Problem: Consider the following problem: given an array a containing n integers (indexed from 0 to n-1), find max_{0 ≤ l ≤ r ≤ n-1} ∑_{l ≤ i ≤ r} (r-l+1) ⋅ a_i. In this problem, 1 ≤ n ≤ 2 000 and |a_i| ≤ 10^6.

In an attempt to solve the problem described, Alice quickly came up with a blazing-fast greedy algorithm and coded it. Her implementation in pseudocode is as follows:
    
    
      
    function find_answer(n, a)  
        # Assumes n is an integer between 1 and 2000, inclusive  
        # Assumes a is a list containing n integers: a[0], a[1], ..., a[n-1]  
        res = 0  
        cur = 0  
        k = -1  
        for i = 0 to i = n-1  
            cur = cur + a[i]  
            if cur < 0  
                cur = 0  
                k = i  
            res = max(res, (i-k)*cur)  
        return res  
      
    

Also, as you can see, Alice's idea is not entirely correct. For example, suppose n = 4 and a = [6, -8, 7, -42]. Then, find_answer(n, a) would return 7, but the correct answer is 3 ⋅ (6-8+7) = 15.

You told Alice that her solution is incorrect, but she did not believe what you said.

Given an integer k, you are to find any sequence a of n integers such that the correct answer and the answer produced by Alice's algorithm differ by exactly k. Note that although the choice of n and the content of the sequence is yours, you must still follow the constraints earlier given: that 1 ≤ n ≤ 2 000 and that the absolute value of each element does not exceed 10^6. If there is no such sequence, determine so.

Input

The first and only line contains one integer k (1 ≤ k ≤ 10^9).

Output

If there is no sought sequence, print "-1".

Otherwise, in the first line, print one integer n (1 ≤ n ≤ 2 000), denoting the number of elements in the sequence.

Then, in the second line, print n space-separated integers: a_0, a_1, …, a_{n-1} (|a_i| ≤ 10^6).

Examples

Input


8


Output


4
6 -8 7 -42


Input


612


Output


7
30 -12 -99 123 -2 245 -300

Note

The first sample corresponds to the example given in the problem statement.

In the second sample, one answer is n = 7 with a = [30, -12, -99, 123, -2, 245, -300], in which case find_answer(n, a) returns 1098, while the correct answer is 1710.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
std::default_random_engine generator;
int rnd(int l, int r) {
  std::uniform_int_distribution<int> distribution(l, r);
  return distribution(generator);
}
template <class T>
inline T gcd(T a, T b) {
  if (a < 0) return gcd(-a, b);
  if (b < 0) return gcd(a, -b);
  return (b == 0) ? a : gcd(b, a % b);
}
const long long mod = 1e9 + 7;
const double pi = 3.141592653589793238462643383279;
int find_answer(int n, vector<int>& a) {
  int res = 0;
  int cur = 0;
  int k = -1;
  for (int i = 0; i <= n - 1; ++i) {
    cur = cur + a[i];
    if (cur < 0) {
      cur = 0;
      k = i;
    }
    res = max(res, (i - k) * cur);
  }
  return res;
}
long long my_answer(int n, vector<int>& a) {
  long long res = 0;
  for (int i = 0; i <= n - 1; ++i) {
    if (a[i] > a[n - 1]) return -1;
    res += a[i];
  }
  return res * n;
}
int main() {
  ios_base::sync_with_stdio(false);
  cout.precision(12);
  cout << fixed;
  cin.tie(0);
  int k;
  cin >> k;
  vector<int> a;
  if (k < 10) {
    cout << "2\n-1 " << k + 2 << endl;
    return 0;
  }
  for (int n = 4; n < 2000; n += 2) {
    int xpy = (k + n - 1) / (n - 1);
    int y = k - (n - 1) * xpy;
    if (xpy - y < 1e6) {
      a.assign(n, -1);
      a[n - 1] = xpy - y;
      a[n - 2] = y;
      for (int i = 0; i < n - 2; i += 2) a[i] = 1;
      cout << n << endl;
      for (int i = 0; i < n; ++i) cout << a[i] << ' ';
      return 0;
    }
  }
  return 0;
}