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;
const int N = 1001;
int tree[N], tmp[N];
int max_height, cur_heaght, num, max_num;
int n, k;
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; ++i) cin >> tree[i];
  for (cur_heaght = max_height = 1; cur_heaght < N; cur_heaght++) {
    num = 0;
    tmp[0] = cur_heaght;
    if (tree[0] == tmp[0]) num++;
    for (int i = 1; i < n; i++) {
      tmp[i] = tmp[i - 1] + k;
      if (tree[i] == tmp[i]) num++;
    }
    if (num > max_num) {
      max_height = cur_heaght;
      max_num = num;
    }
  }
  cout << n - max_num << endl;
  if (n - max_num == 0) return 0;
  tmp[0] = max_height;
  if (tmp[0] - tree[0] > 0)
    cout << "+ " << 1 << ' ' << tmp[0] - tree[0] << endl;
  else if (tmp[0] - tree[0] < 0)
    cout << "- " << 1 << ' ' << tree[0] - tmp[0] << endl;
  for (int i = 1; i < n; ++i) {
    tmp[i] = tmp[i - 1] + k;
    if (tmp[i] - tree[i] > 0)
      cout << "+ " << i + 1 << ' ' << tmp[i] - tree[i] << endl;
    else if (tmp[i] - tree[i] < 0)
      cout << "- " << i + 1 << ' ' << tree[i] - tmp[i] << endl;
  }
  return 0;
}
