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 Problem236B {
    public static void main(String[] args) {
        new Problem236B(new Scanner(System.in)).solve();
    }

    private Scanner in;

    public Problem236B(Scanner in) {
        this.in = in;
    }

    public void solve() {
        int n = in.nextInt(), k = in.nextInt();
        int[] ts = new int[n];
        for (int i = 0; i < n; i++) {
            ts[i] = in.nextInt();
        }

        int nInc = 0;
        int minMod = Integer.MAX_VALUE;
        int start = 0;
        int i;
        for (i = 1; nInc < n; i++) {
            nInc = 0;
            int mod = 0;
            for (int j = 0; j < n; j++) {
                if (ts[j] < i + j*k) {
                    nInc++;
                }
                if (ts[j] != i + j*k) {
                    mod++;
                }
            }
            if (mod < minMod) {
                minMod = mod;
                start = i;
            }
        }

        System.out.println(minMod);
        for (i = 0; i < n; i++) {
            if (ts[i] > start + i*k) {
                System.out.println("- " + (i + 1) + " " + (ts[i] - start - i*k));
            } else if (ts[i] < start + i*k) {
                System.out.println("+ " + (i + 1) + " " + (start + i*k - ts[i]));
            }
        }
    }
}