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 addends(n):
    str1 = str(n)
    list1 = [x for x in str1 if x!='0']
    return(len(list1))
t = int(input())
num = []
for x in range(t):
    num.append(int(input()))
k = []
res = []
for x in range(t):
    y = addends(num[x])
    k.append(y)
for x in range(t):
    count = 0
    str2 = str(num[x])
    list2 = [x for x in str2]
    for y in range(len(list2)):
        if list2[y]!='0' and y!=(len(list2)-1):
            res.append(int(list2[y])*(10**(len(list2)-y-1)))
        elif list2[y]!='0' and y==(len(list2)-1):
            res.append(int(list2[y]))
for x in range(t):
    print("\n",k[x],sep="")
    i = 0
    while i<k[x]:
        print(res[0],end=" ")
        res.pop(0)
        i+=1