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.Scanner;

public class Main {

	public static void main(String args[])
	{
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		int k=scan.nextInt();
		int ar[]=new int[n];
		for(int i=0;i<n;i++)
		{
			ar[i]=scan.nextInt();
		}
		int mincost=Integer.MAX_VALUE;
		int minat=0;
		for(int i=1;i<=1000;i++)
		{
			int cost=0;
			for(int j=0;j<n;j++)
			{
				int x=i+j*k;
				if(x!=ar[j])
				{
					cost++;
				}
			}
			if(mincost>cost)
			{
				mincost=cost;
				minat=i;
			}
		}
		System.out.println(mincost);
		for(int j=0;j<n;j++)
		{
			int cur=minat+j*k;
			if(cur==ar[j])continue;
			if(cur>ar[j])
			{
				System.out.println("+ "+(j+1)+" "+(cur-ar[j]));
			}else {
				System.out.println("- "+(j+1)+" "+(ar[j]-cur));
			}
		}
	}
}
