vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
This is an interactive problem.

There is an unknown integer x (1≤ x≤ n). You want to find x.

At first, you have a set of integers \{1, 2, …, n\}. You can perform the following operations no more than 10000 times:

  * A a: find how many numbers are multiples of a in the current set. 
  * B a: find how many numbers are multiples of a in this set, and then delete all multiples of a, but x will never be deleted (even if it is a multiple of a). In this operation, a must be greater than 1. 
  * C a: it means that you know that x=a. This operation can be only performed once. 



Remember that in the operation of type B a>1 must hold.

Write a program, that will find the value of x.

Input

The first line contains one integer n (1≤ n≤ 10^5). The remaining parts of the input will be given throughout the interaction process.

Interaction

In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer a (1≤ a≤ n for operations A and C, 2≤ a≤ n for operation B). This line desribes operation you make.

If your operation has type C your program should terminate immediately.

Else your program should read one line containing a single integer, which is the answer to your operation.

After outputting each line, don't forget to flush the output. To do it use:

  * fflush(stdout) in C/C++; 
  * System.out.flush() in Java; 
  * sys.stdout.flush() in Python; 
  * flush(output) in Pascal; 
  * See the documentation for other languages. 



It is guaranteed, that the number x is fixed and won't change during the interaction process.

Hacks:

To make a hack, use such input format:

The only line should contain two integers n, x (1 ≤ x ≤ n ≤ 10^5).

Example

Input


10

2

4

0

Output



B 4

A 2

A 8

C 4

Note

Note that to make the sample more clear, we added extra empty lines. You shouldn't print any extra empty lines during the interaction process.

In the first test n=10 and x=4.

Initially the set is: \{1,2,3,4,5,6,7,8,9,10\}.

In the first operation, you ask how many numbers are multiples of 4 and delete them. The answer is 2 because there are two numbers divisible by 4: \{4,8\}. 8 will be deleted but 4 won't, because the number x will never be deleted. Now the set is \{1,2,3,4,5,6,7,9,10\}.

In the second operation, you ask how many numbers are multiples of 2. The answer is 4 because there are four numbers divisible by 2: \{2,4,6,10\}.

In the third operation, you ask how many numbers are multiples of 8. The answer is 0 because there isn't any number divisible by 8 in the current set.

In the fourth operation, you know that x=4, which is the right answer.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Amugae is in a very large round corridor. The corridor consists of two areas. The inner area is equally divided by $n$ sectors, and the outer area is equally divided by $m$ sectors. A wall exists between each pair of sectors of same area (inner or outer), but there is no wall between the inner area and the outer area. A wall always exists at the 12 o'clock position.

 $0$ 

The inner area's sectors are denoted as $(1,1), (1,2), \dots, (1,n)$ in clockwise direction. The outer area's sectors are denoted as $(2,1), (2,2), \dots, (2,m)$ in the same manner. For a clear understanding, see the example image above.

Amugae wants to know if he can move from one sector to another sector. He has $q$ questions.

For each question, check if he can move between two given sectors.


-----Input-----

The first line contains three integers $n$, $m$ and $q$ ($1 \le n, m \le 10^{18}$, $1 \le q \le 10^4$) — the number of sectors in the inner area, the number of sectors in the outer area and the number of questions.

Each of the next $q$ lines contains four integers $s_x$, $s_y$, $e_x$, $e_y$ ($1 \le s_x, e_x \le 2$; if $s_x = 1$, then $1 \le s_y \le n$, otherwise $1 \le s_y \le m$; constraints on $e_y$ are similar). Amague wants to know if it is possible to move from sector $(s_x, s_y)$ to sector $(e_x, e_y)$.


-----Output-----

For each question, print "YES" if Amugae can move from $(s_x, s_y)$ to $(e_x, e_y)$, and "NO" otherwise.

You can print each letter in any case (upper or lower).


-----Example-----
Input
4 6 3
1 1 2 3
2 6 1 2
2 6 2 4

Output
YES
NO
YES



-----Note-----

Example is shown on the picture in the statement.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an array of digits (values lie in range from 0 to 9). The task is to count all the sub sequences possible in array such that in each subsequence every digit is greater than its previous digits in the subsequence.
 
