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 sys import stdout, stdin
from itertools import chain
#import copy

n, k = map(int, stdin.readline().strip().split())

trees = map(int, stdin.readline().strip().split())

unSortedTreesDict = dict( enumerate(trees) )

bases = []

stayers = set()

for ti, t in enumerate(trees):
	fail = False	
	stayersCandidate = set()

	for t2i, t2 in enumerate(trees):
		heightToMatch = (k * (t2i - ti) + t)
		if heightToMatch <= 0:
			fail = True
			break
		elif t2 == heightToMatch:
			stayersCandidate.add(t2i)
	
	if not fail:
		if len(stayersCandidate) > len(stayers):
			stayers = stayersCandidate


basei = list(stayers)[0]
stdout.write("%d\n"%(len(trees) - len (stayers)))

for ti,t in enumerate(trees):
	if ti not in stayers:
		heightToMatch = trees[basei] + (ti - basei) * k

		if t > heightToMatch:
			stdout.write("- %d %d\n"%(ti+1, t - heightToMatch))
		else:
			stdout.write("+ %d %d\n"%(ti+1, heightToMatch - t))
