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:
n=int(input())
def maxs(m):
    s=10
    c=0
    lk=int(m)
    while lk%s ==0:
        c=c+1
        s=s*10
    return c 
ww=[]
for i in range (n):
    t=input()
    ww.append(t)
for i in ww:
    zero=list(i)
    r=len(zero)
    kl=0
    for m in zero:
        if m=="0":
            kl=kl+1    
    print(r-kl)
    cc=0
    zz=[]
    while cc<r:
        if zero[cc]=="0":
            cc=cc+1
        else:
            lll=int(zero[cc])*(10**(r-cc-1))
            zz.append(lll)
            cc=cc+1
    print(' '.join(map(str, zz)))