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;
vector<int> readVI(int n) {
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  return a;
}
vector<vector<int> > readVVI(int n, int m) {
  vector<vector<int> > a(n, vector<int>(m));
  for (int i = 0; i < n; i++) a[i] = readVI(m);
  return a;
}
vector<long long> readVLL(long long n) {
  vector<long long> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  return a;
}
vector<vector<long long> > readVVLL(long long n, long long m) {
  vector<vector<long long> > a(n, vector<long long>(m));
  for (int i = 0; i < n; i++) a[i] = readVLL(m);
  return a;
}
const int MOD = int(1e9) + 7;
const int INF = INT_MAX;
const long long INFF = INT64_MAX;
const double EPS = 1e-9;
const double PI = acos(-1.0);
const int moveX[] = {-1, 0, 1, 0};
const int moveY[] = {0, 1, 0, -1};
void go() {
  int n, cur = 1;
  cin >> n;
  vector<int> ans;
  while (n > 0) {
    int curNum = n % 10;
    curNum *= cur;
    cur *= 10;
    n /= 10;
    if (curNum != 0) ans.push_back(curNum);
  }
  cout << ans.size() << '\n';
  for (auto el : ans) cout << el << ' ';
  cout << '\n';
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int T;
  cin >> T;
  while (T--) go();
  return 0;
}