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
from itertools import groupby
R = lambda:map(int, input().split())
n, k = R()
a = list(R())
b = sorted(a[i] - k * i for i in range(1, n))
c = [(len(list(g[1])), g[0]) for g in groupby(b) if g[0] > 0]
if len(c) > 0:
  m = max(x for x, y in c)
  c = [x for x in c if x[0] == m]
else:
  c = [(0, a[0])]
d = 0
for i in range(len(c)):
  if c[i][1] == a[0]:
    d = i
    print(n - c[d][0] - 1)
    break
else:
  print(n - c[d][0])
for i in range(n):
  ai = c[d][1] + k * i
  if ai > a[i]:
    print("+ {} {}".format(i + 1, ai - a[i]))
  elif ai < a[i]:
    print("- {} {}".format(i + 1, a[i] - ai))