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.InputStreamReader;
import java.util.ArrayList;

public class Main2 {
	public static void main(String args[]) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] st = br.readLine().split(" ");
		int n = Integer.parseInt(st[0]);
		int k = Integer.parseInt(st[1]);
		int[] a = new int[n];
		st = br.readLine().split(" ");
		for(int i = 0 ; i < n ; i++){
			a[i] = Integer.parseInt(st[i]);
		}
		ArrayList<String> great = new ArrayList<String>();
		int minturn = Integer.MAX_VALUE;
		for(int i = 0 ; i < n ; i++){
			ArrayList<String> tmpgreat = new ArrayList<String>();
			int start = a[i];
			int turn = 0;
			boolean isok = true;
			for(int j = 0 ; j < n ; j++){
				if(i == j)continue;
				if(start-(i-j)*k <= 0){
					isok = false;
					break;
				}
				if(start-(i-j)*k != a[j]){
					turn++;
					if(a[j] - (start-(i-j)*k) > 0){
						tmpgreat.add("- "+(j+1)+" "+(a[j] - (start-(i-j)*k)));
					}else{
						tmpgreat.add("+ "+(j+1)+" "+((start-(i-j)*k) - a[j]));
					}
				}
			}
			if(!isok)continue;
			if(turn < minturn){
				minturn = turn;
				great = tmpgreat;
			}
		}
		System.out.println(minturn);
		for(int i = 0 ; i < great.size(); i++){
			System.out.println(great.get(i));
		}
	}
}