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.*;
import static java.lang.Math.*;
import java.awt.Point;
import java.io.*;
import static java.util.Arrays.*;
import java.util.Map.Entry;

public class B {
	public static void main(String[] args) throws Exception {
		int n = ni();
		int k = ni();
		int[] h = new int[n];
		for (int i = 0; i < n; i++)
			h[i] = ni();
		int ans = Integer.MAX_VALUE;
		int target = 0;
		for (int i = 1; i <= 1000; i++) {
			int t = 0;
			for (int j = 0; j < n; j++) {
				if ((k * j) + i != h[j]) {
					t++;
				}
			}
			ans = min(ans, t);
			if (ans == t) {
				target = i;
			}
		}
		out.println(ans);
		for (int i = 0; i < n; i++)
			if (h[i] != ((k * i) + target)) {
				int s = (k * i) + target;
				if (s < h[i]) {
					out.print("- ");
				} else {
					out.print("+ ");
				}
				out.println("" + (i + 1) + " " + abs(h[i] - s));
			}
		out.flush();
	}

	static BufferedReader in;
	static StringTokenizer st;
	static PrintWriter out;

	static void init() {
		in = new BufferedReader(new InputStreamReader(System.in));
		st = new StringTokenizer("");
		out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
				System.out)));
	}

	static {
		init();
	}

	static double nd() throws NumberFormatException, IOException {
		return Double.parseDouble(n());
	}

	static String n() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}

	static int ni() throws NumberFormatException, IOException {
		return Integer.parseInt(n());
	}

	static long nl() throws NumberFormatException, IOException {
		return Long.parseLong(n());
	}

	static void rev(long[] a) {
		for (int s = 0, t = a.length - 1; s < t; s++, t--) {
			long tempLong = a[s];
			a[s] = a[t];
			a[t] = tempLong;
		}
	}

	static void rev(int[] a) {
		for (int s = 0, t = a.length - 1; s < t; s++, t--) {
			int tempLong = a[s];
			a[s] = a[t];
			a[t] = tempLong;
		}
	}

	static void rev(String[] a) {
		for (int s = 0, t = a.length - 1; s < t; s++, t--) {
			String tempLong = a[s];
			a[s] = a[t];
			a[t] = tempLong;
		}
	}

	static void fa(int[][] d, int val) {
		for (int[] axe : d)
			Arrays.fill(axe, val);
	}

	static void fa(int[][][] d, int val) {
		for (int[][] fack : d)
			fa(fack, val);
	}
}
