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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class TreesInARow {

    /**
     * @param args
     * @throws IOException
     */
    public static void main(String[] args) throws IOException {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(bf.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        int a[] = new int[n];
        st = new StringTokenizer(bf.readLine());
        for (int i = 0; i < n; i++)
            a[i] = Integer.parseInt(st.nextToken());
        int lol = -1;
        int max = Integer.MAX_VALUE;
        for (int f = 1; f <= 1000; f++) {
            int count = 0;
            for (int i = 0; i < n; i++) {
                if (a[i] != f + i * k)
                    count++;
            }
            if (count < max) {
                max = count;
                lol = f;
            }
        }
        // System.out.println(lol);
        
        int size = max;
        System.out.println(size);
        for (int i = 0; i < n; i++) {
            if (a[i] > lol + i * k) {
                System.out.println("- " + (i + 1) + " "
                        + (a[i] - (lol + i * k)));
            } else if (a[i] < lol + i * k) {
                System.out.println("+ " + (i + 1) + " "
                        + (-a[i] + (lol + i * k)));
            }
        }

    }

}
