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;

public class B {

    public static void main(String zargs[]) {

        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();
        int k = scanner.nextInt();

        int a[] = new int[n];

        for (int i = 0; i < n; i++)
            a[i] = scanner.nextInt();

        int mincount = 1000;
        int start = 1;

        for (int i = 1; i <= 1000; i++) {
            int curr = 0;
            for (int j = 0; j < n; j++) {
                if (a[j] != i + k * j)
                    curr++;
            }

            if (curr < mincount) {
                mincount = curr;
                start = i;
            }
        }

        System.out.println(mincount);
        for (int i = 0; i < n; i++) {
            if (a[i] != start + i * k)
                print(i + 1, a[i], start + i * k);
        }
    }

    private static void print(int i, int actual, int changed) {
        if (actual < changed)
            System.out.println("+ " + i + " " + (changed - actual));
        else
            System.out.println("- " + i + " " + (actual - changed));
    }

}
