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 Solution {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt(), k = in.nextInt(), temp = 0, max = 1, maxi = 0, t = 0;
		int[] h = new int[n], h1 = new int[n], h2 = new int[n], dp = new int[n];
		for (int i = 0; i < n; i++) 
			h[i] = in.nextInt();

		dp[0] = 1;
		for (int i = 1; i < n; i++) {
			if (h[i] - i * k > 0) {
				dp[i] = 1;
				for (int j = 0; j < i; j++) 
					if (h[i] - h[j] == (i - j) * k) 
						dp[i] = (dp[j] + 1) > dp[i] ? (dp[j] + 1) : dp[i];	
				if (dp[i] > max) {
					max = dp[i];
					maxi = i;
				}
			}
			else
				dp[i] = 0;
		}

		h1[maxi] = h[maxi];
		for (int i = maxi - 1; i >= 0; i--)
			h1[i] = h1[i + 1] - k;
		for (int i = maxi + 1; i < n; i++)
			h1[i] = h1[i - 1] + k;
		
		StringBuilder r = new StringBuilder();
		for (int i = 0; i < n; i++) {
			if ((temp = h[i] - h1[i]) != 0) {
				t++;
				if (temp > 0)
					r.append("-").append(" ").append(i + 1).append(" ").append(temp).append("\n");
				else
					r.append("+").append(" ").append(i + 1).append(" ").append(Math.abs(temp)).append("\n");
			}
		}
		System.out.println(t);
		System.out.println(r.toString());

	}
}
