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 secuencia{
public static PrintWriter out = new PrintWriter(System.out);//HACER FLUSHHHH
public static void main(String args[]) throws IOException{
BufferedReader lector = new BufferedReader(new InputStreamReader(System.in));
String tmp[] =lector.readLine().split(" ");
int a = Integer.parseInt(tmp[0]);
int b = Integer.parseInt(tmp[1]);
String t[] = lector.readLine().split(" ");
int tt[] = new int[a];
for(int n = 0;n<a;n++)
tt[n]=Integer.parseInt(t[n]);
int max = a,maxx=-1;
for(int n = 0;n<a;n++){
int to = 0;
if(tt[n]+(-n)*b<=0)continue;
for(int m = 0;m<a;m++)
if(tt[m]!=tt[n]+(m-n)*b)to++;
max = Math.min(max,to);
if(to==max)maxx=n;
if(max<=1)break;
}
System.out.println(max);
if(maxx==-1){
for(int n = 0,c=1;n<a;n++,c+=b)
System.out.println((tt[n]<c?"-":"+")+" "+(n+1)+" "+Math.abs(tt[n]-c));
}else{
for(int n = 0;n<a;n++)
if(tt[n]!=tt[maxx]+(n-maxx)*b)
System.out.println((tt[n]<tt[maxx]+(n-maxx)*b?"+":"-")+" "+(n+1)+" "+Math.abs(tt[n]-tt[maxx]-(n-maxx)*b));
}
}
}
