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 BTreesInARow {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		int n;
		int k;
		int[] heights;
		int bestRes = Integer.MAX_VALUE;
		int keep = 0;
		int currentRes = 0;
		boolean ignore = false;
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		k = sc.nextInt();
		heights = new int[n];
		
		for (int i = 0; i < n; i++) {
			heights[i] = sc.nextInt();
		}
		
		for (int i = 0; i < n; i++) {
			currentRes = 0;
			ignore = false;
			for (int j = i + 1 ; j < n; j++ ) {
				int value = heights[i] + (j - i) * k;
				if (heights[j] != value) {
					currentRes++;
				}
			}
			
			for (int j = 0; j < i; j++) {
				int value = heights[i] - (i - j) * k;
				if (value <= 0) {
					ignore = true;
					break;
				}
				if (heights[j] != value) {
					currentRes++;
				}
			}
			if (ignore) {
				continue;
			}
			
			if (bestRes > currentRes) {
				bestRes = currentRes;
				keep = i;
			}
		}
		
		System.out.println(bestRes);
		for (int i = 0; i < keep; i++) {
			int value = heights[keep] - (keep - i) * k;
			if (heights[i] == value) {
				continue;
			} else if (heights[i] < value) {
				System.out.println("+ " + (i+1) + " " + (value - heights[i]));
			} else {
				System.out.println("- " + (i+1) + " " + (heights[i] - value));
			}
		}
		
		for (int i = keep+1; i < n; i++) {
			int value = heights[keep] + (i - keep) * k;
			if (heights[i] == value) {
				continue;
			} else if (heights[i] < value) {
				System.out.println("+ " + (i+1) + " " + (value - heights[i]));
			} else {
				System.out.println("- " + (i+1) + " " + (heights[i] - value));
			}
		}
	}

}
