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;
const int N = 200050;
int main() {
  ios_base::sync_with_stdio(false);
  cout.tie(0);
  cin.tie(NULL);
  int t, n, ans, i, j;
  unordered_set<string> gay;
  string s, duh;
  cin >> t;
  while (t--) {
    ans = 0;
    gay.clear();
    cin >> s;
    n = s.size();
    for (i = 0; i < n; ++i) {
      if (s[i] != '0') {
        duh = s[i];
        ++ans;
        for (j = 1; j < n - i; ++j) duh += '0';
        gay.insert(duh);
      }
    }
    cout << ans << endl;
    for (auto x : gay) cout << x << " ";
    cout << endl;
  }
  return 0;
}