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, n, fst, scnd, trd, cnt, last;
  cin >> t;
  while (t--) {
    cnt = 1;
    cin >> n;
    if (n < 10) {
      cout << "1" << endl;
      cout << n << endl;
    }
    if (n < 100 && n >= 10) {
      trd = (n / 10) * 10;
      last = n - trd;
      cnt++;
      if (last == 0) cnt--;
      cout << cnt << endl;
      if (last == 0) {
        cout << trd << endl;
      } else {
        cout << trd << " ";
        if (last != 0) cout << last << endl;
      }
    }
    if (n < 1000 && n >= 100) {
      scnd = (n / 100) * 100;
      n = n - scnd;
      cnt++;
      if (n < 100) {
        trd = (n / 10) * 10;
        last = n - trd;
        cnt++;
      }
      if (trd == 0) cnt--;
      if (last == 0) cnt--;
      cout << cnt << endl;
      if (trd == 0 && last == 0) {
        cout << scnd << endl;
      } else if (last == 0) {
        cout << scnd << " " << trd << endl;
      } else if (trd == 0) {
        cout << scnd << " " << last << endl;
      } else {
        cout << scnd << " ";
        if (trd != 0) {
          cout << trd << " ";
        }
        if (last != 0) {
          cout << last << endl;
        }
      }
    }
    if (n == 10000) {
      cout << "1" << endl;
      cout << n << endl;
    }
    if (n < 10000 && n >= 1000) {
      fst = (n / 1000) * 1000;
      n = n - fst;
      cnt++;
      if (n < 1000) {
        scnd = (n / 100) * 100;
        n = n - scnd;
        cnt++;
        if (n < 100) {
          trd = (n / 10) * 10;
          last = n - trd;
          cnt++;
        }
      }
      if (scnd == 0) cnt--;
      if (trd == 0) cnt--;
      if (last == 0) cnt--;
      cout << cnt << endl;
      if (scnd == 0 && trd == 0 && last == 0) {
        cout << fst << endl;
      } else if (trd == 0 && last == 0) {
        cout << fst << " " << scnd << endl;
      } else if (scnd == 0 && last == 0) {
        cout << fst << " " << trd << endl;
      } else if (last == 0) {
        cout << fst << " " << scnd << " " << trd << endl;
      } else {
        cout << fst << " ";
        if (scnd != 0) cout << scnd << " ";
        if (trd != 0) {
          cout << trd << " ";
        }
        if (last != 0) {
          cout << last << endl;
        }
      }
    }
  }
  return 0;
}