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 static java.lang.Math.*;
import static java.lang.System.currentTimeMillis;
import static java.lang.System.exit;
import static java.lang.System.arraycopy;
import static java.util.Arrays.sort;
import static java.util.Arrays.binarySearch;
import static java.util.Arrays.fill;
import java.util.*;
import java.io.*;

public class Main {

    public static void main(String[] args) throws IOException {
        try {
            if (new File("input.txt").exists())
                System.setIn(new FileInputStream("input.txt"));
        } catch (SecurityException e) {
        }
        new Main().run();
    }

    BufferedReader in;
    PrintWriter out;
    StringTokenizer st = new StringTokenizer("");

    private void run() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }

    void outTree(int oldHight, int newHight, int index){
        if(newHight != oldHight){
            if(newHight > oldHight)
                out.println("+ " + (index) + " " + (newHight - oldHight));
            else
                out.println("- " + (index) + " " + (-newHight + oldHight));
        }
    }
    
    private void solve() throws IOException {
        int n = nextInt(),
                k = nextInt();
        int[]a = new int[n];
        for(int i = 0; i < n; i++)
            a[i] = nextInt();
        int bestTime = 1000 * 1000;
        int bestHight = 0;
        for(int firstHight = 1; firstHight < 4000; firstHight++){
            int time = 0;
            if(firstHight != a[0])
                time++;
            for(int i = 1; i < n; i++)
                if(a[i] != firstHight + i * k)
                    time++;
            if(time < bestTime){
                bestTime = time;
                bestHight = firstHight;
            }
        }
        out.println(bestTime);
        for(int i = 0; i < n; i++){
            if(i == 0){
                outTree(a[i],bestHight,i+1);
            } else {
                outTree(a[i],bestHight + i * k, i+1);
            }
        }
    }
    
    String nextToken() throws IOException {
        while (!st.hasMoreTokens())
            st = new StringTokenizer(in.readLine());
        return st.nextToken();
    }
    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 nextLine() throws IOException {
        st = new StringTokenizer("");
        return in.readLine();
    }
    boolean EOF() throws IOException {
        while (!st.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null)
                return true;
            st = new StringTokenizer(s);
        }
        return false;
    }
}
