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 ii(): return int(input())
def mi(): return map(int, input().split())
def li(): return list(mi())
def binaryToDecimal(binary): 
      
    binary1 = binary 
    decimal, i, n = 0, 0, 0
    while(binary != 0): 
        dec = binary % 10
        decimal = decimal + dec * pow(2, i) 
        binary = binary//10
        i += 1
    return decimal
def padded_bin_with_complement(x):
    if x < 0:
        return bin((2**64) - abs(x))[2:].zfill(64)
    else:
        return bin(x)[2:].zfill(64)
def countDigit(n): 
    count = 0
    while n != 0: 
        n //= 10
        count+= 1
    return count 
for _ in range(ii()):
    n = ii()
    j = countDigit(n)
    n = str(n)
    n1 = list(n)
    a= []
    for i in range(len(n1)):
        if n1[i] != "0":
            a.append(int(n1[i])*10**(j-1))
        j-=1
    print(len(a))
    print(*a)