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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.ListIterator;
import java.util.PriorityQueue;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class CopyOfCopyOfSolution {

    public static void main(final String[] args) throws NumberFormatException, IOException {
        final InputStream inputStream = System.in;
        final OutputStream outputStream = System.out;
        final InputReader in = new InputReader(inputStream);
        final PrintWriter out = new PrintWriter(outputStream);
        final int n = in.nextInt();
        final int k = in.nextInt();
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        int sav = -1;
        int min = 1000000;
        for (int i = 1; i <= 1000; i++) {
            int c = 0;
            int d = 0;
            for (int j = 0; j < n; j++) {
                if (a[j] != (i + d)) {
                    c++;
                }
                d += k;
            }
            if (c < min) {
                min = c;
                sav = i;
            }
        }
        out.println(min);
        int d = 0;
        for (int j = 0; j < n; j++) {
            if (a[j] > (sav + d)) {
                out.println("- " + (j + 1) + " " + (a[j] - sav - d));
            } else if (a[j] < (sav + d)) {
                out.println("+ " + (j + 1) + " " + -(a[j] - sav - d));
            }
            d += k;
        }
        out.close();
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

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

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

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

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

    }
}