Problem Statement

Seeing Rumenaru trying to give Yuyu an integral toy as a birthday present, Sounansha decided to give a toy containing a series as a present.

When a sequence of positive integers $A=(A_1,\ldots,A_N)$ of length $N$ is put into this toy, it outputs the value of $\displaystyle\sum_{i=0}^\infty\binom{2i}i\frac1{16^i}\sum_{j=1}^N\frac{A_j}{2i+j}$.

However, Sounansha has become worried about whether this toy is working properly. Therefore, please write a program that finds the value the toy would output when working properly.

It can be proved that the value returned by this toy can always be expressed as $a+b\sqrt{3}+c\pi$ using rational numbers $a,b,c$, so output these as described in the Notes.

Here, $\displaystyle\binom{2i}i:=\frac{(2i)!}{i!^2}$. Furthermore, it can be proved that the only rational numbers $p,q,r$ satisfying $\displaystyle p+q\sqrt3+r\pi=0$ are $p=q=r=0$.

Notes

When outputting a rational number, first express it as a fraction $\displaystyle\frac pq$. Here, $p,q$ are integers, and $q$ must not be divisible by $998244353$ (under the constraints of this problem, such a representation is always possible). Then, output the unique integer $k$ satisfying $qk\equiv p \left(\text{mod}\ 998244353\right)$ that is at least $0$ and less than $998244353$.

Constraints

$1\le N\le 10^5$

$1\le A_i\le 10^6\ (1\le i\le N)$

All inputs are integers.

Input

$N$
$A_1\ \ldots\ A_N$

Output

Output the $3$ rational numbers $a,b,c$ satisfying $\displaystyle\sum_{i=0}^\infty\binom{2i}i\frac1{16^i}\sum_{j=1}^N\frac{A_j}{2i+j}=a+b\sqrt{3}+c\pi$, separated by spaces.

Sample