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
n, k = list(map(int,input().split(" ")))
ts = list(map(int,input().split(" ")))

aps = dict()
for i in range(n):
  f = ts[i] - k*i
  if f > 0:
    aps[f] = aps.get(f,0) + 1

af = max([i for i in aps.keys()], key=lambda x:aps[x])

print(len([1 for i in range(n) if ts[i] != af + k*i]))

def action(af, i, ts, k):
  if ts[i] > af+k*i:
    return "- %i %i" % (i+1, ts[i] - (af+k*i))
  elif ts[i] < af+k*i:
    return "+ " + str(i+1) + " " + str(af+(k*i) - ts[i])
  else:
    return None
    
acts = [action(af, i, ts, k) for i in range(n)]
acts = [act for act in acts if act]

print("\n".join(acts))
