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.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class B {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        // Scanner scan = new Scanner(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out)); 
        // int n = Integer.parseInt(bf.readLine());
        StringTokenizer st = new StringTokenizer(bf.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(bf.readLine());
         int[] a = new int[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
         int index = -1; int min = Integer.MAX_VALUE;
         hi: for(int i=0; i<n; i++) {
             int counter = 0;
            for(int j=0; j<n; j++) {
                if(a[i] + k*(j-i) <= 0) continue hi;
                if(a[j] - a[i] != k*(j-i))
                    counter++;
            }
            if(counter < min) {
                min = counter;
                index = i;
            }
        }
         out.println(min);
         for(int j=0; j<n; j++) {
                if(a[j] - k*(j-index) != a[index]) {
                    int x = a[index] - (a[j] - k*(j-index));
                    if(x > 0)
                        out.println("+ " + (j+1) + " " + x);
                    else
                        out.println("- " + (j+1) + " " + (-1)*x);
                }
         }
         
        
        // int n = scan.nextInt();
        
        out.close(); System.exit(0);
    }
}
