E. Deleting Numbers SOLUTION CODEFORCES

Deleting Numbers SOLUTION

This is an intelligent issue. There is an obscure whole number x (1≤x≤n). You need to discover x. From the outset, you have a lot of numbers {1,2,… ,n}. You can play out the accompanying activities close to multiple times: 
 
An a: discover what number of numbers are products of an in the current set. 
 
B a: discover what number of numbers are products of an in this set, and afterward erase all products of a, yet x will never be erased (regardless of whether it is a numerous of a). In this activity, an absolute necessity be more noteworthy than 1. 
 
C an: it implies that you realize that x=a. This activity can be just performed once. 
 
Recall that in the activity of type B a>1 must hold. 
 
Compose a program, that will discover the estimation of x. 
 
Info 
 
The main line contains one number n (1≤n≤105). The rest of the pieces of the info will be given all through the communication cycle. 
 
Connection 
 
In each round, your program needs to print a line containing one capitalized letter A, B or C and a number a (1≤a≤n for tasks An and C, 2≤a≤n for activity B). This line desribes activity you make. 
 
In the event that your activity has type C your program ought to end right away. 
 
Else your program should peruse one line containing a solitary number, which is the solution to your activity. 
 
In the wake of yielding each line, remember to flush the yield. 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 different dialects. 
 
It is ensured, that the number x is fixed and won’t change during the association cycle. 
 
Hacks: 
 
To make a hack, utilize such information design: 
 
The main line ought to contain two numbers n, x (1≤x≤n≤105). 
 
Model 
 
inputCopy 
 
10 
 
 
 
 
outputCopy 
 
B 4 
 
A 2 
 
A 8 
 
C 4 
 
Note 
 
Note that to make the example more understood, we included additional unfilled lines. You shouldn’t print any additional vacant lines during the collaboration cycle. 
 
In the principal test n=10 and x=4. 
 
At first the set is: {1,2,3,4,5,6,7,8,9,10}. 
 
In the primary activity, you solicit what number of numbers are products from 4 and erase them. The appropriate response is 2 on the grounds that there are two numbers detachable by 4: {4,8}. 8 will be erased however 4 won’t, on the grounds that the number x will never be erased. Presently the set is {1,2,3,4,5,6,7,9,10}. 
 
In the subsequent activity, you solicit what number of numbers are products from 2. The appropriate response is 4 in light of the fact that there are four numbers distinct by 2: {2,4,6,10}. 
 
In the third activity, you solicit what number of numbers are products from 8. The appropriate response is 0 in light of the fact that there isn’t any number distinguishable by 8 in the current set. 
 
In the fourth activity, you realize that x=4, which is the correct answer.
 

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