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.BufferedReader;
import java.io.InputStreamReader;


public class Main {


	public static void main (String[] args) throws Exception
	{		
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] l = in.readLine().split(" ");
		int n = Integer.parseInt(l[0]);
		int k = Integer.parseInt(l[1]);
		l = in.readLine().split(" ");
		int[] trees = new int[n];
		//int min=Integer.MAX_VALUE;
		//int max=Integer.MIN_VALUE;
		for (int i = 0; i < n; i++) {
			trees[i] = Integer.parseInt(l[i]);
			//min = Math.min(trees[i], min);
			//max = Math.max(trees[i], max);
		}
		int ans = Integer.MAX_VALUE;
		int inita = 0;
		for (int init = 1; init <= 1005 ; init++) {
			int cont = 0;
			for (int i = 0; i < n; i++) {
				if(trees[i]!=init + i*k)
					cont++;
			}
			if(cont < ans)
			{
				ans = cont;
				inita=init;
			}
		}
		System.out.println(ans);
		for (int i = 0; i < n; i++) {
			if(trees[i]>inita+i*k)
			{
				System.out.println("- "+(i+1)+" "+(trees[i]-(inita+i*k)));
			}
			else if(trees[i]<inita+i*k)
			{
				System.out.println("+ "+(i+1)+" "+(-trees[i]+(inita+i*k)));
			}
		}
	}
}