Example 1:
Input : 
a[] = {1, 2, 3, 4}
Output: 
15
Explanation :
There are total increasing subsequences
{1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4},
{2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4},
{1,3,4}, {2,3,4}, {1,2,3,4}
 
Example 2:
Input : 
a[] = {4, 3, 6, 5}
Output:
8
Explanation :
Sub-sequences are {4}, {3}, {6}, {5},
{4,6}, {4,5}, {3,6}, {3,5}
 
Example 3:
Input : 
a[] = {3, 2, 4, 5, 4}
Output : 
14
Explanation :
Sub-sequences are {3}, {2}, {4}, {3,4},
{2,4}, {5}, {3,5}, {2,5}, {4,5}, {3,2,5}
{3,4,5}, {4}, {3,4}, {2,4}
Your Task:
You don't have to print anything, printing is done by the driver function. You have to complete the function countSub() which takes the array a[] and its size N as inputs and returns the count of all increasing subsequences in given array of digits.
 
Expected Time Complexity: O(N)
Expected Auxiliary Space: O( max(a[i]) ) = O(10)
Constraints: 
1 ≤ N ≤ 500
1 ≤ a[i] ≤ 9

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Write a comparator for a list of phonetic words for the letters of the [greek alphabet](https://en.wikipedia.org/wiki/Greek_alphabet).

A comparator is:
> *a custom comparison function of two arguments (iterable elements) which should return a negative, zero or positive number depending on whether the first argument is considered smaller than, equal to, or larger than the second argument*

*(source: https://docs.python.org/2/library/functions.html#sorted)*

The greek alphabet is preloded for you as `greek_alphabet`:

```python
greek_alphabet = (
    'alpha', 'beta', 'gamma', 'delta', 'epsilon', 'zeta', 
    'eta', 'theta', 'iota', 'kappa', 'lambda', 'mu', 
    'nu', 'xi', 'omicron', 'pi', 'rho', 'sigma',
    'tau', 'upsilon', 'phi', 'chi', 'psi', 'omega')
```

