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 Main
{
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		// get input n, k
		int n = in.nextInt();
		int k = in.nextInt();
		// get input a1..an
		int[] a = new int[n + 1];
		for (int i = 1; i <= n; i++)
			a[i] = in.nextInt();;


		// Set minimum to be a big number
		int minimum = (int) 1e7;
		// Set bestStandard = -1
		int bestStandard = -1;

		// for standard = 1 to n
		for (int standard = 1; standard <= n; standard++)
		{
			// Set current = 0
			int current = 0;
			// check how many trees need to be taken care of if we set standard
			int height = a[standard] - k * (standard - 1);

			if (height <= 0)
				continue;
			for (int i = 1; i <= n; i ++)
			{
				if (a[i] != height)
					current ++;
				height += k;
			}
			// if it's less than minimum, bestStandard = standard
			if (current  < minimum)
			{
				minimum = current;
				bestStandard = standard;
			}


		}
		// if it's less than minimum, bestStandard = standard
		int height = a[bestStandard] - k * (bestStandard - 1);
		System.out.println(minimum);
		for (int i = 1; i <= n; i ++)
		{
			if (a[i] != height)
			{
				if (a[i] < height)
				{
					System.out.printf("+ %d %d\n", i, height - a[i]);
				}
				else
				{
					System.out.printf("- %d %d\n", i, a[i] - height);
				}

			}
			height += k;
		}
	}
}
