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
import java.io.*;
import java.util.*;
  
public class Main implements Runnable {
  final boolean isFileIO = false; 
  BufferedReader in;
  PrintWriter out;
  StringTokenizer st = new StringTokenizer("");
  String delim = " ";

  public static void main(String[] args) {
    new Thread(null, new Main(), "", 268435456).start(); 
  }

  public void run() {
    try {
      initIO();
      solve();
      out.close();
    } catch(Exception e) {
      e.printStackTrace(System.err);
      System.exit(-1);
    }
  }

  public void initIO() throws IOException {
    if(!isFileIO) {
      in = new BufferedReader(new InputStreamReader(System.in));
      out = new PrintWriter(System.out);
    } else {
      in = new BufferedReader(new FileReader("domino-covering-2.in"));
      out = new PrintWriter("domino-covering-2.out"); 
    }
  }
  
  String nextToken() throws IOException {
    if(!st.hasMoreTokens()) {
      st = new StringTokenizer(in.readLine());
    }
    return st.nextToken(delim);
  }
 
  String readLine() throws IOException {
    return in.readLine();
  }

  int nextInt() throws IOException {
   return Integer.parseInt(nextToken());
  }

  long nextLong() throws IOException {
    return Long.parseLong(nextToken());
  }

  double nextDouble() throws IOException {
    return Double.parseDouble(nextToken());
  }
  void solve() throws IOException {
    int n, k;
    n = nextInt(); k = nextInt();
    int[] a = new int[n];
    for(int i = 0;i < n; i++) {
      a[i] = nextInt();
    }
    int min = Integer.MAX_VALUE;
    int pos = 1;
    for(int i = 1; i <= 1000; i++) {
      int p = 0;
      for(int j = 0; j < n; j++) {
        if(a[j] != (i + j * k))
          p++; 
      }
      if(min > p) {
        min = Math.min(p, min);
        pos = i;
      }
    }
    out.println(min);
    for(int j = 0; j < n; j++) {
      if(a[j] < pos + j * k) {
        out.println("+ " + (j + 1) + " " + (pos + j * k - a[j]));
      }
      if(a[j] > pos + j * k) {
        out.println("- " + (j + 1) + " " + (a[j] - (pos + j * k)));
      }
    }
  }

} 
