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(void) {
  int n, p, x;
  cin >> n;
  string k;
  queue<int> qu;
  for (int i = 0; i < n; i++) {
    cin >> k;
    p = 0;
    x = k.length();
    for (int i = 0; i < x; i++) {
      if (k[i] != '0') {
        p++;
      }
    }
    qu.push(p);
    for (int i = x - 1; i >= 0; i--) {
      if (k[i] != '0') {
        qu.push(stoi(k[i] + string(x - 1 - i, '0')));
      }
    }
  }
  while (!qu.empty()) {
    cout << qu.front() << endl;
    int i = qu.front();
    qu.pop();
    while (i != 0) {
      cout << qu.front();
      qu.pop();
      if (i > 1) {
        cout << " ";
      }
      if (i == 1) {
        cout << endl;
      }
      i--;
    }
  }
}