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 = map(int, raw_input().split())

trees = map(int, raw_input().split())

actions = ['']*n

pMin = 1001
index = 0

for t in xrange(n):
    start = trees[t]
    first = start - k*t
    height = first
    p = 0
    if first > 0:
        for i in xrange(1, n):
            height += k
            if trees[i] <> height:
                p += 1
                if p > pMin:
                    break
        if p < pMin:
            pMin = p
            index = t

height = trees[index] - k*index
p = 0
for i in xrange(n):
    if trees[i] <> height:
        if trees[i] - height < 0:
            actions[p] = '+ ' + str(i + 1) + ' ' + str(height - trees[i])
        else:
            actions[p] = '- ' + str(i + 1) + ' ' + str(trees[i] - height)
        p += 1
    height += k

print p
if p > 0:
    for j in xrange(p):
        print actions[j]
