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.math.BigInteger;
import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

public class B {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        int[] xs = new int[n];
        for (int i = 0; i < n; i++) {
            xs[i] = in.nextInt();
        }
        int[] same = new int[n];
        for (int i = 0; i < n; i++) {
            int count = 0;
            for (int j = i; j < n; j++) {
                if (xs[i] == xs[j] - (j - i) * k)
                    count++;
            }
            same[i] = -10000*count - i;
        }
        Arrays.sort(same);
        for (int s : same) {
            int count = (-s) / 10000;
            int index = (-s) % 10000;
            int minValue = xs[index] - (index) * k;
            if (minValue > 0) {
                System.out.println(n - count);
                for (int i = 0; i < n; i++) {
                    int newValue = xs[index] - (index - i)*k;
                    if (newValue == xs[i])
                        continue;
                    int diff = newValue - xs[i];
                    if (diff < 0) {
                        System.out.println("- " + (i + 1) + " " + (-diff));
                    } else
                        System.out.println("+ " + (1 +i) + " " + (diff));
                }
                return;
            }
        }
        in.close();
    }
}
