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:
n = int(input())

def isround(nn):
    if nn < 10:
        return True
    sd = str(nn)
    digits = len(sd)
    return (nn - int(sd[0])*10**(digits-1)) == 0

for i in range(n):
    k = int(input())
    ans = []

    sd = str(k)
    ctr = len(sd) - 1
    while k:
        if isround(k):
            ans.append(str(k))
            break
        ff = int(sd[0])*(10**ctr)
        ans.append(str(ff))
        k = k - ff
        sd = str(k)
        ctr = len(sd) - 1
    # zeros = 1
    # while k:
    #     if isround(k):
    #         ans.append(str(k))
    #         break
    #     else:
    #         rem = (k % 10**(zeros))
    #         ans.append(str(rem))
    #         # k = k // 10
    #         k -= rem
    #         zeros += 1
    print(len(ans))
    print(' '.join(ans))