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.awt.Point;
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.lang.Character.Subset;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;

public class marathon
{

	public static ArrayList<Integer> strToInts(String str, String token)
	{
		ArrayList<Integer> result = new ArrayList<Integer>();
		String[] strs = str.split(token);
		for (String string : strs)
			result.add(Integer.parseInt(string));
		return result;
	}

	public static ArrayList<Long> strToLong(String str, String token)
	{
		ArrayList<Long> result = new ArrayList<Long>();
		ArrayList<String> strs = new ArrayList<String>(Arrays.asList(str.split(token)));
		for (String string : strs)
		{
			result.add(Long.parseLong(string));
		}
		return result;
	}

	public static ArrayList<Double> strToDouble(String str, String token)
	{
		ArrayList<Double> result = new ArrayList<Double>();
		ArrayList<String> strs = new ArrayList<String>(Arrays.asList(str.split(token)));
		for (String string : strs)
		{
			result.add(Double.parseDouble(string));
		}
		return result;
	}

	public static void main(String[] args) throws IOException
	{

		// The input and output streams
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); // system
		//BufferedReader in = new BufferedReader(new FileReader("input.txt"));
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

		// Take input
		ArrayList<Integer> params = strToInts(in.readLine(), " ");
		int n = params.get(0);
		int k = params.get(1);
		ArrayList<Integer> arr = strToInts(in.readLine(), " ");
		
		int firstHeight = firstHeight(arr, k);
		StringBuilder ans = new StringBuilder();
		int count = 0;
		for (int i = 0; i < arr.size(); i++)
		{
			int req = firstHeight + k*i;
			int real = arr.get(i);
			int diff = Math.abs(req - real);
			if (arr.get(i) > req)
			{
				ans.append("- " + (i+ 1) + " " + diff + "\n");
				count ++;
			}
			if (real < req)
			{
				ans.append("+ " + (i+ 1) + " " + diff + "\n");
				count ++;
			}
		}
		System.out.println(count);
		System.out.println(ans.toString());
	}

	private static int firstHeight(ArrayList<Integer> arr, int k)
	{
		int bestA = 1;
		int bestCount = (int)(Double.POSITIVE_INFINITY);
		for (int a = 1; a <= 1000; a++)
		{
			int count = 0;
			for (int i = 0; i < arr.size(); i++)
			{
				int req = a + i*k;
				if (arr.get(i) != req)
					count ++;
			}
			if (count < bestCount)
			{
				bestCount = count;
				bestA = a;
			}
		}
		return bestA;
	}

}
