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.Arrays;
import java.util.StringTokenizer;

public class CopyOfCopyOfB {

    public static void main(String[] args) {
        MyScanner in = new MyScanner();

        int n = in.nextInt();
        int k = in.nextInt();
        int[] a = new int[n];

        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }

        int best = 100000;
        int[] bestA = null;

        for (int mid = 0; mid < n; mid++) {
            int[] arr = a.clone();
            int cost = 0;
            for (int i = 0; i < n; i++) {

                int shouldBe = a[mid] + (i - mid) * k;
                if (a[i] != shouldBe) cost++;

                if (shouldBe < 1) cost = 1000000;

                arr[i] = shouldBe;
            }

            if (cost < best) {
                bestA = arr;
                best = cost;
            }
        }

        System.out.println(best);

        for (int i = 0; i < n; i++) {
            if (bestA[i] == a[i]) {
                continue;
            }

            if (bestA[i] < a[i]) {
                System.out
                        .printf("- %d %d\n", i + 1, Math.abs(bestA[i] - a[i]));
            }
            else {
                System.out
                        .printf("+ %d %d\n", i + 1, Math.abs(bestA[i] - a[i]));

            }
        }

    }

    public static class Pair implements Comparable<Pair> {
        int x, y;

        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Pair o) {
            return Integer.compare(this.x, o.x);
        }

        @Override
        public int hashCode() {
            return x ^ y;
        }

        @Override
        public boolean equals(Object o) {
            Pair p = (Pair) o;
            return p.x == x && p.y == y;
        }

    }

    // -----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

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

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    // --------------------------------------------------------
}
