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 MX = 200005;
int N;
int rec[2000];
int arr[2000];
vector<pair<char, pair<int, int> > > v;
int main() {
  int inc;
  cin >> N >> inc;
  for (int i = 0; i < N; i++) cin >> arr[i];
  int MN = +1e9, ELEM_MN = 0;
  for (int ans = 1; ans <= 1000; ans++) {
    int cnt = 0;
    int poten = ans;
    for (int i = 0; i < N; i++) {
      if (arr[i] != poten) cnt++;
      poten += inc;
    }
    if (cnt < MN) MN = cnt, ELEM_MN = ans;
  }
  for (int i = 0; i < N; i++) {
    if (arr[i] == ELEM_MN) {
      ELEM_MN += inc;
      continue;
    }
    if (arr[i] > ELEM_MN)
      v.push_back(make_pair('-', make_pair(i + 1, arr[i] - ELEM_MN)));
    else
      v.push_back(make_pair('+', make_pair(i + 1, ELEM_MN - arr[i])));
    ELEM_MN += inc;
  }
  cout << v.size() << "\n";
  for (int i = 0; i < v.size(); i++)
    cout << v[i].first << " " << v[i].second.first << " " << v[i].second.second
         << "\n";
  return 0;
}
