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.util.*;
import java.io.*;
import java.math.*;
import java.awt.*;
public class Trees
{
    static final int INF = Integer.MAX_VALUE;
    static final int NINF = Integer.MIN_VALUE;
   
    public static void main(String[]args)throws IOException
    {
        Input in = new Input();
        int n = in.nextInt();
        int k = in.nextInt();
        if(n == 0)
        {
            System.out.println(0);
            exit();
        }

        int [] arr = new int[n];
        int [] res = new int[n];

        for(int i = 0; i < n; i++)
            arr[i] = in.nextInt();

        int min = INF;
        int minind = 0;
  outer:for(int i = 0; i < n; i++)
        {
            int cost = 0;
            int constant = arr[i];
            for(int j = i; j-1 >= 0; j--)
            {
                if(arr[j-1] != constant-k)
                    cost++; 

                constant -= k;
                if(constant <= 0)
                    continue outer;
            }
            constant = arr[i];
            for(int j = i; j+1 < n; j++)
            {
                if(arr[j+1] != constant+k)
                    cost++;
                constant += k;
            }

            if(cost < min)
            {
                min = cost;
                minind = i;
            }
        }
        res[minind] = arr[minind];
        for(int i = minind; i-1 >= 0; i--)
            res[i-1] = res[i]-k;
        for(int i = minind; i+1 < n; i++)
            res[i+1] = res[i]+k;
        System.out.println(min);
        for(int i = 0; i < n; i++)
        {
            if(arr[i] == res[i])
                continue;
            if(arr[i] > res[i])
                System.out.println("- "+(i+1)+" "+(arr[i]-res[i]));
            else
                System.out.println("+ "+(i+1)+" "+(res[i]-arr[i]));
        }
    }

    public static void exit()
    {
        System.exit(0);
    }
}

class Input
{
    BufferedReader br;
    StringTokenizer st;

    public Input()
    {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

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

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

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

    public float nextFloat()throws IOException
    {
        return Float.parseFloat(next());
    }

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

    public String next()throws IOException
    {
        if(st == null || !st.hasMoreTokens())
          st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}
