1650 - Cos(NA) 1650 - Cos(NA) 1650 - Cos(NA)

Statistics Sub: 97 | AC: 53 | AC%: 54,64 | Score: 2,33
Created by Xtreme Programming Problem Archive - Jorge Amado Soria Ramírez
Added by ymondelo20 (2011-12-06)
Limits
Total Time: 500 MS |Memory: 62 MB | Output: 64 MB | Size: 29 KB
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Description



May be you know the Cosine's Law.
But, have you ever looked at formula of the form Cos(NA)?
If you haven't looked at them yet, just look at them now:

Cos(2A) = 2Cos^2(A)-1
Cos(3A) = 4Cos^3(A)-3Cos(A)
Cos(4A) = 8Cos^4(A)-8Cos^2(A)+1

These formula will make you believe that any Cos(NA) can be expanded in an expression which contains only one function Cos(A) and all the coefficients are also integers. In this problem your job is to find such a formula for Cos(NA) given the value of N.


May be you know the Cosine's Law.
But, have you ever looked at formula of the form Cos(NA)?
If you haven't looked at them yet, just look at them now:

Cos(2A) = 2Cos^2(A)-1
Cos(3A) = 4Cos^3(A)-3Cos(A)
Cos(4A) = 8Cos^4(A)-8Cos^2(A)+1

These formula will make you believe that any Cos(NA) can be expanded in an expression which contains only one function Cos(A) and all the coefficients are also integers. In this problem your job is to find such a formula for Cos(NA) given the value of N.


May be you know the Cosine's Law.
But, have you ever looked at formula of the form Cos(NA)?
If you haven't looked at them yet, just look at them now:

Cos(2A) = 2Cos^2(A)-1
Cos(3A) = 4Cos^3(A)-3Cos(A)
Cos(4A) = 8Cos^4(A)-8Cos^2(A)+1

These formula will make you believe that any Cos(NA) can be expanded in an expression which contains only one function Cos(A) and all the coefficients are also integers. In this problem your job is to find such a formula for Cos(NA) given the value of N.

Input specification

The input file contains at most 100 lines of inputs. Each line contains a positive integer N (1 <= N <= 50). Input is terminated by a line containing a single zero.

;jsessionid=FB5747DA3AB5F47569DF76458397101F

The input file contains at most 100 lines of inputs. Each line contains a positive integer N (1 <= N <= 50). Input is terminated by a line containing a single zero.

;jsessionid=FB5747DA3AB5F47569DF76458397101F

The input file contains at most 100 lines of inputs. Each line contains a positive integer N (1 <= N <= 50). Input is terminated by a line containing a single zero.

;jsessionid=FB5747DA3AB5F47569DF76458397101F

Output specification

For each line of input except the last one you should produce one line of output. This line should contain the formula (As described in the problem statment) for Cos(NA).
You don't need to print any redundant things in the output such as:
(a) Printing operators in two consecutive places.
(b) Printing the coefficient when it is 1.
(c) Printing the exponent when it is 1.
(d) Just look at the output for details.;jsessionid=FB5747DA3AB5F47569DF76458397101F
For each line of input except the last one you should produce one line of output. This line should contain the formula (As described in the problem statment) for Cos(NA).
You don't need to print any redundant things in the output such as:
(a) Printing operators in two consecutive places.
(b) Printing the coefficient when it is 1.
(c) Printing the exponent when it is 1.
(d) Just look at the output for details.;jsessionid=FB5747DA3AB5F47569DF76458397101F

The input file contains at most 100 lines of inputs. Each line contains a positive integer N (1 <= N <= 50). Input is terminated by a line containing a single zero.

;jsessionid=FB5747DA3AB5F47569DF76458397101F

Sample input

1
2
3
4
0

Sample output

Cos(A)
2Cos^2(A)-1
4Cos^3(A)-3Cos(A)
8Cos^4(A)-8Cos^2(A)+1

Hint(s)

http://coj.uci.cu/24h/
http://coj.uci.cu/24h/
http://coj.uci.cu/24h/

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