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())
if(t >= 1 and t <= pow(10,4)):
    while(t > 0):
        x = int(input())
        if(x >= 1 and x <= pow(10,4)):
            xstr = str(x)
            length = len((str)(x))
            xx = ""
            xxx = 0
            xprev = 0
            k = 0

            for char in xstr:
                if(char != "0"):
                    k += 1
            print(k)

            for i in range(1, length+1):
                #print("i = ",i)
                celoye = (int)(x // (10*pow(10,length)/pow(10,i)/10))
                #print("celoye", celoye)
                osta4a = int(x % (10*pow(10,length)/pow(10,i)/10))
                #print("osta4a", osta4a)
                xxx = int(celoye*(10*pow(10,length)/pow(10,i)/10)-xprev)
                xprev += xxx
                #print("x=", xxx)
                #xstr = str(xint)
                #res = ' '.join(str(xxx))
                if(xxx != 0):
                    print(xxx, end=' ')
            print()
        t -= 1