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.Scanner;
import java.io.*;

public class B {
	static Scanner sc;
	static int n, k, a[], r, cnt, ans[];
	
	static void read() {
		n = sc.nextInt();
		k = sc.nextInt();
		a = new int [n + 1];
		ans = new int [n + 1];
		for (int i = 1; i <= n; i++) {
			a[i] = sc.nextInt();
			ans[i] = n + 1;
		}
	}
	static void solve() {
		for (int i = 1; i <= n; i++) {
			cnt = 0;
			for (int j = 1; j <= n; j++) {
				if ((a[i] - a[j]) != ((i - j) * k)) {
					cnt++;
					if (a[i] + ((j - i) * k) <= 0) {
						cnt = n + 1;
						break;
					}
				}
			}
			ans[i] = cnt;
		}
		r = 1;
		for (int i = 1; i <= n; i++) {
			if (ans[i] < ans[r]) {
				r = i;
			}
		}
	}
	static void write() {
		System.out.println(ans[r]);
		for (int i = 1; i <= n; i++) {
			if ((a[i] - a[r]) != ((i - r) * k)) {
				if (a[i] < (i - r) * k + a[r]) {
					System.out.print("+ ");
				}
				else {
					System.out.print("- ");
				}
				System.out.println(i + " " + Math.abs(((i - r) * k) + a[r] - a[i]));
			}
		}
	}
	
	public static void main(String args[]) throws Exception {
		//sc = new Scanner(new File("input.txt"));
		sc = new Scanner(System.in);
		
		read();
		solve();
		write();
	}
}