Problem Statement

On Planet Iwai, inspired by the name of yiwiy9 (Waiiwaiwai Nine), who is very active on Earth, a game of making 81181819 from 0, 1, and 8 in as few steps as possible is popular. Let us actually try this game ourselves.

You are given a non-negative integer $N$ less than $81181819$.

Among the sequences of positive integers $p_1,p_2,...,p_k$ satisfying all of the following conditions, output one with the minimum $k$.

• $\displaystyle\sum_{i=1}^k p_i +N=81181819$
• When $p_i$ is written in decimal notation, it consists only of $0,1,8$.

If there are multiple such $p$ with the minimum $k$ satisfying the conditions, you may output any of them.

You are given $T$ test cases; answer all of them.

Constraints

• $1\leq T\leq 10$
• $0\leq N< 81181819$
• All inputs are integers.

Input

$T$
$TestCase_1$
$TestCase_2$
$\vdots$
$TestCase_T$

Each test case is given in the following format.

$N$

Output

For the $T$ test cases, output the answers in order to standard output, separated by newlines. For each test case, output $k$ and the sequence $p_1,p_2,...,p_k$ of length $k$ in the following format.

$k$
$p_1$
$p_2$
$\vdots$
$p_k$

Sample

4
81181805
81181798
81181638
0

4
1
1
1
11
2
11
10
1
181
2
81181818
1