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.util.ArrayList;
import java.util.Scanner;

public class Trees {

    public static void main(String[] args) {
        int n, k;
        Scanner in = new Scanner(System.in);
        n = in.nextInt();
        k = in.nextInt();
        int[] a = new int[1001];
        for(int i=0; i<n; i++)
            a[i] = in.nextInt();
        int mn = 1<<30, idx=0;
        for(int i=1; i<=1000; i++)
        {
            int ans=0;
            if(a[0] != i)
                ans++;
            for(int j=1; j<n; j++)
            {
                if(a[j]!=i+j*k)
                {
                    ans++; 
                }
            }
            if(ans < mn)
            {
                mn = ans;
                idx = i;
            }
        }
        ArrayList<String > ans = new ArrayList<String>();
        for(int i=0; i<n; i++)
        {
            if(a[i]!=idx + i*k)
            {
                if(a[i] > idx+i*k)
                {
                    int x=i+1,y=a[i]-idx-i*k;
                    ans.add("- " + x + " " + y);
                }
                else
                {
                    int x=i+1,y=idx+i*k-a[i];
                    ans.add("+ " + x + " " + y);
                }
                    
            }
        }
        System.out.println(ans.size());
        for(int i=0; i<ans.size(); i++)
        {
            System.out.println(ans.get(i));
        }
    }
}
