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.BufferedWriter;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.nio.ByteBuffer;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Stack;


 public class Main{
     
     static long gcd(long a, long b){
         if(a%b==0)return b;
         return gcd(b,a%b);
     }
     
     public static void main(String[] args) throws IOException {
         //String IN = "C:\\Users\\ugochukwu.okeke\\Desktop\\in.file";
         //String OUT = "C:\\Users\\ugochukwu.okeke\\Desktop\\out.file";
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
         
        String[] in = br.readLine().split(" ");
        int n = Integer.parseInt(in[0]);
        int k = Integer.parseInt(in[1]);
        in=br.readLine().split(" ");
        int[] a = new int[n];
        for(int i=0;i<n;i++) a[i] = Integer.parseInt(in[i]);
        int minval = Integer.MAX_VALUE;
        int bst = 1;
        int bcnt = 0;
        for(int i=1;i<=1000;i++){
            int val = i;
            int cnt = 0;
            int pcnt=0;
            for(int j=0;j<n;j++) {
                if(j>0) val+=k;
                
                if(val != a[j]) {
                    cnt += 1;
                    pcnt++;
                }
            }
            
            if(cnt < minval) {
                minval = cnt;
                bst = i;
                bcnt=pcnt;
            }
        }
        
        //System.out.println(minval+" "+bst);
        bw.append(bcnt+"\n");
        for(int i=0;i<n;i++) {
            int val = bst+(i*k);
            //System.out.println(val+" "+a[i]);
            if(val != a[i]) {
                
                if(val > a[i]) {
                    bw.append("+ "+(i+1)+" "+(val-a[i])+"\n");
                }
                else{
                    bw.append("- "+(i+1)+" "+(a[i]-val)+"\n");
                }
            }
        }
        bw.close();
        //done then
         
     }
     
 }