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A. Sum of Round Numbers

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA positive (strictly greater than zero) integer is called round if it is of the form d00...0. In other words, a positive integer is round if all its digits except the leftmost (most significant) are equal to zero. In particular, all numbers from $$$1$$$ to $$$9$$$ (inclusive) are round.

For example, the following numbers are round: $$$4000$$$, $$$1$$$, $$$9$$$, $$$800$$$, $$$90$$$. The following numbers are not round: $$$110$$$, $$$707$$$, $$$222$$$, $$$1001$$$.

You are given a positive integer $$$n$$$ ($$$1 \le n \le 10^4$$$). Represent the number $$$n$$$ as a sum of round numbers using the minimum number of summands (addends). In other words, you need to represent the given number $$$n$$$ as a sum of the least number of terms, each of which is a round number.

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases in the input. Then $$$t$$$ test cases follow.

Each test case is a line containing an integer $$$n$$$ ($$$1 \le n \le 10^4$$$).

Output

Print $$$t$$$ answers to the test cases. Each answer must begin with an integer $$$k$$$ — the minimum number of summands. Next, $$$k$$$ terms must follow, each of which is a round number, and their sum is $$$n$$$. The terms can be printed in any order. If there are several answers, print any of them.

Example

Input

5 5009 7 9876 10000 10

Output

2 5000 9 1 7 4 800 70 6 9000 1 10000 1 10

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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