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.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;


public class TreesinaRow {

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(in.readLine());
        int arr[] = new int [n];
        for(int i = 0;i<n;i++){
            arr[i] = Integer.parseInt(st.nextToken());
        }
        ArrayList<String> ans = new ArrayList<String>();
        ArrayList<String> tmp = new ArrayList<String>();
        int res = 1000000;
        for(int i = 1;i<=1000;i++){
            int temp = 0;
            tmp.clear();
            for(int j = 0;j<n;j++){
                if(arr[j]!=(i+j*k)){
                    temp++;
                    if(arr[j]<(i+j*k)){
                        tmp.add("+ "+(j+1)+" "+((i+j*k)-arr[j]));
                    }
                    else{
                        tmp.add("- "+(j+1)+" "+(arr[j]-(i+j*k)));
                    }
                }
            }
            if(temp<res){
                res = temp;
                ans.clear();
                ans.addAll(tmp);
            }
        }
        out.println(res);
        for(int  i = 0;i<ans.size();i++)
            out.println(ans.get(i));
        in.close();
        out.close();
    }

}
