Problem: A 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 ≤ n ≤ 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 ≤ t ≤ 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 ≤ n ≤ 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 

Solution (in PYTHON3):

Solution:
num = int(input());
while (num > 0) :
    num = num-1;
    t = int(input());
    if (t<10) :
        print("1");
        print(t);
    else :
        check = str(t);
        l = len(check);
        list = [None]*l;
        count=0;
        m =0;
        for i in range(0,l) :
            j=l-1;
            y = int(check[i]);
            if(y != 0):
                temp = str(0);
                j =j-i;
                st = str(y);
                temp = temp*j;
                st= st+temp;
                count = count+1;
                list[m]=st;m=m+1;
        print(count);
        for i in range(0,m) :
            print(list[i],end=" ")
        print();