Problem Statement

One day, your homework included a problem on polynomial division.
However, you are very bad at polynomial division.
So you decided to write a program and have a computer do the calculation for you.
Output the remainder when the given polynomial is divided by \(x^3-x\).

Input

\(D\)
\(a_{0}\) \(a_{1}\) \(\ldots\) \(a_{D}\)

• \(0 \leq D \leq 10000\) represents the degree of the dividend polynomial.
• \(-100 \leq a_{i} \leq 100\) represents the integer coefficients of the dividend polynomial.
• The dividend polynomial is expressed as \(a_{D}x^D + a_{D-1}x^{D-1} + \ldots + a_{2}x^2 + a_{1}x + a_{0}\).
• If \(D \ge 1\), it is guaranteed that \(a_{D} \neq 0\).

Output

Output the remainder when the given polynomial is divided by \(x^3-x\).

Output Format

\(D'\)
\(b_{0}\) \(b_{1}\) \(\ldots\) \(b_{D'}\)

• \(D'\) represents the degree of the remainder polynomial.
• \(b_{i}\) represents the coefficients of the remainder polynomial.
• The remainder polynomial is expressed as \(b_{D'}x^{D'} + b_{D'-1}x^{D'-1} + \ldots + b_{2}x^2 + b_{1}x + b_{0}\).
• If \(D' \ge 1\), it must hold that \(b_{D'} \neq 0\).

Sample

5
1 1 1 0 0 1

2
1 2 1

8
0 -5 0 4 0 1 -1 0 1

0
0

5
-5 0 -1 1 1 1

1
-5 2