#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1010;
int a[MAXN], n, k;
int check(int x, bool print = false) {
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (abs(a[i] - i * k - x) > 0) ans++;
    if (print) {
      if (a[i] == i * k + x) continue;
      if (a[i] < i * k + x)
        cout << '+' << ' ' << i + 1 << ' ' << abs(a[i] - i * k - x) << '\n';
      else
        cout << '-' << ' ' << i + 1 << ' ' << abs(a[i] - i * k - x) << '\n';
    }
  }
  return ans;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  int ans = 1e+6, l = 0;
  for (int i = 1; i < MAXN; i++) {
    if (check(i) < ans) l = i;
    ans = min(ans, check(i));
  }
  cout << ans << endl;
  check(l, 1);
}

### Prompt

Please formulate 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 = 1010;
int a[MAXN], n, k;
int check(int x, bool print = false) {
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (abs(a[i] - i * k - x) > 0) ans++;
    if (print) {
      if (a[i] == i * k + x) continue;
      if (a[i] < i * k + x)
        cout << '+' << ' ' << i + 1 << ' ' << abs(a[i] - i * k - x) << '\n';
      else
        cout << '-' << ' ' << i + 1 << ' ' << abs(a[i] - i * k - x) << '\n';
    }
  }
  return ans;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  int ans = 1e+6, l = 0;
  for (int i = 1; i < MAXN; i++) {
    if (check(i) < ans) l = i;
    ans = min(ans, check(i));
  }
  cout << ans << endl;
  check(l, 1);
}

```