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:

def wa(l):
    s=''
    for i in range(0,l-1,1):
        s+='0'
    return s
def ans(s):
    l=[]
    count=0
    l2=[]
    d=int(s)
    f=len(s)
    while(d!=0):
        r=d%10
        if(r!=0):
            count+=1
        l.append(r)
        d=d//10
    l.reverse()
    print(count)
    for i in l:
        x=int(str(i))
        if(x>0):
            print(str(i)+wa(f),end=' ')
        f-=1
    print()
        
         
t=int(input())
while(t>0):
    a=int(input())
    s=str(a)
    s1="".join(reversed(s))
    d=int(s1)
    s2=str(d)
    if(len(s)==1 or len(s2)==1):
        print(1)
        print(a)
    else:
        ans(s)
    t-=1