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:
import sys,os
from collections import defaultdict, deque
from math import ceil, floor
if sys.version_info[1] >= 5:
    from math import gcd
else:
    from fractions import gcd
sys.setrecursionlimit(10**6)
write = sys.stdout.write
dbg = (lambda *something: print(*something)) if 'TERM_PROGRAM' in os.environ else lambda *x: 0
def main(given=sys.stdin.readline):
    input = lambda: given().rstrip()
    LMIIS = lambda: list(map(int,input().split()))
    II = lambda: int(input())
    MOD = 10**9+7

    N = II()
    for _ in range(N):
        n = input().rstrip()
        ans = []
        for i in range(len(n)):
            x = int(n[i])
            if x != 0:
                ans.append(x * 10**(len(n)-i-1))
        print(len(ans))
        print(*ans)
        

if __name__ == '__main__':
    main()