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.*;
public class Main{
public static void main(String... args)throws IOException{
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
String[] temp = br.readLine().split(" ");
int n = Integer.parseInt(temp[0]);
int k = Integer.parseInt(temp[1]);
int[] t = new int[n];
temp = br.readLine().split(" ");

Set<Integer> all = new HashSet<Integer>();
for (int i=0; i<n; i++){
  t[i]=Integer.parseInt(temp[i]);
  all.add(t[i]-k*i);
}

int min = Integer.MAX_VALUE;
int minX = 1;
for (int x : all){
  if (x<=0) continue;
  int c = 0;
  for (int i=0; i<n; i++){
    if (t[i]!=x+k*i)c++;
  }
  if (c<min){
    min=c;
    minX=x;
  }
}

StringBuilder sb = new StringBuilder();
sb.append(min);
sb.append('\n');
for (int i=0; i<n; i++){
  if (t[i]!=minX+k*i){
    int d = minX+k*i-t[i];
    sb.append(d<0?'-':'+');
    sb.append(' ');
    sb.append(i+1);
    sb.append(' ');
    sb.append(Math.abs(d));
    sb.append('\n');
  }
}
System.out.println(sb);


}
}
