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:
#ROKY
#hUcK
def check(q):
    o=''
    for i in range(0,q-1,1):
        o+='0'
    return o 
t=int(input())
while(t>0):
    a=int(input())
    s=str(a)
    n="".join(reversed(s))
    d=int(n)
    b=str(d)
    if(len(b)==1):
        print(1)
        print(a)
    else:
        p=[]
        cnt=0
        p2=[]
        d=int(s)
        h=len(s)
        while(d!=0):
            r=d%10
            if(r!=0):
                cnt+=1
            p.append(r)
            d=d//10
        p.reverse()
        print(cnt)
        for i in p:
            z=int(str(i))
            if(z>0):
                print(str(i)+check(h),end=' ')
            h-=1
        print()
    t-=1