Problem Statement

You are given $Q$ queries. For each query, construct a sequence $e$ as follows.

• Let $A$ = $sqrt(e_1) + sqrt(e_2) + sqrt(e_3) + ... + sqrt(e_N)$.
• The absolute error |$A-P_i$| is at most $10^{-10}$.
• The length of the sequence $e$ is at most $30$. Also, each $e_i$ is a non-negative integer.

Input

$Q$
$P_1$
$P_2$
...
$P_Q$

Line $1$ contains an integer $Q$ between $1$ and $1 \ 000$, inclusive. $Q$ is the number of queries.
The following $Q$ lines, starting from line $2$, give the target values $P_i$. They satisfy $8 \ 000 \leq P_i \leq 12 \ 000$. Each $P_i$ is given to the 14th or 15th decimal place.
Include a newline at the end.

Output

$N$ $e_1$ $e_2$ ... $e_N$

For each query, print $N$ and $e_i$ separated by spaces on $1$ line, as shown above.
Since you must answer $Q$ queries in total, print $Q$ lines.

Sample

4
10000.00000000000000
11234.00000000000000
10368.22067666386043
11507.39696137537560

1 100000000
1 126202756
1 107500000
3 10000000 15000000 20000000