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 codeforces;

import java.io.PrintWriter;
import java.util.Scanner;


public class TreesinaRow {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        
        int n = in.nextInt(),
            k = in.nextInt();
        
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = in.nextInt();
        
        int[] id = new int[n];
        for (int i = 0; i < n; i++) id[i] = i;
        
        int mini = 0;
        int min = n;
        for (int i = 0; i < n; i++)
            if (i == id[i] && a[i] - i*k > 0) {
                int moves = i;     
                int prev = a[i];
                for (int j = i+1; j < n; j++) {
                    if (a[j] == prev + k) {
                        id[j] = i;
                    }
                    else {
                        moves++;
                    }
                    prev += k;
                }
                
                if (moves < min) {
                    min = moves;
                    mini = i;
                }
            }
        
        out.println(min);
        
        if (mini > 0) {
            int newHight = a[mini] - mini*k;
            out.print(a[0] < newHight ? "+ " : "- ");
            out.print("1 ");
            out.println(Math.abs(a[0] - newHight));
            a[0] = newHight;
        }
        
        for (int i = 1; i < n; i++) {
            if (a[i] != a[i-1] + k) {
                out.print(a[i] < a[i-1] + k ? "+ " : "- ");
                out.print((i+1) + " ");
                out.println(Math.abs(a[i-1] + k - a[i]));
                a[i] = a[i-1] + k;
            }
        }
                
        out.flush();
    }
}
