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 {
	Scanner sc = new Scanner(System.in);
	void doIt()
	{
		int n = sc.nextInt();
		int k = sc.nextInt();
		int [] a = new int[n];
		for(int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		int min_cnt = n;
		int min_h = 0;
		for(int h = 1; h <= 1000; h++) {
			int cnt = 0;
			for(int i = 0; i < n; i++) {
				if(h + k * i != a[i]) cnt++;
			}
			if(cnt < min_cnt) {
				min_cnt = cnt;
				min_h = h;
			}
		}
		System.out.println(min_cnt);
		for(int i = 0; i < n; i++) {
			int h = min_h + k * i;
			if(h < a[i]) System.out.println("- " + (i+1) + " " + (a[i] - h));
			else if(h > a[i]) System.out.println("+ " + (i+1) + " " + (h - a[i]));
		}
	}
	public static void main(String[] args) {
		new B().doIt();
	}

}
