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 countDigit(n): 
    count = 0                                                                                                                            
    while n != 0: 
        n //= 10
        count+= 1
    return count 
t=int(input())
for t in range(0,t):
    
    q= list(map (int, input().rstrip().split()))
    z=[]
    n=q[0]
    k=0
    a=n
    j=0
    sum=0
    step=0 
    d=0
    k=countDigit(n)-1
    
    while(k>=0):
        r=a%10
        if(r!=0):
            d=r*10**j
            z.append(d)
            step=step+1
        j=j+1
        k=k-1
        a//=10
        
        if(sum==n):
            break
    print(step)
    for i in range(0,step): 
        print(z[i], end =" ")
    print("")