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

    for i in range(len(n)):
        t = int(n[i])
        if t != 0:
            ans.append((t * 10**(len(n)-1-i)))
    print(len(ans))
    for i in range(len(ans)):
        print(ans[i], end=" ")
    print()
    # nt = n[1:]
    # r = True
    # for i in nt:
    #     if i != "0":
    #         r = False
    # if r:
    #     print(1)
    #     print(n)
    # else:
    #     nnow = n[:-1]
    #     l.append(n[-1])
    #     ii = 1
    #     tt = len(nnow)
    #     for i in range(tt):
    #         if nnow[-1] == "0":
    #             nnow = nnow[:-1]
    #         else:
    #             tmp = nnow[-1] + (ii*"0")
    #             l.append(tmp)
    #         ii += 1
    #     print(len(l))
    #     print(l)