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
#include <bits/stdc++.h>
using namespace std;
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  vector<int> heights(n);
  for (int i = 0; i < n; ++i) {
    cin >> heights[i];
  }
  int max_length = 0;
  set<int> indexes;
  for (int i = 1; i < 1001; ++i) {
    vector<int> temp_indexes;
    for (int j = 0; j < n; ++j) {
      if (heights[j] == i + j * k) {
        temp_indexes.push_back(j);
      }
    }
    if (temp_indexes.size() > max_length) {
      max_length = temp_indexes.size();
      indexes = set<int>(temp_indexes.begin(), temp_indexes.end());
    }
  }
  cout << heights.size() - indexes.size() << endl;
  int firstItem = heights[*indexes.begin()] - *indexes.begin() * k;
  for (int i = 0; i < n; ++i) {
    if (indexes.find(i) == indexes.end()) {
      if (heights[i] < firstItem + i * k) {
        cout << "+ " << i + 1 << " " << firstItem + i * k - heights[i] << endl;
      } else if (heights[i] > firstItem + i * k) {
        cout << "- " << i + 1 << " " << heights[i] - (i * k + firstItem)
             << endl;
      }
    }
  }
  return 0;
}
