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:
q=int(input())
for _ in range(q):
    t=input()
    if(len(t)==1):
        print(1)
        print(t)
    else:
        temp=0
        for i in range(1,len(t)):
            if(t[i]=='0'):
                pass
            else:
                temp=1
                break
        if(temp==0):
            print(1)
            print(t)
        else:
            num=0
            l=len(t)-1
            ans=[]
            c=0
            #print("len",l)
            for i in t:
                num=int(i)
                #print("num",num)
                if(num!=0):
                    num*=10**l
                    c+=1
                    ans.append(num)
                l-=1
            print(c)
            for i in ans:
                print(i,end=" ")
            print()