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 std::cin;
using std::cout;
using std::endl;
int getint() {
  int x;
  scanf("%d", &x);
  return x;
}
long long int getll() {
  long long int x;
  scanf("%lld", &x);
  return x;
}
const int MAXNKH = 1000 + 10;
const int LOC = 0;
const int MODIFY = 1;
int n, k, ans = 0x7f7f7f7f, ansf[MAXNKH][2], p, f[MAXNKH][2];
int height[MAXNKH];
int main() {
  n = getint();
  k = getint();
  for (int i = 1; i <= n; i += 1) height[i] = getint();
  for (int h1 = 1; h1 <= 1000; h1 += 1) {
    p = 0;
    memset(f, 0, sizeof f);
    for (int i = 1; i <= n; i += 1) {
      if (height[i] - (i - 1) * k != h1) {
        f[++p][LOC] = i;
        f[p][MODIFY] = (h1 + (i - 1) * k) - height[i];
      }
    }
    if (p < ans) {
      ans = p;
      memcpy(ansf, f, sizeof f);
    }
  }
  printf("%d\n", ans);
  for (int i = 1; i <= ans; i += 1)
    printf("%c %d %d\n", (ansf[i][MODIFY] < 0 ? '-' : '+'), ansf[i][LOC],
           std::abs(ansf[i][MODIFY]));
  return 0;
}
