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.*;
import java.util.regex.*;
import java.io.*;
import java.text.*;
import java.math.*;
import java.awt.geom.*;

public class B_TreesInRow {
	public static void main (String[] args) {
		try {
			BufferedReader br = new BufferedReader( new InputStreamReader( System.in ) );
			String[] nk = br.readLine().split(" ");

			int n = Integer.parseInt(nk[0]);
			int k = Integer.parseInt(nk[1]);

			nk = br.readLine().split(" ");
			int[] a = new int[nk.length];
			for (int i=0; i<a.length; ++i) {
				a[i] = Integer.parseInt(nk[i]);
			}
			int tmin = -1, h0 = a[0];
			for (int h = 1; h<=1000; h++) {
				int t = 0;
				for (int i=0; i<n; i++) if (a[i] != h + i*k) t++;
				if (tmin == -1 || t < tmin) {
					h0 = h;
					tmin = t;
				}
			}
			System.out.println(tmin);
			for (int i=0; i<n; i++) if (a[i] != h0 + i*k)
			{
				int d = h0 + i*k - a[i];
				if (d > 0) System.out.println("+ "+ (i+1) + " " + d);
				else System.out.println("- "+ (i+1) + " " + (-d));
			}
		} catch(Exception e) {
		}
	}
}
