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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;


public class T402B {

	public void solve(int n, int k, int[] a) {
		int min = Integer.MAX_VALUE;
		int minv = 0;
		for (int i = 1; i <= 1000; i ++) {
			int count = 0;
			for (int j = 0; j < n; j ++) {
				if (a[j] != i + j * k) {
					count ++;
				}
			}
			if (min > count) {
				min = count;
				minv = i;
			}
		}
		System.out.println(min);
		if (min != 0) {
			
			String[] ans = new String[min];
			int p = 0;
			for (int i = 0; i < n; i ++) {
				if (minv + i * k > a[i]) {
					ans[p ++] = "+ " + (i + 1) + " " + (minv + i * k - a[i]);
				} else if (minv + i * k < a[i]) {
					ans[p ++] = "- " + (i + 1) + " " + (a[i] - minv - i * k);
				}
			}
			for (String v : ans)
				System.out.println(v);
		}
	}
	
	public static void main(String[] args) {
		T402B t = new T402B();
		FastScanner in = new FastScanner();
		int n = in.nextInt();
		int k = in.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i ++) a[i] = in.nextInt();
		t.solve(n, k, a);
	}
	
	static class FastScanner {

		BufferedReader br;
		StringTokenizer st;

		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(nextToken());
		}

		long nextLong() {
			return Long.parseLong(nextToken());
		}

		double nextDouble() {
			return Double.parseDouble(nextToken());
		}

	}

}
