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.*;
public class SinIsh {
public static void main(String [] args){
Scanner in=new Scanner(System.in);
int n=in.nextInt();
int k=in.nextInt();
int array[]=new int[n];
int cnt=0;
int start=0;
int min=Integer.MAX_VALUE;
for(int i=0;i<n;i++){
array[i]=in.nextInt();
}
for(int i=1;i<=1000;i++){
for(int j=0;j<n;j++){
if(array[j]!=i+k*j)
cnt++;
}
min=Math.min(cnt,min);
if(cnt==min)
start=i;
cnt=0;
}
System.out.println(min);
for(int i=0;i<n;i++){
if(array[i]<start+k*i){
System.out.println("+"+" "+(i+1)+" "+Math.abs(array[i]-start-k*i));
}
if(array[i]>start+k*i){
System.out.println("-"+" "+(i+1)+" "+Math.abs(array[i]-start-k*i));
}
}
}
}