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.HashMap;
import java.util.Iterator;

public class TreeHeights {

    public static void main(String[] args)  throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String input = br.readLine();
        String[] tokens = input.split(" ");
        int[] data = new int[tokens.length];
        for (int i=0; i<tokens.length; i++){
            data[i] = Integer.parseInt(tokens[i]);
        }
        input = br.readLine();
        tokens = input.split(" ");
        
        HashMap<Integer,Integer> ptr = new HashMap<Integer,Integer>();
        
        int max = -1;
        int[] heights = new int[data[0]];
        for(int i=0; i<tokens.length; i++){
            heights[i] = Integer.parseInt(tokens[i]);
        //  if(i>0 && heights[i]-heights[i-1]==data[1]){
                int a = heights[i]-((i)*data[1]);
                /*if(a>0 && ptr.containsKey(a)){
                    if(i>1 && heights[i-1]-heights[i-2]==data[1])
                        ptr.put(a, ptr.get(a)+1);
                    else
                        ptr.put(a, ptr.get(a)+2);
                    if(ptr.get(max)<ptr.get(a)){
                        max=a;
                    }
                }
                else if(a>0){
                    ptr.put(a, 2);
                    if(max==-1){
                        max=a;
                    }
                }*/
                
                if(a>0 && ptr.containsKey(a)){
                    ptr.put(a, ptr.get(a)+1);
                }
                else if(a>0){
                    ptr.put(a, 1);
                }
                if(a>0 && (max==-1 || ptr.get(max)<ptr.get(a))){
                    max=a;
                }
        //  }           
        }
        if(max!=-1){
            System.out.println(heights.length-ptr.get(max));            
        }
        else{
            System.out.println(heights.length-1);
            max=heights[0];
        }
        for(int i=0; i<heights.length; i++){
            int newHeight=(max+(i*data[1]));
            if(heights[i]==newHeight)
                continue;
            else if(heights[i]>newHeight){
                System.out.println("- "+(i+1)+" "+(heights[i]-newHeight));
            }
            else{
                System.out.println("+ "+(i+1)+" "+(newHeight-heights[i]));
            }
        }       
    }

}
