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:
N=int(input())
for i in range(N):
    a=input()
    b=int(a)
    count=0
    if b<10:
        print(1)
        print(int(b))
    elif b>=10 and b<100:
        c=b%10
        d=(b//10)*10
        if c!=0:
            count+=1
        if d!=0:
            count+=1
        print(count)
        if c!=0:
            print(int(c),end=' ')
        if d!=0:
            print(int(d))
    elif b>=100 and b<1000:
        d=b%10
        c=(b%100)-d
        e=(b//100)*100
        if c!=0:
            count+=1
        if d!=0:
            count+=1
        if e!=0:
            count+=1
        print(count)
        if c!=0:
            print(int(c),end=' ')
        if d!=0:
            print(int(d),end=' ')
        if e!=0:
            print(int(e))
        
    elif b>=1000 and b<10000:
        d=b%10
        c=(b%100)-d
        f=(b%1000)-c-d
        e=(b//1000)*1000
        if c!=0:
            count+=1
        if d!=0:
            count+=1
        if e!=0:
            count+=1
        if f!=0:
            count+=1
        print(count)
        if c!=0:
            print(int(c),end=' ')
        if d!=0:
            print(int(d),end=' ')
        if f!=0:
            print(int(f),end=' ')
        if e!=0:
            print(int(e))
        
    elif b==10000:
        print(1)
        print(b)