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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class b {

	public static void main(String[] args) throws IOException {
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(bf.readLine());
		int n = Integer.parseInt(st.nextToken());
		int k = Integer.parseInt(st.nextToken());
		StringTokenizer st1 = new StringTokenizer(bf.readLine());
		int[] a = new int[n];

		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(st1.nextToken());
		}
		int max = 0;
		int index = 0;

		for (int i = 0; i < n; i++) {

			int count = 0;
			int j = 0;
			for (; j < n; j++) {
				if (a[j] - a[i] == (j - i) * k) {
					if (j != 0 && a[j] - (j * k) <= 0) {
						break;
					}
					count++;
				}

			}

			if (j == n && count > max) {
				max = count;
				index = i;

			}
		}
		System.out.println(n - max);

		int val;
		for (int i = 0; i < n; i++) {
			val = ((i - index) * k) + a[index];
			if (a[i] < val) {

				System.out.println("+ " + (i + 1) + " " + (val - a[i]));

			} else if (a[i] > val) {
				System.out.println("- " + (i + 1) + " " + (a[i] - val));
			}

		}

	}

}
