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Polynomial sign
Tag(s):

Easy-Medium, Linear Algebra, Mathematics

Problem
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Consider a polynomial function \(f(x)\) with integer coefficients: \(a_0 + a_1 \cdot x + ... + a_n \cdot x^n\). Lets define \(superBig = 10000^{10000^{10000}}\). Someone really wants to know \(sgn(f(superBig))\) and \(sgn(f(-superBig))\). Please, help him to find the sign of these values. Note that \(a_n\) can be zero.

Read more about sgn function on https://en.wikipedia.org/wiki/Sign_function.

Input format

The first line contains single integer n (\(0 \leq n \leq 3 \cdot 10^5\)).

The second line contains \(n+1\) space separated integers \(a_i\) (\(-10^{18} \leq a_i \leq 10^{18}\)) - the coefficients of polynomial.

Output format

Print two space separated integers \(sgn(f(superBig))\) and \(sgn(f(-superBig))\).

Note that these values can be only 1, 0 or 1.

SAMPLE INPUT
1
-100 1
SAMPLE OUTPUT
1 -1
Explanation
  • \(sgn(f(superBig)) =sgn(superBig - 100) = 1\), \(superBig - 100 > 0\)
  • \(sgn(f(-superBig)) =sgn(-superBig - 100) = -1\), \(-superBig - 100 < 0\)
Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 512 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, TypeScript, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

October Circuits '17

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