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
# 402B

from sys import stdin

__author__ = 'artyom'


def read_int_ary():
  return map(int, stdin.readline().strip().split())


n, k = read_int_ary()
a = list(read_int_ary())
mx = i_mx = 0
for i in range(n):
  if a[i] - k * i <= 0:
    continue
  sh = a[i] + k
  count = 0
  for j in range(i + 1, n):
    if a[j] == sh:
      count += 1
    sh += k
  if count > mx:
    mx = count
    i_mx = i

print(n - mx - 1)
sh = a[i_mx] - k * i_mx
for i in range(n):
  if a[i] < sh:
    print('+ ' + str(i + 1) + ' ' + str(sh - a[i]))
  elif a[i] > sh:
    print('- ' + str(i + 1) + ' ' + str(a[i] - sh))
  sh += k