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.Arrays;
import java.util.Scanner;

/**
 * Created by zlp on 14-3-17.
 */
public class Trees {

    public static void main(String[] args)
    {
        int n, k;
        int[] a, b;
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        k = sc.nextInt();

        a = new int[n];
        b = new int[n];
        for (int i = 0;i < n;i++)
        {
            a[i] = b[i] = sc.nextInt() - i * k;
        }

        Arrays.sort(b);
        int most = b[0];
        int most_num = 0;
        for (int i = 0;i < n;i++)
        {
            if (b[i] <= 0) continue;
            int most_cond = b[i];
            int num = 0;
            while (i < n)
            {
                if (b[i] == most_cond) num++;
                else break;
                i++;
            }
            i--;
            if (num > most_num) { most_num = num; most = most_cond; }
        }
        
        System.out.println(n - most_num);

        for (int i = 0;i < n;i++)
        {
            if (a[i] == most) continue;
            int diff = most - a[i];
            if (diff > 0)
            {
                System.out.println("+ " + (i + 1) + " " + diff);
            }
            else
            {
                System.out.println("- " + (i + 1) + " " + (-diff));
            }
        }
    }
}
