#include <bits/stdc++.h>
using namespace std;
int h[1005];
int main() {
  int n, k, pos = 1, m = 0, a, count = 0, b = 0;
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &h[i]);
  }
  for (int i = 1; i <= n; i++) {
    a = h[i];
    for (int j = 1; j <= n; j++) {
      b = a + (j - i) * k;
      if (b <= 0) break;
      if (b == h[j]) count++;
    }
    if (count > m) {
      m = count;
      pos = i;
    }
    count = 0;
  }
  printf("%d\n", n - m);
  if (n != m) {
    a = h[pos] - (pos - 1) * k;
    for (int i = 1; i <= n; i++) {
      b = h[i] - a - (i - 1) * k;
      if (b > 0)
        printf("- %d %d\n", i, b);
      else if (b < 0)
        printf("+ %d %d\n", i, -b);
    }
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
int h[1005];
int main() {
  int n, k, pos = 1, m = 0, a, count = 0, b = 0;
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &h[i]);
  }
  for (int i = 1; i <= n; i++) {
    a = h[i];
    for (int j = 1; j <= n; j++) {
      b = a + (j - i) * k;
      if (b <= 0) break;
      if (b == h[j]) count++;
    }
    if (count > m) {
      m = count;
      pos = i;
    }
    count = 0;
  }
  printf("%d\n", n - m);
  if (n != m) {
    a = h[pos] - (pos - 1) * k;
    for (int i = 1; i <= n; i++) {
      b = h[i] - a - (i - 1) * k;
      if (b > 0)
        printf("- %d %d\n", i, b);
      else if (b < 0)
        printf("+ %d %d\n", i, -b);
    }
  }
  return 0;
}

```