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=input()
list_num=[]
list_of_num_num=[]
list_of_fal_and_tru=[]
list_of_num_3=[]
cnt=0
for i in range(int(t)):
    list_num.append(input())
    if int(list_num[i]) in range(1,11):
        list_of_fal_and_tru.append(True)
    else:
        for j in range(1,len(list_num[i])):
            if int(list_num[i][j])!=0:
                list_of_fal_and_tru.append(False)
                break
            elif j==len(list_num[i])-1:
                list_of_fal_and_tru.append(True)
                break
            else:
                continue
for i in range(len(list_num)):
    cnt=0
    if list_of_fal_and_tru[i]==True:
        list_of_num_num.append('1')
        list_of_num_3.append(list_num[i])
    elif list_of_fal_and_tru[i]==False:
        for j in range(1,len(list_num[i])):
            if list_num[i][j]=="0":
                cnt+=1
        list_of_num_num.append(len(list_num[i]) - cnt)
        for k in range(len(list_num[i])):
            if list_num[i][k]!="0":
                list_of_num_3.append((list_num[i][k]+("0"*(len(list_num[i])-k-1))))
cnt_1=int(list_of_num_num[0])
for i in range(int(t)):
    print(str(list_of_num_num[i]))
    for j in range(int(list_of_num_num[i])):
        if i==0:
            print(list_of_num_3[j],end=" ")
        else:
            cnt_1+=1
            print(list_of_num_3[cnt_1-1],end=" ")
        if j==int(list_of_num_num[i])-1:
            print(end="\n")