## Examples

```python
greek_comparator('alpha', 'beta')   <  0
greek_comparator('psi', 'psi')      == 0
greek_comparator('upsilon', 'rho')  >  0
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given two strings s and t which consist of only lowercase letters.

String t is generated by random shuffling string s and then add one more letter at a random position.

Find the letter that was added in t.

Example:

Input:
s = "abcd"
t = "abcde"

Output:
e

Explanation:
'e' is the letter that was added.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Amanda Air has routes between many different airports, and has asked their most important frequent flyers, members of the AA Frequent Flyer program, which routes they most often fly. Based on this survey, Amanda, the CEO and owner, has concluded that Amanda Air will place lounges at some of the airports at which they operate.

However, since there are so many routes going between a wide variety of airports, she has hired you to determine how many lounges she needs to build, if at all possible, given the constraints set by her. This calculation is to be provided by you, before any lounges are built. Her requirements specifies that for some routes, there must be lounges at both airports, for other routes, there must be lounges at exactly one of the airports, and for some routes, there will be no lounges at the airports.

She is very economically minded and is demanding the absolute minimum number of lounges to be built.

-----Input-----
The first line contains two non-negative integers $1 \leq n,m \leq 200\; 000$, giving the number of airports and routes in the Amanda Catalog respectively. Thereafter follow $m$ lines, each describing a route by three non-negative integers $1 \leq a, b \leq n$ and $c \in \{ 0,1,2\} $, where $a$ and $b$ are the airports the route connects and $c$ is the number of lounges.

No route connects any airport with itself, and for any two airports at most one requirement for that route is given. As one would expect, $0$ is a request for no lounge, $1$ for a lounge at exactly one of the two airports and $2$ for lounges at both airports.

-----Output-----
If it is possible to satisfy the requirements, give the minimum number of lounges necessary to do so. If it is not possible, output impossible.

-----Examples-----
Sample Input 1:
4 4
1 2 2
2 3 1
3 4 1
4 1 2
Sample Output 1:
3

Sample Input 2:
5 5
1 2 1
2 3 1
2 4 1
2 5 1
4 5 1
Sample Output 2:
impossible

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
It's almost summertime, so Big Cat and Little Cat are getting in shape. They decide the core of their fitness plan is to start jogging every day.

Their city consists of $N$ intersections connected by $\mbox{M}$ bidirectional roads. The cats decide that their jogging route should be cyclic (i.e., starting and ending at the same intersection) and consist of $4$ different roads.

The cats also love exploring new places, so each day they want to choose a new route to jog on that is not equal to any of their previous routes. Two routes are considered to be equal if their sets of component roads are equal.

Given a map of the city, can you help our heroic cats determine the maximum number of days they can go jogging so that every route traveled is different? 

Input Format

The first line contains a pair of space-separated integers, $N$ (the number of intersections) and $\mbox{M}$ (the number of roads), respectively.

Each line $\boldsymbol{i}$ of the $\mbox{M}$ subsequent lines contains a pair of space-separated integers, $X_i$ and $Y_i$, defining a bidirectional road connecting intersections $X_i$ and $Y_i$.

Constraints

$1\leq N\leq5\cdot10^4$
$1\leq M\leq10^5$
$1\leq X_i,Y_i\leq N$
Each bidirectional road connects $2$ distinct intersections (i.e., no road connects an intersection to itself).
Each pair of intersections is directly connected by no more than $1$ road.

Output Format

Print the maximum number of days for which the cats can go jogging without repeating a route.

Sample Input
4 6
1 2
2 3
3 4
4 1
1 3
2 4

Sample Output
3

Explanation

There are $3$ different routes:

$1\to2\to3\to4\to1$
$1\to3\to2\to4\to1$
$1\to2\to4\to3\to1$

Recall that each route is a set of intersections forming a cycle, so each unique route is the same regardless of which city on the route the cats start out at. Thus, we print $3$ (the number of routes) as our answer.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We just discovered a new data structure in our research group: a suffix three!

It's very useful for natural language processing. Given three languages and three suffixes, a suffix three can determine which language a sentence is written in.

It's super simple, 100% accurate, and doesn't involve advanced machine learning algorithms.

Let us tell you how it works.

  If a sentence ends with "po" the language is Filipino.  If a sentence ends with "desu" or "masu" the language is Japanese.  If a sentence ends with "mnida" the language is Korean. 

Given this, we need you to implement a suffix three that can differentiate Filipino, Japanese, and Korean.

Oh, did I say three suffixes? I meant four.


-----Input-----

The first line of input contains a single integer $t$ ($1 \leq t \leq 30$) denoting the number of test cases. The next lines contain descriptions of the test cases. 

Each test case consists of a single line containing a single string denoting the sentence. Spaces are represented as underscores (the symbol "_") for ease of reading. The sentence has at least $1$ and at most $1000$ characters, and consists only of lowercase English letters and underscores. The sentence has no leading or trailing underscores and no two consecutive underscores. It is guaranteed that the sentence ends with one of the four suffixes mentioned above.


