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
import sys

entrada1 = [int(x) for x in raw_input().split()]

n = entrada1[0]
k = entrada1[1]
cnt = 0
resp = sys.maxint

comeco = 0

arvores = [int(x) for x in raw_input().split()]

for i in range(1,1005):
	cnt=0
	for j in range(n):
		if arvores[j]!=i+k*j:
			cnt+=1
	if cnt<resp:
		resp = cnt
		comeco = i
print resp

for i in range(n):
	if arvores[i]>comeco+k*i:
		print "- %d %d" % (i+1, arvores[i]-(comeco+k*i))
	elif arvores[i]<comeco+k*i:
		print "+ %d %d" % (i+1, (comeco+k*i)-arvores[i])
