#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
vector<int> ve;
int main() {
  int ch, n, k, bestan = maxn, beg = -1, curan;
  cin >> n >> k;
  for (int i = 0; i < n; i++) {
    cin >> ch;
    ve.push_back(ch);
  }
  for (int i = 0; i < n; i++) {
    if (ve[i] > k * i) {
      curan = 0;
      for (int j = 0; j < n; j++) {
        if (ve[j] != ve[i] + (j - i) * k) {
          curan++;
        }
      }
      if (curan < bestan) {
        bestan = curan;
        beg = i;
      }
    }
  }
  cout << bestan << endl;
  for (int i = 0; i < n; i++) {
    if (ve[i] != ve[beg] + (i - beg) * k) {
      if (ve[i] < ve[beg] + (i - beg) * k) {
        cout << "+ " << i + 1 << ' ' << ve[beg] + (i - beg) * k - ve[i] << endl;
      } else {
        cout << "- " << i + 1 << ' ' << -(ve[beg] + (i - beg) * k - ve[i])
             << endl;
      }
    }
  }
  return 0;
}

### Prompt

Your task is to create a CPP solution to the following problem:

The Queen of England has n trees growing in a row in her garden. At that, the i-th (1 ≤ i ≤ n) tree from the left has height ai meters. Today the Queen decided to update the scenery of her garden. She wants the trees' heights to meet the condition: for all i (1 ≤ i < n), ai + 1 - ai = k, where k is the number the Queen chose.

Unfortunately, the royal gardener is not a machine and he cannot fulfill the desire of the Queen instantly! In one minute, the gardener can either decrease the height of a tree to any positive integer height or increase the height of a tree to any positive integer height. How should the royal gardener act to fulfill a whim of Her Majesty in the minimum number of minutes?

Input

The first line contains two space-separated integers: n, k (1 ≤ n, k ≤ 1000). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 1000) — the heights of the trees in the row. 

Output

In the first line print a single integer p — the minimum number of minutes the gardener needs. In the next p lines print the description of his actions. 

If the gardener needs to increase the height of the j-th (1 ≤ j ≤ n) tree from the left by x (x ≥ 1) meters, then print in the corresponding line "+ j x". If the gardener needs to decrease the height of the j-th (1 ≤ j ≤ n) tree from the left by x (x ≥ 1) meters, print on the corresponding line "- j x".

If there are multiple ways to make a row of trees beautiful in the minimum number of actions, you are allowed to print any of them.

Examples

Input

4 1
1 2 1 5


Output

2
+ 3 2
- 4 1


Input

4 1
1 2 3 4


Output

0

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
vector<int> ve;
int main() {
  int ch, n, k, bestan = maxn, beg = -1, curan;
  cin >> n >> k;
  for (int i = 0; i < n; i++) {
    cin >> ch;
    ve.push_back(ch);
  }
  for (int i = 0; i < n; i++) {
    if (ve[i] > k * i) {
      curan = 0;
      for (int j = 0; j < n; j++) {
        if (ve[j] != ve[i] + (j - i) * k) {
          curan++;
        }
      }
      if (curan < bestan) {
        bestan = curan;
        beg = i;
      }
    }
  }
  cout << bestan << endl;
  for (int i = 0; i < n; i++) {
    if (ve[i] != ve[beg] + (i - beg) * k) {
      if (ve[i] < ve[beg] + (i - beg) * k) {
        cout << "+ " << i + 1 << ' ' << ve[beg] + (i - beg) * k - ve[i] << endl;
      } else {
        cout << "- " << i + 1 << ' ' << -(ve[beg] + (i - beg) * k - ve[i])
             << endl;
      }
    }
  }
  return 0;
}

```