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 CPP):

Solution:
#include <bits/stdc++.h>
int main() {
  int tot;
  scanf(" %d", &tot);
  long int num[tot];
  for (int i = 0; i < tot; i++) {
    scanf(" %ld", &num[i]);
  }
  for (int x = 0; x < tot; x++) {
    if (num[x] <= 10) {
      printf("1\n");
      printf("%ld\n", num[x]);
    } else {
      int count = 1, count2 = 0, j = 0, k = 0;
      long int num2[10];
      long int num99 = num[x];
      while (num99 != 0) {
        long int num22 = (num99 % 10) * count;
        count = count * 10;
        num99 = num99 / 10;
        if (num22 != 0) {
          count2++;
          num2[j] = num22;
          j++;
        }
      }
      printf("%d\n", count2);
      while (count2 > 0) {
        printf("%ld ", num2[k]);
        k++;
        count2--;
      }
      printf("\n");
    }
  }
  return 0;
}