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 t;
string q;
stack<pair<int, int> > s;
int main() {
  cin >> t;
  int i, j;
  while (t > 0) {
    cin >> q;
    int tmp = 0;
    int n = q.length();
    for (i = 0; i < n; ++i) {
      if (q[i] == '0') continue;
      s.push(make_pair((int)q[i] - 48, n - 1 - i));
    }
    cout << s.size() << '\n';
    while (!s.empty()) {
      cout << s.top().first * pow(10, s.top().second) << ' ';
      s.pop();
    }
    cout << '\n';
    --t;
  }
  return 0;
}