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
//package Div_236;
//Xudo xoxlasa Accepted

import java.util.ArrayList;
import java.util.Scanner;
import java.util.TreeMap;

public class B {
public static void main(String[] args) {
	 Scanner sc=new Scanner(System.in);
	 int n=sc.nextInt();
	 int k=sc.nextInt();
	 int [] a=new int[n];
	 for (int i =0; i < a.length; i++) {
		a[i]=sc.nextInt();
	}
	 TreeMap<Integer, ArrayList<String>>mp=new TreeMap<Integer, ArrayList<String>>();
	 ArrayList<String>st=new ArrayList<String>();
	 int t=0;
	 for (int i =0; i <n; i++) {
		 t=0;
		 st=new ArrayList<String>();
		 int y=a[i]-(i+1)*k;
		 if(y+k<=0){t=n+1;mp.put(t, st);continue;}
		for (int j =0; j<i; j++) {
			y=y+k;
			if(a[j]!=y){
				t++;
				if(a[j]>y){
					st.add("- "+(j+1)+" "+(a[j]-y));
				}else{
					st.add("+ "+(j+1)+" "+(-a[j]+y));
					
				}
			}
		}
		y=a[i];
		for (int j =i+1; j <n; j++) {
			y=y+k;
			if(a[j]!=y){t++;
				if(a[j]>y){
					st.add("- "+(j+1)+" "+(a[j]-y));
				}else{
					st.add("+ "+(j+1)+" "+(-a[j]+y));
					
				}
			}
		}
	{mp.put(t,st);}
	}
	 System.out.println(mp.firstKey());
	 st=new ArrayList(mp.get(mp.firstKey()));
	 for(String i:st){
		 System.out.println(i);
	 }
}
}
