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.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
	public static void main(String args[]) throws NumberFormatException,
			IOException {

		Stdin in = new Stdin();
		PrintWriter out = new PrintWriter(System.out);
		int n = in.readInt();
		int k = in.readInt();
		int[] a = new int[n];
		for (int i = 0; i < a.length; i++) {
			a[i] = in.readInt();
		}
		if (n == 1) {
			out.println(0);
		} else {
			int min = 1000;
			int first = a[0];
			int current = 0;
			int temp;
			int from = 1;
			int to = 1000;
			for (int i = from; i <= to; i++) {
				temp = i;
				current = 0;
				for (int t : a) {
					if (t != temp) {
						current++;
					}
					temp += k;
				}

				if (min >= current) {
					min = current;
					first = i;
				}

			}

			temp = first;
			out.println(min);
			for (int i = 0; i < a.length; i++) {
				if (a[i] > temp)
					out.println("- " + (i + 1) + " " + (a[i] - temp));
				else if (a[i] < temp)
					out.println("+ " + (i + 1) + " " + (temp - a[i]));
				temp += k;
			}

		}

		out.flush();

	}

	private static class Stdin {
		InputStreamReader read;
		BufferedReader br;

		StringTokenizer st = new StringTokenizer("");

		private Stdin() {
			read = new InputStreamReader(System.in);
			br = new BufferedReader(read);

		}

		private String readNext() throws IOException {

			while (!st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		private int readInt() throws IOException, NumberFormatException {

			return Integer.parseInt(readNext());

		}

		private long readLong() throws IOException, NumberFormatException {

			return Long.parseLong(readNext());

		}
	}
}
