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

//Codeforces
public class MainCodeforces1 {
	private static MyScanner in;
	private static PrintStream out;
	private static boolean LOCAL_TEST = false;

	private static void solve() throws IOException
	{
		int n = in.nextInt();
		int k = in.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < a.length; i++) {
			a[i] = in.nextInt();
		}
		int minCnt = Integer.MAX_VALUE;
		int minStart = 0;
		for (int start = 1; start <= 1000; start++) {
			int cnt = 0;
			for (int i = 0; i < a.length; i++) {
				if (a[i] != start + (k * i))
					cnt++;
			}
			if (cnt < minCnt) {
				minCnt = cnt;
				minStart = start;
			}
		}
		out.println(minCnt);
		for (int i = 0; i < a.length; i++) {
			if (a[i] < minStart + (k * i)) {
				out.println("+ " + (i + 1) + " " + (minStart + (k * i) - a[i]));

			}
			else if (a[i] > minStart + (k * i)) {
				out.println("- " + (i + 1) + " " + (a[i] - (minStart + (k * i))));
			}
		}
	}

	public static void main(String[] args) throws IOException {
		// helpers for input/output
		out = System.out;
		try {
			String cname = System.getenv("COMPUTERNAME");
			if (!cname.equals(""))
				LOCAL_TEST = true;
		} catch (Exception e) {
		}
		if (LOCAL_TEST) {
			in = new MyScanner("E:\\zin.txt");
		}
		else {
			boolean usingFileForIO = false;
			if (usingFileForIO) {
				// using input.txt and output.txt as I/O
				in = new MyScanner("input.txt");
				out = new PrintStream("output.txt");
			}
			else {
				in = new MyScanner();
				out = System.out;
			}
		}

		solve();
	}

	// =====================================
	static class MyScanner {
		BufferedReader bufReader;
		StringTokenizer strTok;

		public MyScanner() throws IOException
		{
			bufReader = new BufferedReader(new InputStreamReader(System.in));
			strTok = new StringTokenizer("");
		}

		public MyScanner(String inputFile) throws IOException {
			bufReader = new BufferedReader(new InputStreamReader(new FileInputStream(
					inputFile)));
			strTok = new StringTokenizer("");
		}

		String GetNextToken() throws IOException {
			if (!strTok.hasMoreTokens())
				strTok = new StringTokenizer(bufReader.readLine());
			return strTok.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.valueOf(GetNextToken());
		}

		public long nextLong() throws IOException {
			return Long.valueOf(GetNextToken());
		}

		public double nextDouble() throws IOException {
			return Double.valueOf(GetNextToken());
		}

		public String nextString() throws IOException {
			return GetNextToken();
		}

		public String nextLine() throws IOException {
			return bufReader.readLine();
		}

		public int countTokens() {
			return strTok.countTokens();
		}

		public boolean hasMoreTokens() {
			return strTok.hasMoreTokens();
		}
	}

}