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.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;
     
              public class Codeforce{
                 
                 
                 public static void main(String[]args) {
                     Scanner s=new Scanner(System.in);
                        int n=s.nextInt();
                        int k=s.nextInt();
                        int[] a=new int[n];
                        int[] b=new int[n];
                        int ind=0;
                      for(int i=0;i<n;i++){
                          a[i]=s.nextInt();
                         b[i]=a[i];
                      }
                      int count=0;
                      int max=0;
                      int fir=0;
                      for(int j=1;j<=1000;j++){
                          count=0;
                      for(int i=0;i<n;i++){
                         if(j+i*k==a[i])
                             count++;
                      }
                      if(max<count){
                          max=count;
                          fir=j;
                                  
                      }
                               }
                      System.out.println(n-max);
                      for(int i=0;i<n;i++){
                          if(a[i]!=fir+i*k){
                              if(a[i]>fir+i*k)
                              System.out.println("-"+" "+(i+1)+" "+(a[i]-(fir+i*k)));
                              else
                                  System.out.println("+"+" "+(i+1)+" "+(-a[i]+(fir+i*k)));
                          
                          }
                      }
                                  }
                 
              
    }
     