

One can rearrange them in this order: abcd, abed, bbed, fbed. This sequence satisfies the condition.

Sample Input 2

2 5
abcde
abced

Sample Output 2

No

No matter how the strings are rearranged, the condition is never satisfied.

Sample Input 3

8 4
fast
face
cast
race
fact
rice
nice
case

Sample Output 3

Yes

Problem Statement

Your refrigerator has N kinds of ingredients. Let us call them ingredient 1, \dots, ingredient N. You have Q_i grams of ingredient i.

You can make two types of dishes. To make one serving of dish A, you need A_i grams of each ingredient i (1 \leq i \leq N). To make one serving of dish B, you need B_i grams of each ingredient i. You can only make an integer number of servings of each type of dish.

Using only the ingredients in the refrigerator, what is the maximum total number of servings of dishes you can make?

Constraints

• 1 \leq N \leq 10
• 1 \leq Q_i \leq 10^6
• 0 \leq A_i \leq 10^6
• There is an i such that A_i \geq 1.
• 0 \leq B_i \leq 10^6
• There is an i such that B_i \geq 1.
• All input values are integers.

Sample Input 1

2
800 300
100 100
200 10

Sample Output 1

5

This refrigerator has 800 grams of ingredient 1 and 300 grams of ingredient 2.

You can make one serving of dish A with 100 grams of ingredient 1 and 100 grams of ingredient 2, and one serving of dish B with 200 grams of ingredient 1 and 10 grams of ingredient 2.

To make two servings of dish A and three servings of dish B, you need 100 \times 2 + 200 \times 3 = 800 grams of ingredient 1, and 100 \times 2 + 10 \times 3 = 230 grams of ingredient 2, neither of which exceeds the amount available in the refrigerator. In this way, you can make a total of five servings of dishes, but there is no way to make six, so the answer is 5.

Sample Input 2

2
800 300
100 0
0 10

Sample Output 2

38

You can make 8 servings of dish A with 800 grams of ingredient 1, and 30 servings of dish B with 300 grams of ingredient 2, for a total of 38 servings.

Sample Input 3

2
800 300
801 300
800 301

Sample Output 3

0

You cannot make any dishes.

Sample Input 4

10
1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000
0 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 0

Sample Output 4

222222

Problem Statement

You are given a string A consisting of (, x, ).
You can perform the following two types of operations on A any number of times in any order.

• Choose one occurrence of the substring (xx) in A and replace it with xx.
• Choose one occurrence of the substring xx in A and replace it with (xx).

You are given a string B consisting of (, x, ). Determine whether you can make A equal to B.

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

Constraints

• 1 \leq T \leq 3 \times 10^5
• A and B are strings of length between 1 and 2\times 10^6, inclusive, consisting of (, x, ).
• The sum of |A| + |B| over all test cases is at most 2 \times 10^6 (where |A| denotes the length of A).

Sample Input 1

6
(xx)x
x(xx)
(x)x
(xx)
)x()x(
)x()x(
x
(x)
(((((xx)))))x
x((((((((((xx))))))))))
((xx)xx)xx
(x((xx))x)(xx)

Sample Output 1

Yes
No
Yes
No
Yes
Yes

For example, in the first test case, you can make A equal to B by the following procedure:

• Replace the (xx) from the 1st through 4th characters of A with xx. After this operation, A is xxx.
• Replace the xx from the 2nd through 3rd characters of A with (xx). After this operation, A is x(xx).

Problem Statement

You are given a simple connected undirected graph G with N vertices and M edges.
The vertices of G are numbered vertex 1, vertex 2, \ldots, vertex N, and the i-th (1\leq i\leq M) edge connects vertices U_i and V_i.

Find the lexicographically smallest simple path from vertex X to vertex Y in G.
That is, find the lexicographically smallest among the integer sequences P=(P_1,P_2,\ldots,P_{\lvert P\rvert}) that satisfy the following conditions:

• 1\leq P_i\leq N
• If i\neq j, then P_i\neq P_j.
• P_1=X and P_{\lvert P\rvert}=Y.
• For 1\leq i\leq \lvert P\rvert-1, there exists an edge connecting vertices P_i and P_{i+1}.

One can prove that such a path always exists under the constraints of this problem.

You are given T test cases, so find the answer for each.

Constraints

• 1\leq T\leq 500
• 2\leq N\leq 1000
• N-1\leq M\leq \min\left( \frac{N(N-1)}{2},5\times 10^4\right)
• 1\leq X,Y \leq N
• X\neq Y
• 1\leq U_i<V_i \leq N
• If i\neq j, then (U_i,V_i)\neq (U_j,V_j).
• The given graph is connected.
• The sum of N over all test cases in each input is at most 1000.
• The sum of M over all test cases in each input is at most 5\times 10^4.
• All input values are integers.

Sample Input 1

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

Sample Output 1

3 1 2 5
3 2

For the first test case, graph G is as follows:

The simple paths from vertex 3 to vertex 5 on G, listed in lexicographic order, are as follows:

• (3,1,2,5)
• (3,1,2,6,5)
• (3,1,5)
• (3,1,6,2,5)
• (3,1,6,5)
• (3,4,2,1,5)
• (3,4,2,1,6,5)
• (3,4,2,5)
• (3,4,2,6,1,5)
• (3,4,2,6,5)
• (3,5)

Among these, the lexicographically smallest is (3,1,2,5), so output 3,1,2,5 separated by spaces on the first line.

For the second test case, (3,2) is the only simple path from vertex 3 to vertex 2.

Problem Statement

We have a simple directed graph G with N vertices and M edges. The vertices are labeled as Vertex 1, Vertex 2, \ldots, Vertex N. The i-th edge (1\leq i\leq M) goes from Vertex U_i to Vertex V_i.

Takahashi will start at a vertex and repeatedly travel on G from one vertex to another along a directed edge. How many vertices of G have the following condition: Takahashi can start at that vertex and continue traveling indefinitely by carefully choosing the path?

Constraints

• 1 \leq N \leq 2\times 10^5
• 0 \leq M \leq \min(N(N-1), 2\times 10^5)
• 1 \leq U_i,V_i\leq N
• U_i\neq V_i
• (U_i,V_i)\neq (U_j,V_j) if i\neq j.
• All values in input are integers.

Sample Input 1

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

Sample Output 1

4

When starting at Vertex 2, Takahashi can continue traveling indefinitely: 2 \to 3 \to 4 \to 2 \to 3 \to \cdots The same goes when starting at Vertex 3 or Vertex 4. From Vertex 1, he can first go to Vertex 2 and then continue traveling indefinitely again.
On the other hand, from Vertex 5, he cannot move at all.

Thus, four vertices ―Vertex 1, 2, 3, and 4― satisfy the conditions, so 4 should be printed.

Sample Input 2

3 2
1 2
2 1

Sample Output 2

2

Note that, in a simple directed graph, there may be two edges in opposite directions between the same pair of vertices. Additionally, G may not be connected.