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.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
import java.util.*;
import java.util.concurrent.ArrayBlockingQueue;

public class CodeForces {

	public void solve() throws IOException {
		int n = nextInt();
		int k = nextInt();
		int sum = 0;
		
		int[] arr = new int[n];
		
		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
		}
		int nn = -1;
		int minS = Integer.MAX_VALUE;
		for(int i=1;i<1001;i++) {
			int tSum = 0;
			for (int j = 0, l = arr.length; j < l; j++) {
				if(Math.abs(arr[j]-(j)*k-i)!=0) {
					tSum+=1 ;	
				}
				
			}
			if(tSum<minS) {
				minS = tSum;
				nn = i;
			}
		}
		
		

		if (minS == 0) {
			System.out.println(0);
		} else {
			System.out.println(minS);
			for (int i = 0; i < n; i++) {
				int s = arr[i] - i * k - nn;
				if (s != 0) {
					if (s > 0) {
						System.out.print("- ");
					} else {
						System.out.print("+ ");
					}
					System.out.println((i + 1) + " " + Math.abs(s));
				}
			}
		}
	}

	public static void main(String[] args) {
		new CodeForces().run();
	}

	int NOD(int a, int b) {
		while (a != 0 && b != 0) {
			if (a >= b)
				a = a % b;
			else
				b = b % a;
		}
		return a + b;
	}

	BufferedReader reader;
	StringTokenizer tokenizer;
	PrintWriter out;
	boolean isOuterFile = false;

	public void run() {
		try {
			if (isOuterFile) {
				reader = new BufferedReader(new FileReader(
						"C:\\work\\javaprojects\\CodeForces\\SCC.txt"));
				// out = new PrintWriter(new BufferedWriter(new FileWriter(
				// "output.txt")));
				// out = new PrintWriter(System.out);
			} else {
				reader = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			}

			tokenizer = null;

			// long time = System.currentTimeMillis();
			solve();
			// out.println(System.currentTimeMillis() - time);
			reader.close();
			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

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

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

	String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}
}