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
//package R236.B;

import java.util.*;
import java.io.*;

public class TaskB {
    public static void main(String[] args) {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = in.nextInt();
        int k = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        List<String> ans = new ArrayList<String>();
        int min = 1000, minI = 0;
        for (int i = 1; i < 1001; i++) {
            int p = 0;
            for (int j = 0; j < n; j++) {
                if (a[j] != i + k * j) {
                    p++;
                }
            }
            if (p < min) {
                min = p;
                minI = i;
            }
        }
        for (int i = 0; i < n; i++) {
            int t = minI + k * i;
            if (a[i] != t) {
                if (a[i] < t) {
                    ans.add("+ " + (i + 1) + " " + (t - a[i]));
                } else {
                    ans.add("- " + (i + 1) + " " + (a[i] - t));
                }
            }
        }
        out.println(ans.size());
        for (String e : ans) {
            out.println(e + " ");
        }
        out.close();
    }
}

class FastScanner {
    public BufferedReader br;
    public StringTokenizer st;

    public FastScanner(InputStream stream) {
        br = new BufferedReader(new InputStreamReader(stream));
        st = null;
    }

    public String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

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

    public long nextLong() {
        return Long.parseLong(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}
