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:
t = int(input())
for i in range(t):
    n = int(input())
    a = [0, 0, 0, 0, 0]
    j = 0
    c = 0
    num = n
    while n != 0 and j < len(a):
        a[len(a) - j - 1] = n % 10
        j += 1
        n //= 10
    jed = 0
    dz = 0
    setek = 0
    tys = 0
    dztys = 0
    if a[len(a) - 1] != 0:
        jed = a[len(a) - 1]
    if a[len(a) - 2] != 0:
        dz = a[len(a) - 2]
        dz *= 10
    if a[len(a) - 3] != 0:
        setek = a[len(a) - 3]
        setek *= 100
    if a[len(a) - 4] != 0:
        tys = a[len(a) - 4]
        tys *= 1000
    if a[len(a) - 5] != 0:
        dztys = a[len(a) - 5]
        dztys *= 10000
    for x in range(len(a)):
        if a[x] != 0:
            c += 1
    print(c)
    if 1000 <= num <= 10000:
        if dztys != 0:
            print(dztys, end=" ")
        if tys != 0:
            print(tys, end=" ")
        if setek != 0:
            print(setek, end=" ")
        if dz != 0:
            print(dz, end=" ")
        if jed != 0:
            print(jed, end=" ")
        print()
    elif 100 <= num < 1000:
        if setek != 0:
            print(setek, end=" ")
        if dz != 0:
            print(dz, end=" ")
        if jed != 0:
            print(jed, end=" ")
        print()
    elif 10 <= num < 100:
        if dz != 0:
            print(dz, end=" ")
        if jed != 0:
            print(jed, end=" ")
        print()
    else:
        print(jed)