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.*;
import java.util.*;



public class BBB {

    /**
     * @param args
     */
    public static void main(String[] args) throws IOException, InterruptedException {

        BufferedReader k=new BufferedReader(new InputStreamReader(System.in));
        StringBuffer t = new StringBuffer();
        StringTokenizer str=new StringTokenizer(k.readLine());
        int n = Integer.parseInt(str.nextToken());
        int kk = Integer.parseInt(str.nextToken());
        
        int[]tree = new int[n];
        str = new StringTokenizer(k.readLine());
        
        for (int i = 0; i < tree.length; i++) {
            tree[i]=Integer.parseInt(str.nextToken());
        }
            
        
        int max = -1;
        int start = -1;
        
        for (int i = 0; i < tree.length; i++) {
            
            int x = tree[i];
            int count = 0;
            int j;
            for ( j = 0; j < tree.length; j++) {
                
                if( (j - i) * kk +tree[i] == tree[j]){
                    if (j != 0 && tree[j] - (j * kk) <= 0) {
                        break;
                    }
                    count ++;
                    //x = tree[j];
                }
                
            }
            if(j == n&&count  > max){
                
                max = count  ;
                start = i;
            }
        }
        
        int count = 0;

        
        
            
            long s = tree[start]-start * kk;
             count = 0;
             System.out.println(n - max);
            for (int i = 0; i < tree.length; i++) {
                long temp = (s)-tree[i];
                if (temp > 0) {
                    t.append("+ "+(i+1)+" "+temp+"\n");
                    //System.out.println("+ "+(i+1)+" "+temp);
                    
                    count++;
                }
                else if (temp < 0) {
                    temp *= -1;
                    t.append("- "+(i+1)+" "+temp+"\n");
                    //System.out.println("- "+(i+1)+" "+temp);
                    count++;
                }
                s+= kk;
            }
            
            //System.out.println(count);
            System.out.print(t.toString());
            
        }
    

}
