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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

import java.util.*;
import javafx.util.Pair;

public class Main
{

    public static void main(String args[])
    {
        FastScanner input = new FastScanner();

      int n = input.nextInt();
      int k = input.nextInt();
      int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = input.nextInt();
        }
        
        int anscount=Integer.MAX_VALUE;
       StringBuilder result = new StringBuilder();
        
        for (int j = 1; j <=1000; j++) {
            int sum = 0;
            int count=0;
             StringBuilder ans = new StringBuilder();
           
           
            for (int i = 0; i < n; i++) {
            
             if(a[i]<(j+(i*k)))
            {
              count++;
                ans.append("+ "+(i+1)+" "+Math.abs(a[i]-(j+(i*k)))+"\n");
            }
             else if(a[i]>(j+(i*k)))
            {
                count++;
                                ans.append("- "+(i+1)+" "+Math.abs(a[i]-(j+(i*k)))+"\n");

            }
            
             
        }
            if(anscount>count)
            {
                anscount = count;
                result = ans;
                
            }
        }
        
        System.out.println(anscount);
        System.out.println(result);
        
    }

    static class FastScanner
    {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next()
        {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {

            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine() throws IOException
        {
            return br.readLine();
        }
    }

}
