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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.ArrayList;

public class Temp {

	static PrintWriter pw;

	public static void Solve(int n, int k, int[] h) {
		int[] ap = new int[n];
		int max = 0, m=2000;
		ArrayList<String> f = new ArrayList<String>();
		for (int i = 0; i < h.length; i++)
			if (h[i] > max)
				max = h[i];

		ArrayList<String> res = new ArrayList<String>();
		for (int s = 1; s <= max; s++) {
			ap[0] = s;
			res.clear();
			for (int i = 1; i < n; i++) {
				ap[i] = ap[0] + i * k;
			}

			for (int i = 0; i < n; i++) {
				if (h[i] > ap[i]) {
					res.add("- " + (i + 1) + " " + (h[i] - ap[i]));
				}
				if (h[i] < ap[i]) {
					res.add("+ " + (i + 1) + " " + (ap[i] - h[i]));
				}

			}
			
			if(res.size()<=m){
				f.clear();
				m=res.size();
				f.addAll(res);
			}
		}
		pw.println(m);
		for (int i = 0; i < f.size(); i++)
			pw.println(f.get(i));

	}

	public static void main(String args[]) throws IOException {
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
				System.out)));
		StreamTokenizer st = new StreamTokenizer(bf);
		st.nextToken();
		int n = (int) st.nval;
		st.nextToken();
		int k = (int) st.nval;

		int h[] = new int[n];
		for (int i = 0; i < n; i++) {
			st.nextToken();
			h[i] = (int) st.nval;
		}

		Solve(n, k, h);

		bf.close();

		pw.close();
		System.exit(0);

	}
}