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.*;
import java.util.*;
import java.math.*;


public class Main {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer tok;

	
	static void solve() throws Exception {
		int n = nextInt();
		int k = nextInt();
		int[] a = new int[n+1];
		for (int i = 1; i <= n; i++) {
			a[i] = nextInt();
		}
		int minX = 0;
		int minV = Integer.MAX_VALUE;
		for (int x = -a[1] + 1; x <= 1000; x++) {
			int cnt = 0;
			for (int i = 1; i <= n; i++) {
				if (a[i] != (a[1]+x) + k * (i-1)) {
					cnt++;
				}
			}
			if (cnt < minV) {
				minX = x;
				minV = cnt;
			}
		}
		out.println(minV);
		for (int i = 1; i <= n; i++) {
			if (a[i] < (a[1]+minX) + k * (i-1)) {
				out.println("+ " + i + " " + ((a[1]+minX) + k * (i-1) - a[i]));
			} else if (a[i] > (a[1]+minX) + k * (i-1)) {
				out.println("- " + i + " " + (a[i] - ((a[1]+minX) + k * (i-1))));
			}
		}
	}
	
	static int sqr(int x) {
		return x*x;
	}
	
	static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	static long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	static BigInteger nextBigInteger() throws IOException {
		return new BigInteger(next());
	}
	
	static String next() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}
	
	static String nextLine() throws IOException {
		tok = new StringTokenizer("");
		return in.readLine();
	}

	static boolean hasNext() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null) {
				return false;
			}
			tok = new StringTokenizer(s);
		}
		return true;
	}

	public static void main(String args[]) {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(new OutputStreamWriter(System.out));
			//in = new BufferedReader(new FileReader("input.in"));
			//out = new PrintWriter(new FileWriter("output.out"));
			solve();
			in.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			java.lang.System.exit(1);
		}
	}
}