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.PrintWriter;
import java.util.Scanner;




public class CF_3 {
	public static void main(String[] args){
		PrintWriter pw = new PrintWriter(System.out, true);
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int k = sc.nextInt();
		int[] N = new int[n];
		for(int i=0;i<n;i++){
			N[i] = sc.nextInt();
		}
		int a = k*(n-1), b = 0, min = 10000000, index = 0 , c = 0;
		for(int i=1;i<=1000;i++){
			if(i != N[0]){
				b = 1;
			}else{
				b = 0;
			}
			c = i;
			for(int j=1;j<n;j++){
				c+=k;
				if(N[j] != c){
					b++;
				}
			}
			if(b < min){
				min = b;
				index = i;
			}
		}
		pw.println(min);
		c = index;
		
		for(int i=0;i<n;i++){
			if(N[i] < c){
				pw.println("+ "+(i+1)+" "+(c-N[i]));
			}else if(N[i] > c){
				pw.println("- "+(i+1)+" "+(N[i]-c));
			}
			c+=k;
		}
		
		
		
		pw.close();
	}
}
