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:
import math
import atexit
import io
import sys
 
# input = sys.stdin.readline
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER
 
@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
 
def array_to_string(a):
    s = ""
    for i in a:
        s += str(i) + " "
    return s[0:len(s)-1]

def gcd(a,b): 
    if a == 0: 
        return b 
    return gcd(b % a, a) 
  
def lcm(a,b): 
    return (a*b) / gcd(a,b) 
 
t = int(input())
while t>0:
    t = t-1
    n = int(input())
    s = str(n)
    k = 0
    a = []
    for i in range(len(s)):
        if int(s[i])!=0:
            a.append((s[i],len(s)-1-i))
            k += 1
    print(k)
    # print("a",a)
    for i in range(len(a)):
        # print(a[i])
        print(a[i][0]+str(a[i][1]*'0'),end= " ")
    print()