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>
using namespace std;
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n;
    scanf("%d", &n);
    if (n < 10) {
      cout << 1 << '\n' << n << '\n';
    } else {
      vector<string> vec;
      int count = 0;
      string s = to_string(n);
      for (int i = 0; i <= s.size() - 1; i++) {
        if (s[i] != '0') {
          count++;
          char newc = s[i];
          stringstream sso;
          sso << newc;
          string news;
          sso >> news;
          for (int j = i + 1; j < s.size(); j++) news += '0';
          vec.push_back(news);
        }
      }
      cout << count << '\n';
      for (int i = 0; i <= vec.size() - 1; i++) cout << vec[i] << " ";
      cout << '\n';
    }
  }
}