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

public class TreesInARow {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int[] arr = new int[n];
		for(int i=0;i<n;i++)
			arr[i] = sc.nextInt();
		int min = n+1;
		String ans = "";
		for(int i=0;i<n;i++){
			if(arr[i] - i*k <= 0)
				continue;
			int in = 0;
			StringBuilder sb = new StringBuilder();
			for(int j=0;j<i;j++)
				if(arr[j] != arr[i] - i*k + j*k){
					in++;
					if(arr[j] > arr[i] - i*k + j*k)
						sb.append("- " + (j+1) +" " + (arr[j] -( arr[i] - i*k + j*k)) + "\n");
					else
						sb.append("+ " + (j+1) + " " + (( arr[i] - i*k + j*k) - arr[j]) + "\n");
				}

			for(int j=i+1;j<n;j++)
				if(arr[j] != arr[i] - i*k + j*k){
					in++;
					if(arr[j] > arr[i] - i*k + j*k)
						sb.append("- " + (j+1) + " " + (arr[j] -( arr[i] - i*k + j*k)) + "\n");
					else
						sb.append("+ " + (j+1) + " " + (( arr[i] - i*k + j*k) - arr[j]) + "\n");
				}
			if(in < min)
			{
				min = in;
				ans =sb.toString();
			}
		}
		PrintWriter pw = new PrintWriter(System.out);
		pw.println(min);
		if(ans.length()!=0)
			pw.println(ans);
		pw.flush();
		pw.close();
	}
	static class Scanner{
		StringTokenizer st;BufferedReader br;
		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
		public String next() throws IOException 
		{while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());return st.nextToken();}
		public int nextInt() throws IOException {return Integer.parseInt(next());}
		public long nextLong() throws IOException {return Long.parseLong(next());}
		public String nextLine() throws IOException {return br.readLine();}
		public double nextDouble() throws IOException {return Double.parseDouble(next());}
		public boolean ready() throws IOException {return br.ready();}
	}
}
