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.Arrays;
import java.util.Scanner;

public class ProblemB {
	public static void main(String[] args) throws Exception{
		Scanner input = new Scanner(System.in);
		
		int n = input.nextInt();
		int k = input.nextInt();
		int[] a = new int[1234567];
		int[] h = new int[n];
		int i, maxi=0;
		for(i=0;i<1234567;i++) a[i]=0;
		for(i=0;i<n;i++){
			int oh = (h[i] = input.nextInt()) - i*k;
			if(oh > 0){
				a[oh]++;
				if(a[oh] > a[maxi]) maxi = oh;
			}
		}
		System.out.println(n - a[maxi]);
		for(i=0;i<n;i++){
			int diff = maxi+i*k - h[i];
			if(diff > 0) System.out.println("+ "+(i+1)+" "+diff);
			else if(diff < 0) System.out.println("- "+(i+1)+" "+(-diff));
		}
		input.close();
	}
}