-----Output-----

For each test case, print a single line containing either "FILIPINO", "JAPANESE", or "KOREAN" (all in uppercase, without quotes), depending on the detected language.


-----Example-----
Input
8
kamusta_po
genki_desu
ohayou_gozaimasu
annyeong_hashimnida
hajime_no_ippo
bensamu_no_sentou_houhou_ga_okama_kenpo
ang_halaman_doon_ay_sarisari_singkamasu
si_roy_mustang_ay_namamasu

Output
FILIPINO
JAPANESE
JAPANESE
KOREAN
FILIPINO
FILIPINO
JAPANESE
JAPANESE



-----Note-----

The first sentence ends with "po", so it is written in Filipino.

The second and third sentences end with "desu" and "masu", so they are written in Japanese.

The fourth sentence ends with "mnida", so it is written in Korean.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an array(0-based indexing), you have to find the max sum of i*A[i] where A[i] is the element at index i in the array. The only operation allowed is to rotate(clock-wise or counter clock-wise) the array any number of times.
Example 1:
Input:
N = 4
A[] = {8,3,1,2}
Output: 29
Explanation: Above the configuration
possible by rotating elements are
3 1 2 8 here sum is 3*0+1*1+2*2+8*3 = 29
1 2 8 3 here sum is 1*0+2*1+8*2+3*3 = 27
2 8 3 1 here sum is 2*0+8*1+3*2+1*3 = 17
8 3 1 2 here sum is 8*0+3*1+1*2+2*3 = 11
Here the max sum is 29 
Your Task:
Your task is to complete the function max_sum which takes two arguments which is the array A [ ] and its size and returns an integer value denoting the required max sum.
Expected Time Complexity: O(N).
Expected Auxiliary Space: O(1).
Constraints:
1<=N<=10^{4}
1<=A[]<1000

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Little Artem got n stones on his birthday and now wants to give some of them to Masha. He knows that Masha cares more about the fact of receiving the present, rather than the value of that present, so he wants to give her stones as many times as possible. However, Masha remembers the last present she received, so Artem can't give her the same number of stones twice in a row. For example, he can give her 3 stones, then 1 stone, then again 3 stones, but he can't give her 3 stones and then again 3 stones right after that.

How many times can Artem give presents to Masha?


-----Input-----

The only line of the input contains a single integer n (1 ≤ n ≤ 10^9) — number of stones Artem received on his birthday.


-----Output-----

Print the maximum possible number of times Artem can give presents to Masha.


-----Examples-----
Input
1

Output
1

Input
2

Output
1

Input
3

Output
2

Input
4

Output
3



-----Note-----

In the first sample, Artem can only give 1 stone to Masha.

In the second sample, Atrem can give Masha 1 or 2 stones, though he can't give her 1 stone two times.

In the third sample, Atrem can first give Masha 2 stones, a then 1 more stone.

In the fourth sample, Atrem can first give Masha 1 stone, then 2 stones, and finally 1 stone again.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are a manager of a prestigious soccer team in the JOI league.

The team has $N$ players numbered from 1 to $N$. The players are practicing hard in order to win the tournament game. The field is a rectangle whose height is $H$ meters and width is $W$ meters. The vertical line of the field is in the north-south direction, and the horizontal line of the field is in the east-west direction. A point in the field is denoted by ($i, j$) if it is $i$-meters to the south and $j$ meters to the east from the northwest corner of the field.

After the practice finishes, players must clear the ball. In the beginning of the clearance, the player $i$ ($1 \leq i \leq N$) stands at ($S_i, T_i$). There is only one ball in the field, and the player 1 has it. You stand at ($S_N, T_N$) with the player $N$. The clearance is finished if the ball is passed to ($S_N, T_N$), and you catch it. You cannot move during the clearance process.

You can ask players to act. But, if a player acts, his fatigue degree will be increased according to the action. Here is a list of possible actions of the players. If a player has the ball, he can act (i),(ii), or (iii). Otherwise, he can act (ii) or (iv).

* (i) Choose one of the 4 directions (east/west/south/north), and choose a positive integer $p$. Kick the ball to that direction. Then, the ball moves exactly p meters. The kicker does not move by this action, and he loses the ball. His fatigue degree is increased by $A \times p + B$.
* (ii) Choose one of the 4 directions (east/west/south/north), and move 1 meter to that direction. If he has the ball, he moves with it. His fatigue degree is increased by $C$ regardless of whether he has the ball or not.
* (iii) Place the ball where he stands. He loses the ball. His fatigue degree does not change.
* (iv) Take the ball. His fatigue degree does not change. A player can take this action only if he stands at the same place as the ball, and nobody has the ball.



Note that it is possible for a player or a ball to leave the field. More than one players can stand at the same place.

Since the players just finished the practice, their fatigue degrees must not be increased too much. You want to calculate the minimum possible value of the sum of fatigue degrees of the players for the clearance process.





Example

Input

6 5
1 3 6
3
1 1
0 4
6 5


Output

26

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Snuke has N sticks.
