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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class B402 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int K = in.nextInt();
        int[] A = new int[N];
        for (int n=0; n<N; n++) {
            A[n] = in.nextInt();
        }
        Map<Integer,Integer> map = new HashMap<>();
        int maxCount = 0;
        int maxBase = 1;
        for (int n=0; n<N; n++) {
            int base = A[n] - n*K;
            if (base <= 0) continue;
            int count = map.getOrDefault(base, 0);
            count++;
            map.put(base, count);
            if (count > maxCount) {
                maxCount = count;
                maxBase = base;
            }
        }
        int answer = 0;
        StringBuilder output = new StringBuilder();
        for (int n=0; n<N; n++) {
            int expected = maxBase + n*K;
            int diff = expected - A[n];
            if (diff != 0) {
                answer++;
                if (diff > 0) {
                    output.append("+ ").append(n+1).append(' ').append(diff).append('\n');
                } else {
                    output.append("- ").append(n+1).append(' ').append(-diff).append('\n');
                }
            }
        }
        System.out.println(answer);
        System.out.print(output);
    }

}
