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 B {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		int[] a = new int[n];
		ArrayList<String> ans = new ArrayList<String>();
		for(int i = 0; i < n; i ++)
		{
			a[i] = in.nextInt();
		}
		int x = -1;
		int min = 987654321;
		for(int i = 0; i < n; i ++)
		{
			int tot = 0;
			for(int j = 0; j < i; j ++)
			{
				int sb = a[i] - k*(i - j);
//				System.out.println("i: " + i + " j: " + j +" at: " + a[j] + " sb " + sb);
				if(a[j] != sb)
					tot++;
				if(sb <= 0)
				{
					tot = 987654321;
					break;
				}
			}
			for(int j = i + 1; j < n; j ++)
			{

				int sb = a[i] + k*(j - i);
//				System.out.println("i: " + i + " j: " + j +" at: " + a[j] + " sb " + sb);

				if(a[j] != sb)
					tot++;
			}
			if(tot < min)
			{
//				System.out.println(tot + " " + min + " " + i);
				min = tot;
				x = i;
			}
		}
//		System.out.println(x + "!");
		for(int i = 0; i < x; i ++)
		{
			int sb = a[x] - k*(x - i);
//			System.out.println(i + " " +a[i] + " " + sb + " ??");
			if(sb == a[i])
				continue;
			sb = sb - a[i];
			ans.add((sb < 0 ? "- " : "+ ") + (i + 1) + " " + Math.abs(sb));
		}
		for(int i = x + 1; i < n; i ++)
		{
			int sb = a[x] + k*(i - x);
//			System.out.println(i + " " +a[i] + " " + sb + " ??");
			if(sb == a[i])
				continue;
			sb = sb - a[i];
			ans.add((sb < 0 ? "- " : "+ ") + (i + 1) + " " + Math.abs(sb));
		}
		System.out.println(ans.size());
		for(String e: ans)
			System.out.println(e);
	}
}