The length of the i-th stick is l_i.
Snuke is making a snake toy by joining K of the sticks together.
The length of the toy is represented by the sum of the individual sticks that compose it.
Find the maximum possible length of the toy.

-----Constraints-----
 - 1 \leq K \leq N \leq 50
 - 1 \leq l_i \leq 50
 - l_i is an integer.

-----Input-----
Input is given from Standard Input in the following format:
N K
l_1 l_2 l_3 ... l_{N}

-----Output-----
Print the answer.

-----Sample Input-----
5 3
1 2 3 4 5

-----Sample Output-----
12

You can make a toy of length 12 by joining the sticks of lengths 3, 4 and 5, which is the maximum possible length.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The bustling town of Siruseri has just one sports stadium. There
are a number of schools, colleges, sports associations, etc. that
use this stadium as the venue for their sports events. 
 Anyone interested in using the stadium has to apply to the Manager
of the stadium indicating both the starting date (a positive integer
S) and the length of the sporting event in days (a positive integer D)
they plan to organise.  Since these requests could overlap it may not
be possible to satisfy everyone.  

It is the job of the Manager to decide who gets to use the
stadium and who does not. The Manager, being a genial man, would like
to keep as many organisations happy as possible and hence would
like to allocate the stadium so that maximum number of events are held.


Suppose, for example, the Manager receives the following 4 requests: 



Event No.
Start Date
Length

125
297
3156
493


He would allot the stadium to events 1, 4 and 3. Event 1 begins on day 2
and ends on day 6, event 4 begins on day 9 and ends on day 11 and event
3 begins on day 15 and ends on day 20. You can verify that it is not possible
to schedule all the 4 events (since events 2 and 3 overlap  and only one of 
them can get to use the stadium).


Your task is to help the manager find the best possible allotment (i.e.,
the maximum number of events that can use the stadium).

Input format

The first line of the input will contain a single integer N (N ≤ 100000)
indicating the number of events for which the Manager has received a request.
Lines 2,3,...,N+1  describe the requirements of the N events.  
Line i+1 contains two integer Si and Di indicating the starting date 
and the duration of event i. You may assume that 1 ≤ Si ≤ 1000000 and 
1 ≤ Di ≤ 1000.


Output format

Your output must consist of a single line containing a single integer M,
indicating the maximum possible number of events that can use the stadium.

Example:
Sample input:

4
2 5
9 7
15 6
9 3

Sample output:

3

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Special Numbers 
Mani has encountered a problem on Special numbers in Bytecode. A number S is called a special number if its digits are in an arithmetic progression modulo 10. He has an array consisting of all numbers from 1 to N and needs your help to find the number of special numbers in the array. He has promised you a significant share of the prize money if he wins the contest :p 
Note:
123,99,802 are special numbers.
146 is not a special number 

-----Input-----

Input consists of 1 integer - the value of N

-----Output-----
Print one integer in the first line - the solution to this problem

-----Constraints-----
- 1 ≤ Number of digits in N ≤ 105

Example

Input

123

Output

102

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Firecrackers scare Nian the monster, but they're wayyyyy too noisy! Maybe fireworks make a nice complement.

Little Tommy is watching a firework show. As circular shapes spread across the sky, a splendid view unfolds on the night of Lunar New Year's eve.

A wonder strikes Tommy. How many regions are formed by the circles on the sky? We consider the sky as a flat plane. A region is a connected part of the plane with positive area, whose bound consists of parts of bounds of the circles and is a curve or several curves without self-intersections, and that does not contain any curve other than its boundaries. Note that exactly one of the regions extends infinitely.


-----Input-----

The first line of input contains one integer n (1 ≤ n ≤ 3), denoting the number of circles.

The following n lines each contains three space-separated integers x, y and r ( - 10 ≤ x, y ≤ 10, 1 ≤ r ≤ 10), describing a circle whose center is (x, y) and the radius is r. No two circles have the same x, y and r at the same time.


-----Output-----

Print a single integer — the number of regions on the plane.


-----Examples-----
Input
3
0 0 1
2 0 1
4 0 1

Output
4

Input
3
0 0 2
3 0 2
6 0 2

Output
6

Input
3
0 0 2
2 0 2
1 1 2

Output
8



-----Note-----

For the first example, $000$ 

For the second example, [Image] 

For the third example, $\text{Q)}$

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are N children standing in a line. Each child is assigned a rating value.

You are giving candies to these children subjected to the following requirements:


       Each child must have at least one candy.
       Children with a higher rating get more candies than their neighbors.


What is the minimum candies you must give?

Example 1:


Input: [1,0,2]
Output: 5
Explanation: You can allocate to the first, second and third child with 2, 1, 2 candies respectively.


Example 2:


Input: [1,2,2]
Output: 4
Explanation: You can allocate to the first, second and third child with 1, 2, 1 candies respectively.
             The third child gets 1 candy because it satisfies the above two conditions.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.