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.IOException;
import java.text.ParseException;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeSet;

/**
 * http://codeforces.com/contest/402/problem/B
 */
public class B {

	public static void main(String[] args) throws IOException, ParseException {
		new B().doJob();
	}

	private void doJob() throws ParseException, IOException {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			int k = scanner.nextInt();
			int[] a = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = scanner.nextInt();
			}
			int min = Integer.MAX_VALUE;
			int val = 0;
			for (int v=1; v<=1000; v++) {
				int cnt = 0;
				for (int j = 0; j < n; j++) {
					if (a[j] != v + j * k) {
						cnt++;
					}
				}
				if (cnt < min) {
					val = v;
					min = cnt;
				}
			}
			StringBuilder res = new StringBuilder();
			for (int i = 0; i < n; i++) {
				int expectedVal = val + i * k;
				if (expectedVal > a[i]) {
					res.append("+ ").append(i + 1).append(" ").append(expectedVal - a[i])
							.append(System.lineSeparator());
				} else if (expectedVal < a[i]) {
					res.append("- ").append(i + 1).append(" ").append(a[i] - expectedVal)
							.append(System.lineSeparator());
				}
			}
			System.out.println(min);
			System.out.println(res.toString());
		}
	}

}
