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
#include <bits/stdc++.h>
using namespace std;
int getnum() {
  char c = getchar();
  int num, sign = 1;
  for (; c < '0' || c > '9'; c = getchar())
    if (c == '-') sign = -1;
  for (num = 0; c >= '0' && c <= '9';) {
    c -= '0';
    num = num * 10 + c;
    c = getchar();
  }
  return (num * sign);
}
int A[1004];
int used[1004], p, ind;
int main() {
  int n = getnum();
  int k = getnum();
  p = 100000;
  for (int i = 1; i <= n; i++) A[i] = getnum();
  for (int i = 1; i <= n; i++) {
    if (used[i] == 1) continue;
    if (A[i] - (i - 1) * k <= 0) {
      used[i] = 1;
      continue;
    }
    int c = 0;
    for (int j = i, t = A[i]; j <= n; j++, t += k) {
      if (A[j] == t) {
        used[j] = 1;
        c++;
      }
    }
    c = n - c;
    if (p > c) {
      ind = i;
      p = c;
    }
  }
  cout << p << endl;
  for (int i = ind, t = A[ind]; i >= 1; i--, t -= k) {
    if (A[i] == t) continue;
    if (A[i] > t)
      putchar('-');
    else
      putchar('+');
    printf(" %d %d\n", i, abs(A[i] - t));
  }
  for (int i = ind, t = A[ind]; i <= n; i++, t += k) {
    if (A[i] == t) continue;
    if (A[i] > t)
      putchar('-');
    else
      putchar('+');
    printf(" %d %d\n", i, abs(A[i] - t));
  }
}
