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.Scanner;
import java.util.ArrayList;

public class Olimp {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);

        int n = scan.nextInt(), k = scan.nextInt();
        ArrayList<Integer> trees = new ArrayList(n);

        for (int i = 0; i < n; i++) {
            trees.add(scan.nextInt());
        }

        int changes, minChanges = n, minChangesIndex = 0;

        for (int i = 0; i < n; i++) {
            changes = n;
            int y0 = trees.get(i) - k * i;

            if (y0 > 0) {
                for (int j = 0; j < n; j++) {
                    if (trees.get(j) == k * j + y0) {
                        changes--;
                    }
                }
                if (minChanges > changes) {
                    minChanges = changes;
                    minChangesIndex = i;
                }
            }

        }
        System.out.println(minChanges);

        int y0 = trees.get(minChangesIndex) - k * minChangesIndex;
        for (int j = 0; j < n; j++) {
            int delta = trees.get(j) - (k * j + y0);

            if (delta < 0) {
                System.out.println("+ " + (j + 1) + " " + Math.abs(delta));
            }
            if (delta > 0) {
                System.out.println("- " + (j + 1) + " " + Math.abs(delta));
            }
        }

    }

}