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.*;
import java.util.*;

public class Solution {

    private BufferedReader in;
    private PrintWriter out;
    private StringTokenizer st;

    private String next() throws Exception {
        if(st == null || !st.hasMoreElements())
            st = new StringTokenizer(in.readLine());
        return st.nextToken();
    }

    private int nextInt() throws Exception {
        return Integer.parseInt(next());
    }
    private long nextLong() throws Exception {
        return Long.parseLong(next());
    }
    private double nextDouble() throws Exception {
        return Double.parseDouble(next());
    }

    private void run() throws Exception {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        // The solution of the problem goes here
        int n = nextInt();
        int k = nextInt();
        int[] a = new int[n];
        for(int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        int[] b = new int[n];
        int ss = 1, m, ans = Integer.MAX_VALUE;;
        for(int s = 1; s <= 1000; s++) {
            m = 0;
            for (int i = 0; i < n; i++) {
                if(a[i] != s + k * i) {
                    m++;
                }
            }
            if (ans > m) {
                ans = m;
                ss = s;
            }
        }
        out.println(ans);
        int t;
        for (int i = 0; i < n; i++)
            if(a[i] != ss + k * i) {
                t = a[i] - ss - k * i;
                out.println(((t > 0) ? "- ":"+ ") + (i + 1) + " " + Math.abs(t));
            }
        out.close();
    }

    public static void main(String[] args) throws Exception {
        new Solution().run();
    }
}