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.*;
import java.util.*;
import java.awt.*;

public class Main {
	static BufferedReader br = new BufferedReader( new InputStreamReader(System.in) );
	static StringTokenizer st = new StringTokenizer("");
	static String next()	throws Exception	{
		
		while	( !st.hasMoreTokens() )	{
			String s = br.readLine();
			if	( s == null )	return	null;
			st = new StringTokenizer( s );
		}
		return	st.nextToken();
	}
	
	public static void main(String [] asda)	throws Exception	{
		PrintWriter out = new PrintWriter( new BufferedOutputStream(System.out) );
		//

		int N = Integer.parseInt( next() );
		int K = Integer.parseInt( next() );
		int [] v = new int [N];
		for (int i = 0; i < N; i++)
			v[i] = Integer.parseInt( next() );
		
		int min = 1;
		int minChanges = 10000;
		for (int val = 1; val <= 1000; val++)	{
			int changes = 0;
			for (int i = 0, x = val; i < N; i++, x += K)	{
				if	( v[i] != x )
					changes++;
			}
			if	( changes < minChanges )	{
				min = val;
				minChanges = changes;
			}
		}
		if	( minChanges == 10000 )
			minChanges = 0;
		out.println(minChanges);
		for (int i = 0, x = min; i < N; i++, x += K)	{
			if	( v[i] == x )
				continue;
			out.print( v[i] > x ? '-' : '+' );
			out.println( " " + (i + 1) + " " + Math.abs(v[i] - x) );
		}
		//
		out.flush();
		System.exit(0);
	}

}





