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 i in range(int(input())):
    n=int(input())
    if n>1000:
        t=n%1000
        if t==0:
            print(1)
            print(n)
        else:
            s=t%100
            if s==0:
                print("2")
                print(n-t,t)
            else:
                k=s%10
                if k==0:
                    if t-s==0:
                        print("2")
                        print(n-t,s)
                    else:
                        print("3")
                        print(n-t,t-s,s)
                else:
                    if t-s==0 and s-k==0:
                        print("2")
                        print(n-t,k)
                    elif t-s==0:
                        print("3")
                        print(n-t,s-k,k)
                    elif s-k==0:
                        print("3")
                        print(n-t,t-s,k)
                    else:
                        print("4")
                        print(n-t,t-s,s-k,k)
    
    elif n>100 and n<1000:
        t=n%100
        if t==0:
            print("1")
            print(n-t)
        else:
            s=n%10
            if s==0:
                print("2")
                print(n-t,t)
            else:
                if t-s==0:
                    print("2")
                    print(n-t,s)
                else:
                    print("3")
                    print(n-t,t-s,s)
    elif n>10 and n<100:
        t=n%10
        if t==0:
            print("1")
            print(n-t)
        else:
            print("2")
            print(n-t,t)
    else:
        print("1")
        print(n)