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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Map;
import java.util.Queue;
import java.util.StringTokenizer;
import java.io.BufferedReader;

import javax.management.Query;



public class fstclass {
	static Map<Integer, Integer> mp = new HashMap<>();
	public static void main(String[] args) {
		InputStream inputStream = System.in;
        InputReader in = new InputReader(inputStream);
        int n, m, i, j;
        n = in.nextInt();
        m = in.nextInt();
        int[] a = new int[3030];
        for(i = 1; i <= n; i ++) {
        	a[i] = in.nextInt();
        }
        int ans = 0, id = -1;
        for(i = 1; i <= n; i ++) {
        	int cnt = 0;
        	boolean ok = true;
        	for(j = 1; j <= n; j ++) {
        		if(a[j] - a[i] == (j - i) * m) {
        			cnt ++;
        		}
        		if(a[i] + (j - i) * m <= 0)
        			ok = false;
        	}
        	if(ans < cnt && ok == true) {
        		ans = cnt;
        		id = i;
        	}
        }
        System.out.println(n - ans);
        for(i = 1; i <= n; i ++) {
        	if(a[id] - a[i] != (id - i) * m) {
        		if(a[id] - (id - i) * m > a[i])
        			System.out.println("+ " + i + " " + (a[id] - (id - i) * m - a[i]));
        		else
        			System.out.println("- " + i + " " + (a[i] - a[id] + (id - i) * m));
        	}
        }
	}
	
	
	
	
	
	
	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}
